T Perdikis

S Psarakis
email: psarakis@aueb.gr

P Castagliola

G Celano

An EWMA-type Chart based on Signed Ranks with Exact Run Length Properties

Keywords: nonparametric control chart, Wilcoxon signed rank statistic, Phase II control chart

In this work, a new distribution-free Phase II EWMA-type chart based on the Wilcoxon signed rank statistic is introduced and its exact Run Length properties are discussed. A proper discrete Markov-chain approach is used for the determination of the Average Run Length in the in-control and out-of-control process operating conditions and its exact performance is derived without any knowledge of the distribution of sample observations. In addition, an algorithm for the determination of the chart's optimal design has been developed. Moreover, the performance of our proposed chart is compared with several existing nonparametric schemes available from literature. Finally, two illustrative examples are provided to show the practical implementation of our proposed chart.

Introduction

Quality improvement is of high importance for the manufacturing industries and, as a result, statistical methods play a vital role in this direction. SPM (Statistical Process Monitoring) techniques allow the on-line monitoring of the product's characteristic to be performed during production. Control charts are the most important tool to perform statistical process monitoring. They are an on-line process monitoring technique whose purpose is to detect shifts in the process as quickly as possible. One of the most commonly used control chart is the Shewhart-type control chart, see [START_REF] Shewhart | Statistical Method from the Viewpoint of quality control[END_REF]. Shewhart control charts are easy to design and able to detect large shifts in the parameter of interest during the process monitoring. On the other hand, in cases where small shifts of process parameters are likely to occur, memory-type control charts like the EWMA (Exponentially Weighted Moving Average, see [START_REF] Roberts | Properties of Control Chart Zone Tests[END_REF]) or the CUSUM (Cumulative Sum, see [START_REF] Page | Continuous Inspection Schemes[END_REF]) charts are preferable.

It should be noted that the design and operations of control charts are commonly based on the assumption that the observations, collected over time, are random variables following the Normal distribution or at least some continuous distribution.

However, in many cases this assumption is violated since, in practice, the actual distribution of the characteristic to be monitored is unknown. As a result, a new class of distribution-free (nonparametric) control schemes have been introduced into the literature. Chakraborti et al. presented in [START_REF] Chakraborti | Nonparametric Control Charts: an Overview and Some Results[END_REF] an extensive literature review, illustrating the design and operations of several univariate nonparametric control charts. Recently, Chakraborti and Graham presented in [5] an updated version of the former review by adding recent publications related to univariate and multivariate nonparametric charting techniques in SPM. Regarding the use of nonparametric techniques in EWMA-type control charts, Amin and Searcy introduced in [START_REF] Amin | A Nonparametric Exponentially Weighted Moving Average Control Scheme[END_REF] a nonparametric EWMA procedure for monitoring the location of a measurement based on the Wilcoxon signed rank statistic. Li et al. suggested in [START_REF] Li | Nonparametric CUSUM and EWMA Control Charts for Detecting Mean Shifts[END_REF] two nonparametric extensions of the CUSUM and EWMA control charts using the Wilcoxon rank-sum test. Graham et al. investigated in [START_REF] Graham | A Nonparametric EWMA Sign Chart for Location Based on Individual Measurements[END_REF] a distribution-free EWMA sign chart for location based on individual measurements and they presented in [START_REF] Graham | A Nonparametric Exponentially Weighted Moving Average Signed-Rank Chart for Monitoring Location[END_REF] a nonparametric EWMA chart based on the Wilcoxon signed rank statistic. Yang et al. introduced in [START_REF] Yang | A New Nonparametric EWMA Sign Control Chart[END_REF] a modified EWMA sign chart using the arcsine transformation. Graham et al. proposed in [START_REF] Graham | Distribution-Free Exponentially Weighted Moving Average Control Charts for Monitoring Unknown Location[END_REF] a modified distribution-free binomial-type EWMA chart called the EWMA-EX chart, in which exceedance statistics are used. Extensions of nonparametric EWMA-type schemes based on the sign statistic can be found in [START_REF] Aslam | A New Exponentially Weighted Moving Average Sign Chart using Repetitive Sampling[END_REF][START_REF] Riaz | A Sensitive Non-Parametric EWMA Control Chart[END_REF][START_REF] Lu | An Extended Nonparametric Exponentially Weighted Moving Average Sign Control Chart[END_REF]. Chakraborty et al. proposed in [START_REF] Chakraborty | A Generally Weighted Moving Average Signed-Sank Control Chart[END_REF] a distribution-free Generally Weighted Moving Average (GWMA) control chart based on the Wilcoxon signed rank statistic. Abid et al. investigated in [START_REF] Abid H Mand Nazir | An Efficient Nonparametric EWMA Wilcoxon Signed-Rank Chart for Monitoring Location[END_REF] the performance of an EWMA signed rank chart under ranked set sampling. Haq presented in [START_REF] Haq | A conparametric EWMA Chart with Auxiliary Information for Process Mean[END_REF] a new nonparametric EWMA sign chart using an auxiliary-information-based (AIB) estimator of the process mean and, in [START_REF] Haq | A New Nonparametric Synthetic EWMA Control Chart for Monitoring Process Mean[END_REF], he proposed a new synthetic EWMA (SynEWMA) sign chart based on the arcsine transformation for monitoring the process mean. Recently, Raza et al. presented in [START_REF] Raza | A New Nonparametric Double Exponentially Weighted Moving Average Control Chart[END_REF] a Double Exponentially Weighted Moving Average (DEWMA) control chart based on the Wilcoxon signed rank statistic. Finally, Abbas et al. proposed in [START_REF] Abbas | Enhanced Nonparametric Control Charts Under Simple and Ranked Set Sampling Schemes[END_REF] two DEWMA schemes based on the Wilcoxon signed rank statistic in which simple random and rank set sampling techniques are investigated.

It is worth stretching that, regarding the design phase of an EWMA-type control chart a proper computation of its RL (Run length) properties is crucial. Specifically, for the determination of the design parameters λ (smoothing parameter) and K (control limit parameter) of an EWMA-type chart, a search algorithm needs to be run, for a particular shift in the process, in order to find the optimal pair (λ * , K * ) which minimizes the out-of-control ARL, under the constraint ARL = ARL 0 where ARL 0 is a predefined value of the in-control ARL. In conventional EWMA-type schemes the RL properties are often obtained by using the Markov Chain approach of Brook and Evans presented in [START_REF] Brook | An Approach to the Probability Distribution of CUSUM Run Length[END_REF], which is based on a discretization of the control limits interval into m subintervals. In the case of measurement data (usually assuming normality) as the number of subintervals, m, increases the method of Brook and Evans tends to give reliable approximations of the chart's RL properties. Generally, the nonparametric statistics (such as sign, Wilcoxon signed rank, etc.) used by the distribution-free schemes mentioned above, are defined on a discrete domain. When the standard continuous EWMA chart is applied to discrete data, a common technique in order to compute its RL properties is to use simulation-based techniques. The main disadvantage of this approach is that it leads to approximated results which depend on the number of runs. Additionally, Weiß in [START_REF] Weiß | EWMA Monitoring of Correlated Processes of Poisson Counts[END_REF] stated that the approach presented in [START_REF] Brook | An Approach to the Probability Distribution of CUSUM Run Length[END_REF], when applied to an EWMA control chart for count data, leads to an approximation of the chart's actual statistical performance, which does not necessarily converge as the number of the Markov chain states increases. In a recent work of Wu et al. in [START_REF] Wu | A Distribution-free EWMA Control Chart for Monitoring Time-Between-Events-and-Amplitude Data[END_REF] where a distribution-free EWMA-TBEA (Time Between Events and Amplitude) control chart based on the sign statistic is considered, they showed that the approach of Brook and Evans yields to unreliable results since it is seriously affected by the number of subintervals, m. In order to overcome this problem, Castagliola et al. in [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF] introduced a new class of EWMA-type nonparametric scheme using the sign statistic called as the CEWMA SN chart. The design of the CEWMA SN chart is based on the approach of Rakitzis et al. who introduced in [START_REF] Rakitzis | A New Memory-type Monitoring Technique for Count Data[END_REF] a new memory type EWMA chart (denoted as the CEWMA control chart) for monitoring count data from a Poisson distribution. This chart is able to monitor the process location when the observations have an unknown distribution and, at the same time, it guarantees exact results for their run length distribution without any approximation. Tang et al. in [START_REF] Tang | A New Nonparametric Adaptive EWMA Control Chart with Exact Run Length Properties[END_REF] extended the approach of [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF] and proposed an adaptive distribution-free EWMA sign chart using an adaptive feature in the smoothing parameter. As Castagliola et al. pointed out in [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF], the design of the CEWMA chart can be utilised for any other nonparametric test statistics besides the sign test statistic. As far as we are concerned, in EWMA-type schemes based on the Wilcoxon signed rank statistic presented in the literature, their out-of-control RL properties are derived based on a specified distribution and using simulation-based techniques. In this current work, we aim to present a new nonparametric EWMA chart based on the recursive formula proposed in [START_REF] Rakitzis | A New Memory-type Monitoring Technique for Count Data[END_REF] in which the Wilcoxon signed rank statistic will be utilised. We also aim to provide a methodology for the exact determination of the RL properties of a EWMA-type chart based on signed ranks not only for the in-control but also for the out-of-control cases.

The paper is organized as follows. In section 2, the CEWMA SN chart is reviewed. Section 3, consists of a brief review of the statistical properties and operations of the Wilcoxon signed rank statistic and an exact formula for the computation of its general distribution is provided. In sections 4 and 5, our proposed nonparametric scheme based on the Wilcoxon signed rank statistic is introduced along with a specified algorithm for the computation of the exact in-and out-of-control ARL values based on a proper discrete Markov Chain model. In Section 6, the optimal design parameters are provided for different shifts of the process location. Moreover, our proposed chart is numerically compared with several nonparametric control charts proposed in the SPM. In Section 7, two illustrating examples are discussed to show a practical implementation of the operation of our proposed chart. Finally, in Section 8, some concluding remarks and suggestions for future work are discussed.

The CEWMA SN control chart

As it was noted before, when the standard EWMA chart is applied to discrete data, the Markov chain method of Brook and Evans (see [START_REF] Brook | An Approach to the Probability Distribution of CUSUM Run Length[END_REF]) leads to an approximation of its actual statistical performance. Using the approach presented in [START_REF] Rakitzis | A New Memory-type Monitoring Technique for Count Data[END_REF] and the Shewhart sign control chart proposed in [START_REF] Amin | Nonparametric Quality Control Charts based on The Sign Statistic[END_REF], Castagliola et al. introduced in [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF] a new nonparametric EWMA-type chart based on the sign statistic (CEWMA SN chart) for monitoring shifts in the location parameter providing exact results for its Run Length distribution.

Let X be a quality characteristic following an unknown continuous distribution with c.d.f. (cumulative distribution function) F X (x|θ) where θ is the location parameter to be monitored. With reference to the Phase II implementation of the control chart, when the process is in-control we have θ = θ 0 , (assumed as known). On the other hand, when the process is out-of-control, we have θ = θ 1 . Suppose that at each sampling point t = 1, 2, . . . a subgroup {X t,1 , X t,2 , . . . , X t,n } of size n is collected. The plotting statistic, Y t , for the CEWMA SN control chart is obtained through the following formula:

(γ x + γ y )Y t + R t = γ x SN t + γ y Y t-1 + R t-1 Bt-1 , SN t = n j=1 sign(X t,j -θ 0 ),
where sign(x) = -1, 0 or +1 if x < 0, x = 0 or x > 0, respectively. Note that, the condition sign(x) = 0 corresponds to occasional events occurring in practice due to rounding-off errors of the measurement system. Additionally, (γ x , γ y ) ∈ N 2 are two fixed positive integer-valued parameters, B t-

1 def = γ y Y t-1 + R t-1
, and Y t is the quotient of the Euclidean division

γ x SN t + B t-1 γ x + γ y ,
where . . . denotes the rounded towards zero integer and R t is the remainder of this Euclidean division defined as:

R t = γ x SN t + B t-1 -(γ x + γ y )Y t .
As stated in [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF], when the initial values Y 0 = y 0 , R 0 = r 0 and the current values SN t , Y t-1 , R t-1 are fixed, both Y t and R t are uniquely defined. The initial values y 0 and r 0 , are set equal to y 0 = r 0 = 0. However, if a head-start feature is desired, any choice of y 0 = 0 or r 0 = 0 can be considered. For a better understanding of the operation and design of the CEWMA SN plotting statistic the reader is advised to refer to [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF].

The Run length properties of the CEWMA SN chart are obtained based on the fact that SN t is defined on {-n, -n + 2, . . . , n -2, n} and its distribution can be obtained based on the relationship SN t = 2D t -n, where D t is the number of observations {X t,1 , X t,2 , ...X t,n } larger than θ 0 . If the process is in-control, P(X t,j > θ 0 |θ = θ 0 ) = P(X t,j < θ 0 |θ = θ 0 ) = p 0 = 0.5. As a result, D t is a binomial random variable with parameters n and p 0 = 0.5. On the other hand, let p 1 = P(X t,j > θ 0 |θ = θ 1 ) = 1 -F X (θ 0 |θ 1 ) be the probability of having an observation larger than the in-control median θ 0 when the process runs out-of-control with median θ = θ 1 . Assuming that the median is the location parameter of interest, values of p 1 close to p 0 = 0.5 correspond to small shifts, while values of p 1 close to 0 or 1 correspond to large shifts from θ 0 to θ 1 . In addition, since the in-control distribution of SN t is symmetric about 0, the control limits (UCL, LCL) and the center line (CL) are equal to LCL = -K, CL = 0 and UCL = K where K = {2, 4 . . . , n} (if n is an even integer) or K = {1, 3 . . . , n} (otherwise). The process is declared to be in-control if -K < Y t < K and out-ofcontrol otherwise. Regarding the computation of the optimal design parameters of the CEWMA SN chart a discrete Markov chain approach is used which will be also utilised in our proposed scheme.

The Wilcoxon signed rank (WSR) statistic

Suppose that at each sampling point a subgroup {X t,1 , X t,2 , . . . , X t,n } of size n, following a continuous symmetric distribution, is collected at time t = 1, 2, . . .. Let L t,j ∈ {1, 2, . . . , n} denote the rank of the absolute value of the differences |X t,j -θ 0 | , j = 1, 2, ..., n for subgroup t = 1, 2, . . . . By definition, the Wilcoxon signed rank statistic SR t is equal to

SR t = n j=1 sign(X t,j -θ 0 )L t,j , and it is defined on {-n(n+1) 2 , -n(n+1) 2 + 2, . . . , n(n+1) 2 -2, n(n+1) 2 }.
Therefore, SR t is the sum of the signed ranks. It should be noted that the domain on which SR t is defined contains zero only if n(n+1) 2 is an even integer. The statistic SR t can also be expressed as:

SR t = 2SR + t - n(n + 1) 2 ,
where SR + t is the sum of the positive ranks only. Under the null hypothesis (i.e. for p = 0.5), the p.m.f. (probability mass function) f SR + t (s|n) of SR + t can be easily and exactly obtained (see [START_REF] Mccornack | Extended Tables of the Wilcoxon Matched Pair Signed Rank Statistic[END_REF], for instance) by recursively evaluating the number N SR + t (s|n) of subsets of integers in {1, . . . , n} having a sum equal to s ∈ {0, 1, . . . , n(n+1) 2 }, i.e.

N SR + t (s|n) = N SR + t (s|n -1) + N SR + t (s -n|n -1),
and by computing

f SR + t (s|n) = N SR + t (s|n) 2 n .
Computing the p.m.f. f SR + t (s|n, p) of SR + t (exactly, without any approximation) under the alternative hypothesis (i.e. p = 0.5) is more tricky. The solution we opted in this paper consists in evaluating firstly the p.g.f. (probability generating function) G SR + t (ω) of SR + t as (see [START_REF] Bennett | On the Non-Null Distribution of Wilcoxon's Signed Rank Test[END_REF])

G SR + t (ω) = n i=1 (pω i + q),
where q = 1 -p and to obtain the p.m.f. f SR + t (s|n, p) of SR + t by differentiating G SR + t (ω), s times, for ω = 0, using the formula

f SR + t (s|n, p) = 1 s! G (s) SR + t (ω) ω=0 , where
G (s) SR + t (ω) is the s th derivative of G SR + t (ω). As G SR + t (ω) is a polynomial of degree n(n+1) 2 then, for s ∈ {0, 1, . . . , n(n+1) 2 }, G (s) SR + t (ω) is a polynomial of degree n(n+1) 2
-s and we can write

1 s! G (s) SR + t (ω) = n(n+1) 2 -s j=0 c s,j w j ,
where c s,j is the coefficient of degree j corresponding to the polynomial (ω) = 0.0016 and we have f SR + t (10|4, 0.2) = 0.0016. Because polynomials can be efficiently coded as vectors of coefficients, fast arithmetic operations (addition, multiplication and power) and derivation can be efficiently implemented (as in Matlab for instance) and the evaluation of f SR + t (s|n, p) can be obtained in a very fast way. It should be noted that this method can also be applied when p = 0.5, i.e. for the null hypothesis case.

Design of the CEWMA WSR control chart

As for the design of the CEWMA SN control chart, at each sampling point, the plotting statistic Y t for the CEWMA WSR control chart is obtained through the following formula:

(γ x + γ y )Y t + R t = γ x SR t + γ y Y t-1 + R t-1 Bt-1
.

(1) Concerning the initial values y 0 and r 0 for Y 0 and R 0 they are both set to y 0 = r 0 = 0. The process is declared to be in-control if -K < Y t < K and out-of-control otherwise where K ∈ {2, . . . , n(n+1) 2 }. Let us consider an example presented in Table 2 in order to clarify the design and operations of the charting statistic Y t of our proposed scheme. A simulated dataset containing m = 15 subgroups of size n = 10 have been simulated where the first 10 subgroups are considered as in-control samples (p 0 = 0.5) and the other 5 subgroups as out-of-control samples (p 1 = 0.8). For illustrative purposes the design parameters are γ x = 1 and γ y = 5, respectively and no head-start feature is used (i.e. Y 0 = 0 and R 0 = 0). The values of Y t are computed as follows: It is interesting to note that the values of the charting statistic, Y t react similarly as for a classical EWMA chart, i.e. they are randomly distributed around zero when the process is in-control (samples 1 -10) and they start to increase when a shift occurs (samples 11 -15). This fact has also been mentioned in [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF]. Also note that, our proposed scheme can both be extended to monitor any particular quantiles (provided that the sample size n is large enough) by changing the value p 0 = 0.5 to any other value of interest.

• For t = 1 we have Y 0 = 0, R 0 = 0, SR 1 = -
It is well acknowledged into the literature that in a conventional EWMA chart varying the value of the smoothing parameter, λ, allows more weight to be assigned to the past, or to the current observations. As pointed out in [START_REF] Rakitzis | A New Memory-type Monitoring Technique for Count Data[END_REF], if γ x < γ y then the CEWMA scheme assigns more weight to the past observations while, if γ x > γ y , this scheme assigns more weight to the most recent ones. Additionally, the corresponding limiting conditions for the CEWMA WSR chart in the case where λ = 1 or λ = 0 can be expressed respectively as:

• for γ x > 0 and γ y = 0 we have Y t = SR t and R t = r 0 , t = 1, 2, . . .. Consequently, in this situation, the CEWMA WSR chart coincides with the nonparametric Shewhart-type control chart based on signed ranks proposed in [START_REF] Bakir | A Distribution-Free Shewhart Quality Control Chart based on Signed-Ranks[END_REF]. • for γ x = 0 and γ y > 0 we have Y t = y 0 and R t = r 0 , t = 1, 2, . . .

Run length properties of the CEWMA WSR chart

In order to obtain the exact RL properties of our proposed scheme, the discretetime Markov chain approach presented for the CEWMA SN control chart is used. Specifically, the transition probability matrix P is defined as:

P = Q r 0 1 =        q -b,-b q -b,-b+1 . . . q -b,b-1 q -b,b r -b q -b+1,-b q -b+1,-b+1 . . . q -b+1,b-1 q -b+1,b r -b+1 . . . . . . . . . . . . . . . . . . q -b+1,-b q b-1,-b+1 . . . q b-1,b-1 q b-1,b r b-1 0 0 . . . 0 0 1       
where Q is the (2b+1, 2b+1) matrix of transient probabilities q i,j , 0 = (0, 0, . . . , 0) and r = 1 -Q1. Similar to the approach used for the CEWMA and CEWMA SN charts, at time t -1 the transient states of the discrete-time Markov chain will be defined as the integers b t-1 ∈ {-b, -b+1, . . . , +b} where b = γ x +Kγ y -1. More specifically, assuming that at time t -1, as long as y t-1 ∈ {-K + 1, . . . , K -1} the process is declared to be in-control, the transient states of the discrete-time Markov chain are defined as the integers b t-1 ∈ {γ y ×y t-1 +r t-1 } where r t-1 ∈ {-γ x -γ y +1, . . . , γ x +γ y -1}. As a consequence, the minimum, b min , and the maximum, b max , numbers of states are defined as b min = γ y (-K + 1) -γ x -γ y + 1 = -γ x -Kγ y + 1 and b max = γ y (K -1) + γ x + γ y -1 = γ x + Kγ y -1 respectively where b = b max = -b min . As a result, the total number of transient states is 2b + 1 = 2(γ x + Kγ y -1) + 1. Finally, the transient probabilities q i,j will be computed as detailed in Algorithm 1.

The RL properties of the CEWMA WSR chart will be obtained using the fact that RL is a Discrete Phase-type (DPH) random variable of parameters (Q, q) (see Algorithm 1 Computation of transient probabilities q i,j

Define n, K, γ x , γ y and p 1 . b ← γ x + Kγ y -1.

for i = -b, -b + 1, . . . , b -1, b do for SR = -n(n+1) 2 , -n(n+1) 2 + 2, . . . , n(n+1) 2 -2, n(n+1) 2 do y ← γx×SR+i γx+γy . if -K < y < K then r ← γ x × SR + i -(γ x + γ y ) × y. j ← γ y × y + r. q i,j ← q i,j + f SR + SR+ n(n+1) 2 2
|n, p 1 . end if end for end for [START_REF] Neuts | Matrix-Geometric Solutions in Stochastic Models-An Algorithmic Approach[END_REF][START_REF] Latouche | Introduction to Matrix Analytic Methods in Stochastic Modeling[END_REF]). Specifically, the p.m.f. f RL (t|Q, q) and the c.d.f. F RL (t|Q, q) of RL are defined for t = 1, 2 . . . and they are respectively, equal to:

f RL (t|Q, q) = q Q t-1 r, F RL (t|Q, q) = 1 -q Q t 1.
So, the Average Run Length ARL = E(RL) and the Standard Deviation Run Length SDRL = σ(RL) will be computed as:

ARL = q (I -Q) -1 1, SDRL = 2q (I -Q) -2 Q1 + ARL(1 -ARL),
where q = (q -b , q -b+1 , . . . , q b-1 , q b ) is the vector of initial probabilities associated with the 2b + 1 transient states. Assuming that y 0 = r 0 = 0 then q i = 0 for i ∈ {-b, -b + 1, . . . , -1, 1, . . . , b} and q 0 = 1.

Performance Comparisons

In this work, the parameter θ 0 will be considered as the median of the process distribution, so we assume p 0 = 0.5. For fixed values of the sample size n and p 1 = P(X t,j > θ 0 |θ = θ 1 ), in order to obtain the optimal combination of the design parameters (K * , γ *

x , γ * y ) which will provide the minimum corresponding out-ofcontrol ARL, a specific search algorithm is used aiming to select the optimal values of (K, γ x , γ y ) which guarantee the following conditions:

(K * , γ * x , γ * y ) = argmin (K,γx,γy) ARL(K, γ x , γ y , n, p 1 ) ARL(K * , γ * x , γ * y , n, p 0 ) = ARL 0
where ARL 0 = 370.4 is the target in-control ARL value. Due to the fact that the charting statistic, Y t , is a discrete random variable, it is not possible to find an optimal combination (K * , γ *

x , γ * y ) that exactly meets the constraint ARL(K * , γ * x , γ * y , n, p 0 ) = ARL 0 . Similarly to the design of the CEWMA SN chart, we suggest to accept, as tentative design parameters, all those combinations of parameters (K * , γ *

x , γ * y ) satisfying the following condition:

D(K * , γ * x , γ * y , n) = ARL(K * , γ * x , γ * y , n, p 0 ) -ARL 0 ARL 0 ≤ δ ( 2
)
where δ is a predefined constant. For the determination of the optimal parameters for n = {10, . . . , 25} in the CEWMA SN chart, Castagliola et al. set δ = 0.05 (see [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF]), to ensure that the corresponding optimal combination of (K * , γ *

x , γ * y ) will be obtained successfully. Based on our findings, we saw that in general the CEWMA WSR chart guarantees a smaller error than the CEWMA SN chart with respect to the constraint on the nominal in-control performance. As a consequence, for the determination of the design parameters of the CEWMA WSR control chart we suggest to set δ = 0.01. Additionally, since ARL(K, γ x , γ y , n, p 1 ) = ARL(K, γ x , γ y , n, 1 -p 1 ) we will only focus on shifts p 1 ∈ (0, 0.5) as the same results would have been obtained for p 1 ∈ (0.5, 1). As a consequence, for given values of n and p 1 , the optimal combination of the design parameters (K * , γ *

x , γ * y ) will be obtained through the searching Algorithm 2.

Algorithm 2 Computation of optimal combination (K * , γ * x , γ * y ) Define n and p 1 ∈ (0, 0.5). ARL 0 ← 370.4. ARL * ← ∞. for K = 1, . . . , n(n+1)

2 do for γ x = 1, 2, . . . do γ y ← 0. repeat γ y ← γ y + 1 until D(K, γ x , γ y , n) ≤ 0.01 if ARL(K, γ x , γ y , n, p 1 ) < ARL * then ARL * ← ARL(K, γ x , γ y , n, p 1 ), K * ← K, γ * x ← γ x and γ * y ← γ y .

end if end for end for

In the following tables some results regarding the performance of our proposed chart are provided, including comparisons with the CEWMA SN chart. In Table 3, the optimal combinations (K * , γ *

x , γ * y ) for our proposed chart are given, along with the corresponding in-control and out-of-control ARLs for n = {10, . . . , 25}. Based on the results presented in Table 3 it can be concluded that when p 1 < 0.5, for large values of the sample size or large shifts (p 1 0) the corresponding optimal ARL 1 values tend to decrease. In addition, for fixed values in the sample size, as the value of p 1 < 0.5 becomes closer to 0.5 the "smoothing ratio" γx γx+γy and the value of the control limit K of our proposed chart also tend to decrease. For example for n = 20 and p 1 ∈ {0.05, . . . , 0.2}, we have γx γx+γy = 10 10+3 = 0.77 and the control limit equals to K = 117. On the other hand for p 1 = 0.4 the corresponding smoothing ratio equals to γx γx+γy = 4 4+27 = 0.13 and K = 39. It is worth mentioning that these findings are consistent with the ones of the CEWMA (see [START_REF] Rakitzis | A New Memory-type Monitoring Technique for Count Data[END_REF]) and CEWMA SN (see [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF]) charts.

In Table 4 the performance of our proposed chart is compared to the CEWMA SN chart for n ∈ {5, . . . , 25} and p 1 ∈ {0.05, 0.1, . . . , 0.45}. In order to make fair comparisons, we obtained the optimal design parameters of the CEWMA SN with corresponding D(K * , γ *

x , γ * y , n) ≤ 0.01 (except from some values of n where the bound 0.01 in (2) has been replaced by 0.02), for n ∈ {5, 6, . . . , 25} and p 1 ∈ {0.05, 0.1, . . . , 0.45}. The ∆ values are defined as:

∆ = 100 × ARL SR -ARL SN ARL SN ,
where ARL SN and ARL SR are the ARL values of the CEWMA SN and CEWMA WSR charts respectively. A negative value for ∆ corresponds to an outperformance of the CEWMA WSR scheme versus the CEWMA SN chart. According to our findings, it can be concluded that when 5 ≤ n ≤ 15, for large shifts (p 1 ≤ 0.2) in 55% of the cases the CEWMA WSR scheme has a better performance. In addition for small to moderate shifts (p 1 > 0.2) in 60% of the cases the CEWMA WSR chart also outperforms the CEWMA SN chart. On the other hand, for n > 15, when p 1 ≤ 0.2 or p 1 > 0.2 the CEWMA WSR chart performs better only in 38% of the cases. As a consequence, in most cases, our proposed scheme has an overall better performance when n < 15 and as the sample size increases the CEWMA SN chart performs better.

In Tables 5 (for n = 10) and 6 (for n = 20) the CEWMA WSR chart is compared with other nonparametric schemes presented in the literature. More specifically, we examined the performance of the CEWMA WSR chart against the CEWMA SN chart, the two EWMA sign charts proposed by Yang et al. in [START_REF] Yang | A New Nonparametric EWMA Sign Control Chart[END_REF], denoted as standard sign EWMA (EWMA) and arcsine sign EWMA (A-EWMA), the distribution free cumulative sum mean chart (CUSUM) of Yang et al. in [START_REF] Yang | A New Non-Parametric CUSUM Mean Chart[END_REF] and the modified sign EWMA chart proposed by Lu in [START_REF] Lu | An Extended Nonparametric Exponentially Weighted Moving Average Sign Control Chart[END_REF] (S-GWMA). For the computation of the in-and out-of-control ARL values of the competitors of the CEWMA WSR chart, a Monte Carlo simulation was performed, except for the CEWMA SN chart where the exact Markov chain approach was used. Regarding the design parameters of each chart, for the CEWMA WSR and CEWMA SN charts (K, γ x , γ y ) have been selected to get the optimal performance for each chart; for the EWMA charts proposed in [START_REF] Yang | A New Nonparametric EWMA Sign Control Chart[END_REF], the pair (λ, W ) corresponds to the optimal values of the smoothing parameter λ and the distance W . Moreover, the pair (k, h) corresponds to the values of the reference value k and the decision interval h of the CUSUM chart. Finally, (q, α, W ) correspond to the values of the design parameters for the S-GWMA chart. For more information regarding the design and operations of the above schemes the reader is advised to see [START_REF] Yang | A New Nonparametric EWMA Sign Control Chart[END_REF][START_REF] Lu | An Extended Nonparametric Exponentially Weighted Moving Average Sign Control Chart[END_REF][START_REF] Yang | A New Non-Parametric CUSUM Mean Chart[END_REF].

Based on the results presented in Tables 5 and6 it can be concluded that the CEWMA WSR chart outperforms its competitors for moderate to large shifts (p 1 < 0.3). On the other hand, for small shifts, i.e. when p 1 tends to be close to 0.5 the standard or the arcsine transformed EWMA chart have better performance. Finally, in cases where 0.25 < p 1 < 0.3 the use of the S-GWMA chart or the SN EWMA can be considered.

γ X 3 3 - - - - γ Y 5 16 - - - - K 75 4 - - - - λ - - 0.05 0.05 - - W - - 2.487 2.487 - 2.709 k - - - - 1.0 - h - - - - 11.62 - q - - - - - 0.9 α - - - - - 0.9

Illustrative Examples

Motivated by existing works related to applications of nonparametric schemes for monitoring the characteristic of interest in a process, we present two examples, originally discussed by Celano et al. in [START_REF] Celano | On the Implementation of the Shewhart Sign Control Chart for Low-volume Production[END_REF] and [START_REF] Celano | The Performance of the Shewhart Sign Control Chart for Finite Horizon Processes[END_REF] respectively, to show a practical Phase II implementation of the design and operations of our proposed chart. In should be noted that the distributions of the observations are unknown and so no control chart based on normality assumption can be implemented. In the first one (entitled as the Radial example), the quality characteristic to be monitored is the radial error, which is defined as "a quality characteristic frequently monitored in hole drilling processes of mechanical parts and assembly processes of printed circuit boards". In the second one (entitled as the Beverage example), the quality characteristic of interest is the quantity of CO 2 dissolved in soft drink PET (polyethylene terephthalate) bottles.

Radial example

In this example, at each sampling point t, a subgroup of size n = 20 is collected in order to detect a shift in the median of the quality of interest such that p 0 = 0.5 shifts to p 1 = 0.3. As shown in Table 3, the optimal parameters to be used are K * = 57, γ * x = 7, and γ * y = 22. In addition, the in-control value of the median for the radial error is θ 0 = 0.338. In Table 7 the differences between X t,j and θ 0 for t ∈ {1, 2 . . . , 10} are provided and the values of SR t , Y t and R t are also reported. Using the recursive formula presented in [START_REF] Shewhart | Statistical Method from the Viewpoint of quality control[END_REF] the values of the charting statistic Y t are computed as follows: • For t = 10 we have In Figure 1 the differences X t,j -θ 0 for t ∈ {1, 2 . . . , 10} are plotted, where at each sampling point t, some values are tied together. The values of the charting statistic Y t are plotted in Figure 2. It can be seen that at the 4 th sampling point (t = 4) an out-of-control signal is given stating that the process median has changed.

• For t = 1 we have Y 0 = 0, R 0 = 0, SR 1 =

Beverage example

In this example, at each sampling point t, a subgroup of size n = 7 is collected in order to detect a shift in the median of the quality of interest such that p 0 = 0.5 shifts to p 1 = 0.4. Based on the results obtained by the optimization method presented in Section 6 (Algorithm 3) the optimal parameters are equal to K * = 6, γ * x = 10, and γ * y = 140. In Table 8 the deviations between X t,j and θ 0 for t ∈ {1, 2 . . . , 10} are illustrated, (Figure 3), along with the corresponding values of SR t , Y t and R t , (for confidentiality reasons, the in-control / target median value θ 0 of the quality characteristic is not provided). Regarding the computation of the ranks, L t,j , in presence of ties, we have used the average rank method:, i.e., for the rank allocated to a group of ties / ex-aequos we have assigned the average of the ranks that would have been allocated to these observations if they would have been all different. Consequently, similarly to the above example, using the recursive formula presented in (1) the values of the charting statistic Y t are computed as:

• For t = 1 we have Y 0 = 0, R 0 = 0, SR 1

Concluding Remarks

In this paper, we designed a new EWMA distribution-free control chart based on signed ranks using a new memory-type EWMA technique, introduced by Rakitzis et al. in [START_REF] Rakitzis | A New Memory-type Monitoring Technique for Count Data[END_REF] and extended by Castagliola et al. in [START_REF] Castagliola | An EWMA-Type Sign Shart with Exact Run Length Properties[END_REF] to the nonparametric case.

As it was explained in the previous sections, the use of the conventional approach of Brook and Evans [START_REF] Brook | An Approach to the Probability Distribution of CUSUM Run Length[END_REF] in nonparametric EWMA charts yields to an unreliable determination of their exact RL properties. The proposed CEWMA WSR scheme is designed with guaranteed exact Run Length properties obtained by a specific finite state Markov chain approach without any approximations. In addition, for almost all the nonparametric schemes based on the Wilcoxon signed rank statistic, their out-of-control performances are examined via Monte-Carlo simulation-based techniques for a given distribution. On the other hand, for our proposed chart the run length properties are examined and computed exactly for both the in-control and the out-of-control conditions regardless of the observations' underlying distribution. Moreover, the performance of the CEWMA WSR chart was examined and compared to several existing distribution-free control charts available from the literature. Our results show that the CEWMA WSR chart can be an efficient means in detecting moderate to large shifts in the process.

Many future work directions are worth of interest in this field of research. For instance, it would be interesting to improve our chart's overall shift detection properties by using the adaptive feature in the smoothing parameter, as it was proposed in [START_REF] Tang | A New Nonparametric Adaptive EWMA Control Chart with Exact Run Length Properties[END_REF], where the sign statistic was used. In addition, it would be challenging to extend the CEWMA WSR chart to the multivariate case. Finally, the use of of the proposed EWMA control chart can be extended to other non-parametric statistics as, for instance, the Mann-Whitney, and the Ansari-Bradley statistics.

•

  [START_REF] Haq | A conparametric EWMA Chart with Auxiliary Information for Process Mean[END_REF] and the equation to be solved is 6× Y 1 + R 1 = 1 × (-17) + 5 × 0 + 0 = -17. The unique solution of this equation (as an Euclidean division) is Y 1 = -2 and R 1 = -5. • For t = 2 we have Y 1 = -2, R 1 = -5, SR 2 =15 and the equation to be solved is 6 × Y 2 + R 2 = 1 × (15) + 5 × (-2) -5 = 0. The unique solution of this equation is Y 2 = 0 and R 2 = 0. . . . For t = 15 we have Y 14 = 15, R 14 = 0, SR 15 = 47 and the equation to be solved is 6 × Y 15 + R 15 = 1 × (47) + 5 × (15) + 0 = 122. The unique solution of this equation is Y 15 = 20 and R 15 = 2.

  45 and the equation to be solved is 29 × Y 1 + R 1 = 7 × 45 + 22 × 0 + 0 = 315. The unique solution of this equation (as an Euclidean division) is Y 1 = 10 and R 1 = 25. • For t = 2 we have Y 1 = 10, R 1 = 25, SR 2 = 27 and the equation to be solved is 29 × Y 2 + R 2 = 7 × (27) + 22 × (10) + 25 = 434. The unique solution of this equation is Y 2 = 14 and R 2 = 28. . . .

Y 9 = 10 ,

 910 R 9 = 11, SR 10 = 18 and the equation to be solved is 29 × Y 10 + R 10 = 7 × (18) + 22 × (10) + 11 = 357. The unique solution of this equation is Y 10 = 12 and R 10 = 9.

Figure 1 .

 1 Figure 1. Radial error example: individual value plot of the observations

Figure 2 .

 2 Figure 2. Radial error example: the CEWMA WSR chart for the Phase II sample presented in Table 7

Figure 3 .•

 3 Figure 3. Beverage example: individual value plot of the observations

Figure 4 .

 4 Figure 4. Beverage example: the CEWMA WSR chart for the Phase II sample presented in Table 8

  For a better understanding of this approach let us consider the following example with n = 4 and p = 0.2. In this case SR + t ∈ {0, 1, . . . , 10} and we have• 1 0! G SR + t(ω) = 0.0016ω 10 + 0.0064ω 9 + 0.0064ω 8 + 0.032ω 7 + 0.032ω 6 + 0.0512ω 5 + 0.128ω 4 + 0.128ω 3 + 0.1024ω 2 + 0.1024ω + 0.4096. The coefficients c 0,j are listed in the first row (for s = 0) of Table1. Replacing ω = 0 in this polynomial gives f SR + t (0|4, 0.2) = 0.4096. • Now, if we evaluate the first derivative, we have1 1! G

				1 s! G	(s) SR + t	(ω).
			(1)
			SR +
	• If we evaluate the 9 th derivative, we have 1 9! G	(9) SR + t	(ω) = 0.016ω + 0.0064. The
	coefficients c 9,j are listed in the row corresponding for s = 9 of Table 1. Replacing
	ω = 0 in this polynomial gives f SR + t (9|4, 0.2) = 0.0064. A final derivative gives
	1 10! G	(10) SR + t

t

(ω) = 0.016ω 9 + 0.0576ω 8 + 0.0512ω 7 + 0.224ω 6 + 0.192ω 5 + 0.256ω 4 + 0.512ω 3 + 0.384ω 2 + 0.2048ω + 0.1024. The coefficients c 1,j are listed in the second row (for s = 1) of Table

1

.

Replacing ω = 0 in this polynomial gives f SR + t (1|4, 0.2) = 0.1024. . . .

Table 1 .

 1 Computation of the p.m.f. of SR + t for n = 4 and p = 0.2

	s	c s,10	c s,9	c s,8	c s,7	c s,6	c s,5	c s,4	c s,3	c s,2	c s,1	c s,0	t f SR +	(s|4, 0.2)
		0.0016 0.0064 0.0064 0.0320 0.0320 0.0512 0.1280 0.1280 0.1024 0.1024 0.4096	0.4096
		-	0.0160 0.0576 0.0512 0.2240 0.1920 0.2560 0.5120 0.3840 0.2048 0.1024	0.1024
		-	-	0.0720 0.2304 0.1792 0.6720 0.4800 0.5120 0.7680 0.3840 0.1024	0.1024
		-	-	-	0.1920 0.5376 0.3584 1.1200 0.6400 0.5120 0.5120 0.1280	0.1280
		-	-	-	-	0.3360 0.8064 0.4480 1.1200 0.4800 0.2560 0.1280	0.1280
		-	-	-	-	-	0.4032 0.8064 0.3584 0.6720 0.1920 0.0512	0.0512
		-	-	-	-	-	-	0.3360 0.5376 0.1792 0.2240 0.0320	0.0320
		-	-	-	-	-	-	-	0.1920 0.2304 0.0512 0.0320	0.0320
		-	-	-	-	-	-	-	-	0.0720 0.0576 0.0064	0.0064
		-	-	-	-	-	-	-	-	-	0.0160 0.0064	0.0064
	10	-	-	-	-	-	-	-	-	-	-	0.0016	0.0016

Table 2 .

 2 An example of calculation of Yt and Rt given SRt

	t	SRt	Yt	Rt
	0	-	0	0
	1	-17	-2	-5
	2	15	0	0
	3	21	3	3
	4	-7	1	5
	5	-15	0	-5
	6	-13	-3	0
	7	-31	-7	-4
	8	-9	-8	0
	9	37	0	-3
	10	47	7	2
	11	25	10	2
	12	13	10	5
	13	27	13	4
	14	21	15	0
	15	47	20	2

Table 3 .

 3 Optimal combinations (K * , γ * x , γ * y ) (first line of each block) for the CEWMA WSR chart along with the corresponding in-control ARL's (second line) and the out-of-control (ARL, SDRL) (third line) for n ∈ {10, . . . , 25} and p 1 ∈ {0.05, 0.1, . . . , 0.45}

	p 1

Table 4 .

 4 Comparison between the CEWMA SN and CEWMA WSR chart for n ∈ {5, . . . , 25} and p 1 ∈ {0.05, 0.1, . . . , 0.45}

	p 1

Table 6 .

 6 ARL values of the CEWMA WSR chart, the CEWMA SN chart, the standard and the arcsine transformed EWMA chart, the CUSUM chart and the S-GWMA chart (n = 20, p 0 = 0.50, ARL 0 ≈ 370)

	p	CEWMA WSR CEWMA SN EWMA A-EWMA	CUSUM S-GWMA
	0.50	370.6	370.2	370.0	367.6	373.7	370.9
	0.45	84.7	37.3	31.0	30.9	40.3	33.0
	0.40	20.2	11.4	12.3	12.2	11.7	11.5
	0.30	4.9	4.5	5.6	5.4	4.5	4.7
	0.25	3.3	3.5	4.4	4.2	3.5	3.7
	0.20	2.6	2.9	3.7	3.5	2.9	3.0
	0.15	2.1	2.4	3.2	2.9	2.4	2.5
	0.10	1.8	2.1	2.9	2.5	2.1	2.2
	0.05	1.5	2.0	2.6	2.1	2.0	2.0

Table 7 .

 7 Radial error example: Phase II dataset of t = 1, . . . 10 subgroups of size n = 20 and the corresponding values for SRt, Yt and Rt

	X t,j

Table 8 .

 8 Beverage example: Phase II dataset of t = 1, . . . 10 subgroups of size n = 7 and the corresponding values for SRt, Yt and Rt X t,j -θ 0

		t	1	2	3	4	5	6	7	SRt	Yt	Rt
		1	-0.01 -0.04	0.08	-0.08	0.03	-0.02 0.08	2	0	20
		2	-0.05	0.01	0.01	0.06	0.00	0.00	0.11	15	1	20
		3	0.06	-0.05 -0.01 -0.03	0.04	0.05	0.07	13	1	140
		4	0.03	-0.02	0.02	0.04	0.02	-0.01 0.08	20	3	30
		5	0.02	0.07	0.01	0.03	0.01	0.01	0.08	28	4	130
		6	0.11	0.10	0.08	0.10	0.11	0.04	0.06	28	6	70
		7	0.08	0.11	0.12	0.12	0.13	0.12	0.06	28	7	146
		8	0.07	0.04	0.06	0.07	0.07	0.05	0.07	28	9	50
		9	0.04	0.01	0.01	0.00	-0.02	0.03	0.08	19	10	0
		10 -0.01	0.04	0.02	0.00	0.01	0.01	0.14	21	10 110
							Dissolved C0 2
		0.15
		0.10
	t,j -θ 0	0.05
	X
		0.00
		-0.05
		1	2		3	4	5	6	7	8		9	10
							sample


Personalised versus standard dosimetry approach of selective internal radiation therapy in patients with locally advanced hepatocellular carcinoma (DOSISPHERE-01): a randomised, multicentre, open-label phase 2 trial Etienne Garin, Lambros Tselikas, Boris Guiu, Julia Chalaye, Julien Edeline, Thierry de Baere, Eric Assénat, Vania Tacher, Corentin Robert, Marie Terroir-Cassou-Mounat, et al. To cite this version: Etienne Garin, Lambros Tselikas, Boris Guiu, Julia Chalaye, Julien Edeline, et al.. Personalised versus standard dosimetry approach of selective internal radiation therapy in patients with locally advanced hepatocellular carcinoma (DOSISPHERE-01): a randomised, multicentre, open-label phase 2 trial. The Lancet Gastroenterology & Hepatology, 2021, 6 (1), pp.17-29. 10.1016/S2468-1253(20)30290-9. hal-02998830


Keywords: General Public, Chemical Engineering, Collaborative / Communication / Writing, Humor /

The purpose of this study is to present a learning activity that gamifies an argumentation exercise by combining both a bibliographic research activity and an oral argument. The exercise is organized as a competitive battle to engage and motivate students after training in bibliographic research. Students are divided into four teams of 4-7 students and are involved in a 2-round tournament starting with the Semi-Final round: the two winners of each semi-final meet in the final and the two losers in a playoff for third place. Each match is divided in two halves of 10 minutes: one to prepare their work and the second to present it and interact with the opposite team. At the end, the two spectator teams vote for the winning team and educators referee having the final decision. A symbolic prize (university goodies) is offered to the final winning team and each team is graded by the educators, on the basis of their two matches. The feedback received from students that participated in this exercise during the 2016-2020 period has been evaluated and corroborates the increase of motivation and teamwork through such activities. At the end, the advantages and limitations of such an activity are discussed.

■ INTRODUCTION

Generation Y, also known as the millennial generation or the Net Gen 1 , refers to persons born between 1980 and 2010 [START_REF] Howell | Generational Forecasting in Academic Medicine: A Unique Method of Planning for Success in the Next Two Decades[END_REF][START_REF] Wessels | Generation Y Students: Appropriate Learning Styles and Teaching Approaches in the Economic and Management Sciences Faculty[END_REF][START_REF] Lancaster | When Generations Collide: Who They Are, Why They Clash, How to Solve the Generational Puzzle at Work[END_REF] . Most of the students from "Generation Y" in the Western world were born into a world of information technology; they are identified as preferring to multitask [START_REF] Coulter-Smith | Changing Minds: Multitasking During Lectures[END_REF] rather than focusing on one thing at a time. Educators across disciplines are taking note of the challenges and opportunities associated with teaching this unique group [START_REF] Eckleberry-Hunt | The Challenges and Opportunities of Teaching "Generation Y[END_REF] . Generation Y prefers to work in groups with hands-on experiences [START_REF] Mangold | Educating a New Generation: Teaching Baby Boomer Faculty about Millennial Students[END_REF][START_REF] Carver | Attaining Organizational Commitment across Different Generations of Nurses[END_REF] . They enjoy trial and error [START_REF] Mangold | Educating a New Generation: Teaching Baby Boomer Faculty about Millennial Students[END_REF] . Generation Y may not value reading and listening [START_REF] Wolf | There's a Crisis of Reading Among Generation Z https://psmag[END_REF] to lectures as highly as has been traditional in education [START_REF] Eckleberry-Hunt | The Challenges and Opportunities of Teaching "Generation Y[END_REF][START_REF] Mangold | Educating a New Generation: Teaching Baby Boomer Faculty about Millennial Students[END_REF] . They want learning to be creative, interactive, and fun; and they enjoy thinking outside the box [START_REF] Lipkin | Y in the Workplace: Managing the Me First Generation[END_REF] . Core values of the generation Y include online social connectedness, teamwork, free expression, close relationships with authority figures [START_REF] Eisner | [END_REF] , creativity, work-life flexibility, and use of technology [START_REF] Eckleberry-Hunt | The Challenges and Opportunities of Teaching "Generation Y[END_REF] . Generation Y has characteristics that affect learning [START_REF] Berkup | Working With Generations X And Y In Generation Z Period: Management Of Different Generations In Business Life[END_REF] , but these differences are not necessarily weaknesses. To ensure success, educators need to understand that Generation Y cannot be forced into the mold of past generations and to adopt new strategies that adapt education to this generation. In this aim, educators have focused on several core areas:

(1) interactive teaching with new technology, such as the use of Augmented Reality [START_REF] Dunnagan | Production and Evaluation of a Realistic Immersive Virtual Reality Organic Chemistry Laboratory Experience: Infrared Spectroscopy[END_REF][START_REF] Eriksen | Visualizing 3D Molecular Structures Using an Augmented Reality App[END_REF][START_REF] Estudante | Using Augmented Reality to Stimulate Students and Diffuse Escape Game Activities to Larger Audiences[END_REF][START_REF] An | Evaluation of Augmented Reality Application Usage and Measuring Students' Attitudes toward Instrumentation[END_REF] , video learning [START_REF] Jordan | Effectiveness of Student-Generated Video as a Teaching Tool for an Instrumental Technique in the Organic Chemistry Laboratory[END_REF][START_REF] Belton | Teaching Process Simulation Using Video-Enhanced and Discovery/Inquiry-Based Learning: Methodology and Analysis within a Theoretical Framework for Skill Acquisition[END_REF][START_REF] Debacq | Delivering Remote Food Engineering Labs in COVID-19 Time[END_REF][START_REF] Dietrich | Attempts, Successes, and Failures of Distance Learning in the Time of COVID-19[END_REF] or QR code [START_REF] Bonifácio | Offering QR-Code Access to Information on Nobel Prizes in Chemistry[END_REF][START_REF] Williams | Smart Phones, a Powerful Tool in the Chemistry Classroom[END_REF][START_REF] Yip | Evaluation of an Online Instructional Database Accessed by QR Codes To Support Biochemistry Practical Laboratory Classes[END_REF] (2) gamification, using games [START_REF] Adair | Chemical Pursuit: A Modified Trivia Board Game[END_REF][START_REF] Azizan | Improving Teamwork Skills and Enhancing Deep Learning via Development of Board Game Using Cooperative Learning Method in Reaction Engineering Course[END_REF][START_REF] Brydges | Catalyze! Lowering the Activation Barriers to Undergraduate Students' Success in Chemistry: A Board Game for Teaching Assistants[END_REF][START_REF] Da Silva Júnior | Stereochemistry Game: Creating and Playing a Fun Board Game To Engage Students in Reviewing Stereochemistry Concepts[END_REF][START_REF] Martín-Lara | Playing a Board Game to Learn Bioenergy and Biofuels Topics in an Interactive, Engaging Context[END_REF][START_REF] Pippins | Element Cycles: An Environmental Chemistry Board Game[END_REF][START_REF] Triboni | Developing a European-Style Board Game To Teach Organic Chemistry[END_REF][START_REF] Coudret | Fun with Flags and Chemistry[END_REF][START_REF] Dietrich | Chem and Roll: A Roll and Write Game To Illustrate Chemical Engineering and the Contact Process[END_REF] or trending ones such as escape games [START_REF] Dietrich | Escape Classroom: The Leblanc Process-An Educational "Escape Game[END_REF][START_REF] Peleg | A Lab-Based Chemical Escape Room: Educational, Mobile, and Fun![END_REF][START_REF] Vergne | Escape the Lab: An Interactive Escape-Room Game as a Laboratory Experiment[END_REF][START_REF] Yayon | Do-It-Yourself: Creating and Implementing a Periodic Table of the Elements Chemical Escape Room[END_REF][START_REF] Monnot | New Approaches to Adapt Escape Game Activities to Large Audience in Chemical Engineering: Numeric Supports and Students' Participation[END_REF][START_REF] Clapson | ChemEscape: Educational Battle Box Puzzle Activities for Engaging Outreach and Active Learning in General Chemistry[END_REF][START_REF] Debacq | Delivering Remote Food Engineering Labs in COVID-19 Time[END_REF] or (3) more communication and systematic feedback 39 . To increase the "fun" aspect of the teaching, serious games 40 are a good solution as they permit the practice of communication, live feedback between students or from teachers, interaction and team building. Moreover, any form of competitive game may bring out the best in people and push them to excel, it allows students to exploit their real capabilities and maximize their true potential [START_REF] Lati | Exposure to Nanoscience and Nanotechnology Using Guided-Inquiry-Based Activities with Silica Aerogel To Promote High School Students' Motivation[END_REF] . Collaborative activity coupled with immediate feedback within a practical context appears as a key to cater for the interests and habits of the "Generation Y". With this purpose in mind, some educators have tried to bring students together around a tournament activity (clash of chemists [START_REF] Le Maire | Clash of Chemists: A Gamified Blog To Master the Concept of Limiting Reagent Stoichiometry[END_REF] ) to create and share personal analogies explaining the difference between stoichiometric and nonstoichiometric reaction conditions in a recreational environment. Others have developed Battle Box [START_REF] Clapson | ChemEscape: Educational Battle Box Puzzle Activities for Engaging Outreach and Active Learning in General Chemistry[END_REF] for practicing competitive escape games in a chemical environment. In all these examples, competition is not the central element, but it is a way of stimulating the students and making them more active than in a face-to-face class.

These activities can therefore be linked to flipped and blended learning strategies which prioritize active learning during class [START_REF]Flip Your Classroom: Reach Every Student in Every Class Every Day[END_REF] . The main objectives of this paper are to present an activity based on the use of a battle of debate (with a match and round-elimination system) following a training with a bibliographic research tool suited to chemical engineering. Argumentation can be defined as a dialogical activity where the positions of each can be transformed and enriched. [START_REF] Nonnon | Activités argumentatives et élaboration de connaissances nouvelles : le dialogue comme espace d'exploration[END_REF] Argumentation appears as an essential operation for the development of reflective and critical thinking. Thus, the educational objectives for students are: (i) to develop skills related to argumentation; (ii) to develop skills related to finding scientific information autonomously; (iii) to develop skills related to cooperation and teamwork, and (iv) to develop skills related to oral fluency. The educational objectives of the teachers are: (1) to diversify learning situations, (2) to offer entertaining learning situations and assessments that make it possible to unlock blockages related to writing/conventional classes, (3) to offer learning situations that implement simple, rapid assessments, (4) to engage in intense exchange with students, and (5) to provide learning situations that foster both engagement and healthy competition between students, while promoting teamwork, cooperation, and peer review.

■ DESCRIPTION OF THE ACTIVITY

This activity has been conducted with students from the third year in Chemical The activity is composed of 4 distinct phases: (1) the research (2) the pooling (3) the battle and (4) the arbitration phase. The 24-student group is divided into 4 groups of 6 students. The teams can be imposed by the teacher in order to promote diversity or they can be formed randomly [START_REF]Keamk -Créer des équipes aléatoires et équilibrées[END_REF] . The team can choose their name, or it may be recommended to educators to come up with the group names such as a color (green, blue, red and yellow as depicted in Figure 1). The teacher team is composed of a librarian trainer and two teachers in chemical engineering playing the role of referee of the matches. The first two games are the semi-finals, each winning team advances to the final, and each losing team advances to the playoff for third place (see Figure 1). Each team will thus play 2 matches in total.

The research phase

As part of the preparation for the Battle, an 85 minutes training session in bibliographic research skills is conducted to a group of 24 students in the early morning, from 8 am to 9:15 am, in a training room equipped with 12 computer stations and a video projector. The librarian trainer introduces the session, he presents the information skills training program, recalls the instructions and the breakdown of the morning and presents tools for finding scientific information about chemical engineering. The shortterm goal is to prepare the students for the questions they will be asked during a tenminute session facing two teams of students' (called the battle). At the end of this training session, they will be able to demonstrate their competences by knowing how to gather the maximum amount of reliable, quality information on a chemical process in a given time. The long-term objective is for them to be able to apply what they learnt in order to prepare their year-end report and also be able to reinvest them in a professional perspective. Based on the example of a classical process that will be the common thread throughout the activity, the trainer will gradually teach them to adopt an effective search strategy. Defining the need for information is the first step: it allows the students to refocus their research and save time. The trainer then presents the tools that are useful for defining concepts and key words, and essential terminologies which will allow them to access the various platforms of scientific publishers and databases.

At the same time, the trainer asks the students to use tools such as an encyclopedia of engineering techniques (e.g., a French technical and scientific documentary databaseonline with subscription 46 ), then a terminological dictionary for French-English translation (bank of terminological files written by the Quebec office for the French language 47 ), he broadcasted a short video on the use of the Wikipedia collaborative encyclopedia 48 . The training concludes with the presentation and online test of Ullmann's Encyclopedia of Industrial Chemistry 49 , which provides comprehensive science and technology coverage in all areas of industrial chemistry. The third step is to teach the students how to build search equations by knowing how to use operators and advanced tool modules (truncation, Booleans, proximity, etc.). This is illustrated live by the trainer, always with the one chemical process serving as an example. After which a short period of discussion in the form of questions and answers on the student's ability to define the relevance criteria for reliability of printed or digital information in order to develop their critical thinking and vigilance. The trainer finally explains the interest of carrying out bibliographic research on the various scientific publishing platforms to which the university library has subscribed, emphasizing the quality, academic level and reliability of the resources presented. He explains the different access methods, such as: Elsevier's Science Direct and Web of Knowledge, international and multidisciplinary bibliographic and bibliometric documentary databases and also search engines: (scholar.google.fr and lens.org); the catalog of the Toulouse university library network (archipel.univ-toulouse.fr); the open access platforms: HAL developed by the CNRS (hal.archivesouvertes.fr), patent site (wipo.int/patentscope). To conclude this phase, the trainer reveals a flipchart giving the subject where the battle will take place. Subjects are chemical processes, e.g. the Toyo process, the Stamicarbon process, the chloralkali process, the Haber-Bosh process, among others. The librarian teacher stops his classes and lets the students begin their documentary research on the chemical process.

The pooling phase

The students are invited to work on the different aspects of the process that will enable them to implement an argumentation in response to a subject / a problem. At this point they know the "chemical process" but they do not know the exact question of each battle match. This is a very important stage in which the students apply what they have learned about bibliographic research, pooling their preparation and comparing their ideas.

Students know that they are going to have to defend their argument collectively and the team consistency may be the factor that will make the difference during the battle. The students have to work very seriously during this phase in order to gather the maximum of information and to share the best items, while ensuring that everyone understands the subject of the argument (Figure 2). Before the end of this phase of 90 minutes, the teachers-referees complete the match line-up (depicted in Figure 1) without the students.

The Battle

After a few words to introducing the rules, the teacher reveals the first two teams who will compete against each other on the model of a hip-hop battle [START_REF] Dodds | Hip Hop Battles and Facial Intertexts[END_REF] or an oratorical joust [START_REF]Tournament of Young Chemists in Ukraine: Engaging Students in Chemistry through a Role-Playing Game-Style Competition[END_REF] .

The two teams are chosen by drawing lots. From this point, students are expected to be able to present a question, a topic or a theme on the chosen chemical process. They must understand what is being said by others students and provide constructive criticism [START_REF] Kennedy | In-Class Debates: Fertile Ground for Active Learning and the Cultivation of Critical Thinking and Oral Communication Skills[END_REF] , answers, and finally respecting rules to the debate (speaking rules, listening rules, duration…).

The teacher then gives the subject of the first match (a particular point of the process, a unit operation, the utility of the molecule produced, drawing the flowsheet of the process, the advantages, and disadvantages of the process, etc.), the two teams then have 10 minutes' preparation time to adapt and share their knowledge on this specific subject.

The two remaining teams, knowing they will face each other in the second match but not yet knowing their precise battle topic, may use this time to continue to strategize on the global subject. Five minutes before the end of the preparation time, the two competing teams are called in front of the battle white board (divided into two parts by a central line) to start writing/drawing important elements. Once the preparation time has elapsed, the battle starts, for a duration of 10 minutes. During the battle, each student is invited to speak, and everyone's contribution is considered important. It is not a matter of judging other students but of examining their proposal, thinking and rebounding on them. The error has a privileged place in the debate, being considered as a source of learning.

During the battle, the "leader team" begins and the "challenger team" can stop them as soon as they identify a mistake or consider that something important was forgotten. The "challenger team" then becomes the "leader team" and can continue the presentation.

The teachers play the role of referees: they must give the floor to each team, making sure the speaking time of each team is respected, may ask another speaker to replace his teammate, may ask the other team to confirm/negate a point that has just been stated by a team, questioning both teams at the same time, asking a team to question the other, etc. During the battle, the students of each team encourage each other widely during this session, getting caught up in the game. It is common to hear "go ahead and try!" when the student on the board is a little hesitant to try [START_REF] Engels | L'utilisation du médiateur ludique pour favoriser le développement des compétences non-académiques en formation supérieure[END_REF] . A good-natured competitive spirit often develops between the two teams, creating a real "confrontation".

The arbitration phase

At the end of each battle, the two other teams must designate the most convincing team, justifying their choice on criteria related to both knowledge and method. A smartphone voting system is used to collect the results. This is an important moment, in which the students progress in terms of methodology as they discuss, as a group, the validity of one example, or the quality of one explanation over another. Very quickly, students get caught up in the game and develop listening skills and peer assessment skills 54 . At the end of each vote, a score is given to each team (on the format: A, mastered, B, acquired, C, in the process of learning, or D, not acquired), the score is reported on the score table and one team is declared the winner (except for the final and the thirdplace match were teams can be ex aequo). The evaluation criteria include the quality, precision and richness of the technical vocabulary used in the field concerned and the structuring of the answers 55 . Preparation and argumentation are evaluated through the knowledge of the subject, the quality of the arguments, the respect of the number of interventions per member, and the teamwork. At the end of the activity, the scores will be averaged for each group as the final score for the session. During this phase, students realize that victory is disconnected from the score: a team can lose a match even with the grade A if the other team gives better explanations or accurate examples.

It should be noted that a small symbolic gift (goodies from the university) is offered to the winning team. The duration of the battle is 1 hour and 30 minutes, i.e., around 4 hours for the whole activity with the preparation phase and the research phase.

■ STUDENT'S EVALUATION

A total of 210 students participated in these activities. At the end of the session in the years 2018/2019 and 2019/2020 (106 students'), the teachers invited all students to evaluate the activity by completing a printed form containing twenty-one questions with responses based on a Likert 56 scale (the response rate was 97.2% -106 answers). Data are presented in Figure 3 and Figure 4. In general, all statements showed high levels of agreement ("agree" and "strongly agree") on the benefits of the battle, ranging from 62.3% to 96.8% of those surveyed.

DISCUSSION

Used experimentally and improved by INSA students and educators for four years (2016/2017 to 2019/2020), this activity now experiences an overall positive result: (i) It promotes teamwork and cooperation among students: very quickly, students understand that the oral participation of all members of the group is a criterion for deciding between two teams (and it could be imposed by the teacher/referees). The students who are most comfortable with argumentation or who took the lead in the preparation phase take advantage of the pooling phase to help the students who have the most difficulty in progressing with the chemical process; (ii) It encourages the students to deepen their knowledge: after the first match of the activity, some students were no longer satisfied with the knowledge provided in the preparation table. They understand that the additional knowledge brought will sometimes allow them to make a difference in battles.

They will therefore look for the most precise information; (iii) It promotes mutual listening and a co-construction of skills: during the arbitration phase, the students must spot errors or inaccuracies in knowledge; (iv) It facilitates the learning of knowledge because it mobilizes at least 4 conditions promoting long-term information retention: (a) to have understood the process to be able to apply it orally, (b) to mobilize active memorization by questioning teammates, not only during the mutualization phase but also during the battle phase with the opposite team, (c) to repeat the knowledge at extended intervals (2 matches per battle) and (d) to receive immediate feedback to rectify any misunderstanding and take advantage of the error. This activity was therefore a good strategy to engage students in bibliographic research training with a direct, original, and innovative application session. In our format, the activity was designed for a half-day but, in view of the free-response section of the questionnaire, we recommend applying it (if possible) in a full-day session to give the students more time to search for information, to interact with one another and to empower their communication skills. Educators need to be careful about the composition of the teams and the number of team members. Too small a number could lead to unbalanced teams in terms of level/leadership and too large a number will lead to difficulty for students to find their place and interact. From our experience, we propose an ideal number of 4-5 students per team. We also strongly recommend that the educator take the time to explain the rules clearly before the session, in order to explain that victory or ranking are not the goal of the session (a team can lose its 2 matches even with the maximum grade A), but communication, discussion, learning and fun are the only objectives.

The introduction of argumentative practices in science teaching profoundly modifies the respective roles of the teacher and the students 57 : it is no longer the authority of the teacher who establishes what is true by stating what has to be learned. It is the students who, through their activities, co-construct their knowledge. Working in a battle context means taking risks for teachers. Their position during the battle can be destabilizing because they lose the monopoly on questions and answers [START_REF] Gaussel | Développer l'esprit critique par l'argumentation : de l'élève au citoyen[END_REF] . This attitude is the opposite of frontal teaching, where the teacher provides knowledge, and the questioning serves to verify understanding.

Changing the role of the teacher is the first necessary condition for the success of the battle. This raises the question of the position of the teacher in the debate. Should they intervene or, on the contrary, take a back seat to encourage the progression 58 of the students' questioning? A wide range of practices attempt to regulate these processes without really providing any precision. It is then up to the teacher to find the level of "guidance" necessary to conduct the debate 59 . During the battle, teachers may act as mediators and conduct the debate. Their participation should not prevent the confrontation of points of view.

The debate is therefore regulated by the moderator who structures the session by putting forward the position of the different student-debaters, by facilitating their exchanges, and in some cases by trying to arbitrate conflicts. The role of the teacher is to: (1) create a dynamic, tension and attention by reformulating certain divergences in the form of questions, sometimes by creating doubt.... "Are you sure?" [START_REF]Le Battle : faire vivre le débat dans les organisations de manière ludique et inspirante[END_REF] (2) Coach teams by encouraging them to defend their point of view by proposing a constructed argument.

(3) Rhythm the battle. The two teams exchange their arguments one after the other, answering successive questions from the moderator in front of the audience. Speaking time is limited, to stimulate exchanges and get straight to the point. The moderator is therefore necessary to ensure that the rules of the game are respected. He is a referee, and a successful battle is one where the participants bring the debate by themselves by exploring the different aspects of their subject.

CONCLUSION

The purpose of this study was to present a learning activity that gamifies the argumentation between teams of students on a chemical engineering process. The present work therefore provides a creative and original activity based on the use of an argumentation exercise combining a bibliographic research activity with the oral expression of an argument. The feedback received from students that participated in this exercise for the 2016-2020 period has been evaluated and not only corroborates the increase of motivation and active behavior of students for such activities, but also confirms that this activity helped them to work on their communication skills, mutual aid skills, argumentation skills and bibliographic research skills. The educator should be careful about the length of the session (full day or half day but not less), the composition of the teams -with an optimal number of 4-5 members -and clearly clarifying the objectives before the session to avoid frustration and disappointment. Finally, the battle promoted exchanges between students and also, to a lesser extent, exchanges with the teacher in an entertaining and stimulating environment. This activity also promoted critical thinking and reflection on the students' course, which are important skills for students to develop. The pedagogical approach used with Generation Y students meets the needs and demands of this generation, while allowing the teacher to achieve their own goals. Generation Z will be a continuation of Generation Y, with exacerbated characteristics, especially with regard to creativity and the use of new technologies. The new generation will soon be at university, with even more expectations in terms of academic approach. The development of educational mediators is still in its beginning stages and promises to expand significantly in the coming years.

Tournament

  Battle: Gamifying Bibliographic Research and Oral Argumentation Applied to Chemical Engineering Topics Anne-Laure Aymard 1 , Johanne Teychene 2 , Stéphanie Laborie 2 , Mickael Bertrand 3 & Nicolas Dietrich 2 1: BIB'INSA, Université de Toulouse, INSA, Toulouse, France 2: Toulouse Biotechnology Institute (TBI), Université de Toulouse, CNRS, INRA, INSA, Toulouse, France 3: Académie de Dijon, France ■ ABSTRACT

  Engineering and Environment courses at INSA Toulouse from academic year 2016/2017 to 2019/2020. It is part of an 18 hours classes, and it has been deployed after a series of lectures (5 h) covering the topic of chemical engineering. All these activities took place face to face before the lockdown due to the COVID19 epidemic in mid-March 2020.

Figure 1 .

 1 Figure 1. Tournament game scoreboard.

Figure 2 .

 2 Figure 2. Pooling phase for each of the 4 groups before the Battle.

Figure 3 .

 3 Figure 3. Student responses relating to the use of battle activity. Total number of respondents = 106 (academic years 2018/2019 and 2019/2020).

Figure 4 .

 4 Figure 4. Student responses relating to the use of battle activity. Total number of respondents = 106 (academic years 2018/2019 and 2019/2020).

ASSOCIATED CONTENT

Tournament game scoreboard (PDF)

AUTHOR INFORMATION

Corresponding Author

Nicolas DIETRICH E-mail: nicolas.dietrich@insa-toulouse.fr


Kevin Robert

Didier Stiévenard

Dominique Deresmes

Camille Douard

Antonella Iadecola

David Troadec

Pardis Simon

Nicolas Nuns

Maya Marinova

Marielle Huvé

Pascal Roussel

Thierry Brousse
email: thierry.brousse@univ-nantes.fr

Christophe Lethien
email: christophe.lethien@univ-lille.fr

A Demortière

E Eustache

V De Andrade

D Pech

M Brunet

H Durou

P Huang

V Mochalin

Y Gogotsi

P.-L Taberna

Y Hwang

M F El-Kady

Y Wang

L Wang

Y Shao

K Marsh

M Brachet

Novel insights into the charge storage mechanism in pseudocapacitive vanadium nitride thick

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Secondary batteries 1 are conventional electrochemical energy storage systems used to power nomadic devices. Unfortunately, the mobility of such devices is limited by lengthy charging times and a deterioration in battery performance at upwards of a few thousand cycles. The Internet of Things (IoT) is a revolutionary technology aimed at creating an ecosystem of interconnected devices in order to improve our daily lives 2 . Autonomy and mobility are crucial parameters with respect to powering IoT micro-devices, and energy storage systems capable of delivering high energy density at high charge / discharge rates are a fundamental prerequisite for next-generation IoT networks 3 . Lithium micro-batteries (MBs) 4,5 and carbon micro-supercapacitors (MSCs) [6][7][8] are currently the most viable candidates for powering smart and miniaturized sensors. Regarding the former, such MBs are hampered by the low charge / discharge rates whereas the latter are limited to the low capacitance of the carbon electrodes. MSCs based on pseudocapacitive materials are a class of electrochemical capacitors where fast redox reaction occur near the surface of the electrode material 9-12 , providing higher energy densities than carbon-based MSCs. However, the main issue with these is designing a pseudocapacitive material that combines rapid ion diffusion and fast electron transport in thick electrodes. Following the discovery of the pseudocapacitive properties of RuO2 13 , numerous transition metal oxides -TMO -(MnO2, T-Nb2O5….) [14][15][16][17][18][19] and a two-dimensional transition metal carbidenamely MXene [20][21][22] were investigated. Whereas TMOs show low electrical conductivity, MXene combine rapid electron transport in the 2D metal carbide with fast redox reactions at the TMO-like surface. However, depositing MXene films using deposition methods issuing from the microelectronics industry proves challenging when a scaleup of the technology is required.

Transition Metal Nitrides (TMN) are a widely-studied class of materials owing to their favorable electrical and electrochemical properties. Molybdenum and vanadium nitrides 23,24 clearly demonstrated outstanding pseudocapacitive properties (> 700 F g -1 ) in aqueous electrolyte, even though the charge storage mechanism of vanadium nitride remained unclear 24,25 . Sputtered bifunctional vanadium nitride (VN) film was shown to be an intrinsically efficient current collector and electrode material for on-chip MSCs due to its electrochemical and electrical properties 12 . This sputtering based-strategy clearly facilitates the scaling up of the technology, by following the same roadmap that we recently proposed for on-chip MSCs based on nanoporous carbon-derived carbide films 6 . Herein, various scientific issues ranging from fundamental concerns to the technological fabrication of MSCs on a silicon wafer are addressed. The charge storage process occurring in sputtered VN films is thoroughly investigated in order to explain their remarkably high areal and volumetric capacitances. To this end, we employed a combination of numerous advanced characterization techniques such as Operando X-Ray Absorption Spectroscopy under synchrotron radiation, as well as powerful surface techniques like X-ray Photoelectron Spectroscopy (XPS) coupled with Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) and Electron Energy Loss Spectroscopy (EELS) analysis at the nanoscale in a Transmission Electron Microscope (TEM). Our findings show that we have succeeded in extending the limits of VN films deposited via production-compatible microelectronic deposition methods in order to attain the highest areal (1.2 F cm -2 ) and volumetric (> 700 F cm -3 ) capacitance values hitherto reported, to our knowledge, in the domain of MSCs in aqueous electrolyte. Additionally, in situ Atomic Force Microscopy (AFM) imaging of VN-based MSCs revealed their favorable cycling behavior (~ 50 000 cycles). It can thus be concluded that the performance of these MSCs certainly fulfills the requirements of IoT miniaturized devices in terms of rate capabilities and long-term cycling.

Charge Storage mechanism in vanadium nitride films

Figure 1A depicts the used strategy to investigate the charge storage process in sputtered VN films. To maximize the film capacitance, it is important to clearly identify and understand the key role of the sputtering temperature on the VN morphology. SEM cross-section analysis and AFM top-surface imaging of the 340 nm-thick sputtered VN films are reported in Figure 1B and Figure S1 vs the heating temperature. The higher the temperature, the higher the ad-atoms' mobility 12,26 , the lower the inter-columnar spacing. At 20 °C, the RMS roughness was 3.9 nm indicating the homogeneity of the film's surface (Figure 1C). For higher temperatures, the roughness increased up to 16 nm, in good agreement with the observation of increasingly dense bright spots. These spots correspond to pyramidal patterns (Figure 1B).

Judging by these AFM images, and based on recent methods published by our group 27 , it was deduced that the projected length, Lp (Figure 1C), decreased from 36 to 16.5 µm. Concurrently, the contribution of the pyramids to Lp increased from 0 up to 14 µm for high temperature deposition. The AFM images in Figure 1D highlight the formation of a pyramidal-type pattern at 350 °C for 2 µm-thick films, confirming the formation of pyramids at high temperatures.

Finally, based on Lp, we evaluated the specific surface, Se, of 340-nm thick VN films (Figure 1E), which decreased from 12.5 down to 5 cm 2 per cm 2 footprint as the temperature shifted from room temperature (RT) to 450 °C. Electrochemical analysis of those VN films was then conducted. As expected, the cyclic voltammogram (CV) exhibited a rectangular shape (Figure 1F), and the higher the temperature, the lower the CV areas. On one hand, at 5 mV s -1 , the capacitance decreased from 42 to 30 mF cm -2 when the temperature was increased from RT to 450 °C (Figure 1G). On the other hand, the electrical conductivity (Figure 1G) increases linearly with the temperature. To maximize the specific surface, the areal capacitance while keeping sufficiently high the conductivity, the compromise consists in depositing the vanadium nitride film at 100 °C.

This study confirmed the key role that temperature plays in determining pyramidal patterns, capacitance values and specific surface areas.

In order to investigate the charge storage mechanism in sputtered and crystallized VN films (Figure S1, Supplementary Materials (SM) section), surface analyses were initially carried out on 100 nm-thick sample. Three square-shaped craters were drilled into the VN film using the ToF-SIMS equipment. The 1 st crater was bored down to the silicon substrate to assess the etching rate of the VN and Si3N4 layers. The 2 nd crater was stopped approximately in the middle of the VN layer (≈ 50 nm), while the 3 rd crater was etched down to the VN / Si3N4 interface (Figure 2A & Figure S2A). The ToF-SIMS depth profile reveals the presence of vanadium nitride, oxide and oxynitride species (Figure 2B). Then, the sample was transferred from the ToF-SIMS to the XPS chamber under vacuum in order to analyze the film at the surface and inside the 2 nd and 3 rd SIMS craters.

Figure 2C shows the high-resolution XPS spectra for V 2p and O 1s core levels from the surface to the VN / Si3N4 interface: we found an oxygen component at the surface as well as in the craters.

The V 2p core level at the VN surface is rather complex. The first contribution of the V 2p3/2 level is measured at 513.70 eV. This is consistent with the formation of the VN species. In order to fit the spectrum adequately, two additional V 2p doublets with V 2p3/2 BE at 514.8 and 516.8 eV were required. Those peaks were observed in the V 2p core level spectra of the 2 nd and 3 rd craters, but with a lower intensity as compared to the surface. As concerns the XPS, considering the presence of oxygen and the oxynitride peak in N 1s spectra (Figure S2D), the 2 nd contribution can be ascribed to a vanadium (III) oxide or VN1-xOx oxynitride, whereas the last peak at higher BE can be ascribed to a vanadium (IV) oxide 28 . To summarize, ToF-SIMS paired with XPS analyses confirm the presence of vanadium nitride, vanadium oxide (+III and + IV) and a small amount of vanadium oxynitride in the films, from their surface to the VN / Si3N4 interface.

So as to obtain further insight into the charge storage process and to refine the XPS conclusions, additional investigations were deemed necessary. The charge storage mechanism in VN nanocrystals was studied 24 by Kumta et al in 2006, whereby ex situ XPS analysis confirmed the formation of a vanadium oxide shell (0.5 nm) surrounding the vanadium nitride core of the nanocrystals. However, they found it difficult to predict the type of vanadium oxides (VxOy) via ex situ XPS analyses. To address this issue, we opted to study 1 µm-thick sputtered VN films by operando XAS at the V-K edge in a KOH electrolyte. Additionally, EELS/TEM analysis was carried out to identify the position of the vanadium oxide layer within the sputtered columnar vanadium nitride film. The experimental method for the operando XAS measurement (Figure S3) is detailed in the SM, where all the parameters were optimized to maximize the signal to noise ratio (Figure S4A-F).

The CV (2 nd cycle) is shown in Figure 3A. Fast data acquisition of the XAS signal allows for a fine sampling of the charge storage process, so as to achieve accurate monitoring of the oxidation state of the transition metal. Absorption spectra reported in Figure 3B clearly highlight a shift of the absorption threshold upon charge / discharge cycling. The plot showing the energy shift of the applied potential exhibits a triangular shape (Figure 3C), similar to that of pseudocapacitive material 29,30 . To find the vanadium species involved in the charge storage mechanism, in Figure 3D we plot the evolution of the absorption edge for VxOy (cross points) and VN (square point) reference compounds (Figure S4G) vs the valence of the vanadium element. In this graph, we also show the energy absorption edges (circular points) measured during the operando XAS analysis (Figure 3B-C andS4H-I). Not surprisingly, this graph clearly indicates that VN could not be responsible for the pseudocapacitive processa vanadium oxide layer seems to be the key player in the fast charge transfer occurring during the redox process, confirming the hypothesis proposed by Kumta et al. While in 2006 we found it difficult to find the type of VxOy involved in the process by ex situ XPS 24as observed in our XPS / ToF-SIMS experimentsthe originality of this, hitherto unreported, study deals with the accurate determination of the vanadium oxidation degree in the vanadium oxide species upon charge / discharge cycling. From these operando XAS measurements, the average oxidation state was found to vary from 3.56 to 3.66 (correlated with XPS analyses), meaning that the XANES capacitance is approximately 88 mF cm -2 . This capacitance is a perfect match with that of 1 µm-thick VN film (~ 90 mF cm -2 ). Once we had demonstrated that a mixed vanadium oxide V2O3 / VO2type is involved in the charge storage mechanism, the question arose as to where the VxOy are located within the VN film. To tackle this issue, TEM analysis and EELS spectroscopy with a nanosized-spot was performed on 7 µm-thick sputtered VN film. The Figure 3E-F perfectly illustrates the columnar morphology of the film.

Between two VN columns, we observe brighter contrast in the TEM image and darker areas in the HAADF images, corresponding to porosities and/or areas with lower atomic density. Figure 3G shows the EELS spectra measured within the VN column (blue line) and between two VN columns (pink line). The EELS spectrum (blue line) in the VN column shows the V-L3,2 edge at 517 eV, and the negligible intensity at 531 eV corresponding to the O-K edge. The pink line clearly indicates a shift of V-L3,2 edge towards higher energy (518.1 eV), accompanied by a considerable increase of the O-K edge at 531 eV. We observe a higher oxidation state of V in the area between the VN columns, corresponding to the formation of VxOy.

Based on these findingsfinally able to fully comprehend the charge storage process involved in sputtered VN films operating in aqueous electrolytewe reached the conclusion that the sputtered VN film acts as a conductive scaffold for electron transport, while the amorphous mixedvalence vanadium oxides (+III / + IV), located at the edge of each column, are the redox-active material allowing fast charge transfer (Figure 1A). This conclusion resonates with that of a previous publication investigating MXene electrodes, where the conductive carbide layer enables rapid electron transport and where the TMO-like surface is the redox-active center 22 . Such findings reaffirm the suitability of sputtered VN for MSC applications.

Electrode design providing high areal and volumetric performance

As previously demonstrated, capacitance of the VN films decreases and electrical conductivity increases at higher deposition temperatures. Consequently, an intermediate temperature of 100 °C was chosen for the sputtering deposition since, at this temperature, VN is a suitable current collector and an efficient pseudocapacitive electrode. To enhance the surface capacitance, an interesting approach is to deposit a thicker layer providing that (1) the deposition method is compatible with the microelectronics industry, and (2) that the electrical conductivity of the electrode material is sufficiently high for fast electron transport. AFM analysis is shown in Figure 4A where the evolution of Lp and Se vs the film thickness is reported. The top-view and the SEM cross-section images, the roughness, the evolution of the electrical conductivity as well as the X-Ray Diffraction analyses of the VN films are shown in Figure S5, confirming the polycrystalline nature of the VN films (PDF card 000-035-1768) and the good conducting properties of those VN films. The Se is clearly enhanced to a 70 cm 2 per cm 2 footprint area for 16 µm-thick VN film. As a result, the areal capacitance is increased as depicted in the CV plots (Figure 4B). Further discussion regarding the ion kinetics within the VN films is provided in the SM. As mentioned, the areal and volumetric capacitance values are remarkable and unique: a surface capacitance of up to 1.2 F cm -2 was measured at 5 mV s -1 for 16 µm-thick VN film (Figure 4C), which is 6 times higher than our previous results 12 . This translates into a volumetric capacitance of 700 F cm -3 . For thinner films, the volumetric capacitance value increases up to 1300 F cm -3 (Figure 4C). It is noteworthy that the 16 µm-thick VN film retains more than 80 % of the initial capacitance for 50 000 cycles (Figure 4D). A benchmarking of the achieved areal performance (square points) as compared to state-of-the-art (pseudo)capacitive electrodes is furnished in Figure 4E. The 7 µmthick carbon-derived carbide (CDC) film 31,32 delivers 0.1 F cm -2 in organic electrolyte 6, 33 . In aqueous electrolyte 6 , 5 µm-thick CDC films deliver up to 0.2 F cm -2 . MXene Ti3C2-T electrode is a very attractive material, also from the point of view of areal and volumetric capacitances: 5 µmthick Ti3C2-T "clay" electrodes deliver up to a 0.4 F cm -2 / 900 F cm -3 capacitance values when measured in 1M H2SO4 34 . The volumetric capacitance of a Ti3C2-T electrode (3 µm-thick) decreases to 400 F cm -3 in 1M KOH 20 . The corresponding areal capacitance value (120 mF cm -2 ) is twice as low as the one we obtained (Figure S6C) with a 2.5 µm-thick VN film (> 250 mF cm - 2 / 1000 F cm -3 ) in 1M KOH. Moreover, one faces a similar issue here with respect to producing MXene 20,21,34 films via deposition methods that are compatible with the microelectronics industry and suitable for MSC applications. These sputtered VN films thus provide the most favorable compromise between surface and volumetric capacitances when compared to cutting-edge electrodes, while keeping the electrical conductivity high in the absence of a conductive agent in order to facilitate fast electron transport for miniaturized devices. Having reached a fundamental understanding of the charge storage process and film optimizations, we succeeded in fabricating on-chip interdigitated MSC based on VN electrodes on a 3-inch silicon wafer. An assessment of the electrode degradation upon cycling was carried out using in situ AFM in 1M KOH.

Micro-supercapacitors based on VN films

CDC films 6 have already been analyzed by AFM in ionic liquid electrolyte 35 to track the volume expansion of the electrode upon cycling. To ascertain the aging of the VN electrode, we develop an experimental test setup (Figure S7) in order to trace the volume expansion of the interdigitated electrodes tested in 1M KOH (Figure 5A). A movie demonstrating the in situ characterization of the MSC in 1M KOH is furnished in the SM. The interdigitated topology is illustrated in Figure 5B, where the etching process was stopped at the VN / Si3N4 interface. AFM imaging of the VN electrodefirstly in the absence of liquid, then soaked in water and then in 1M KOH electrolyte, respectivelywas performed prior to in situ analysis (Figure S7C andS7D). The AFM images attest to the absence of volume expansion and chemical degradation in either the electrode or the AFM tip (90 minutes test). We then studied the degradation of the VN film upon cycling in 1M KOH by applying a voltage plateau from -0.4 V down to -1 V vs Hg/HgO (and inversely) for 2 minutes on the 1 st electrode (Figure 5B). The 2 nd electrode remained unbiased so as to compare the potential volume expansion. From cross-section AFM images, we measured the thickness of the VN operating electrode, using the Si3N4 surface as a reference (Figure 5C). The thickness of the VN electrode is shown to remain constant regardless of the applied potential, i.e. there is no expansion of the VN electrode upon cycling, validating the long-term cycling (50 000 cycles).

Finally, the performance of on-chip MSCs are evaluated. Galvanostatic charge / discharge cycling is shown in Figure 5D. The energy densities of 7 µm-thick and 16 µm-thick MSCs (Ragone plot density which is 16 times higher that of MSCs based on CDC films 6 tested in 1M H2SO4. The maximum power density remains stable at around 4 mW cm -2 , regardless of film thickness.

Our work provides a fresh perspective on the charge storage mechanism of sputtered VN films in KOH electrolyte. We succeed in fine-tuning the VN properties in order to synthesize bi-functional films (i.e. for use as both current collector & electrode material for on-chip MSCs). These bifunctional VN thick films (16 µm) exhibit both high specific area (70 cm 2 per cm 2 ) and areal capacitance (1.2 F cm -2 ), as well as both high volumetric capacitance (> 700 F cm -3 ) and capacitance retention (50 000 cycles). It is noteworthy that these MSCs are constructed using a CMOS-compatible microfabrication technique and tested using in situ AFM methods to verify 10 cycling stability. In light of the above, the present study clearly paves the way for the collective fabrication of miniaturized energy storage devices on a silicon wafer, and thus for the efficient powering of next-generation IoT micro-devices.

Figure 1 -

 1 Figure 1 -A. Overview of the strategy used to study the charge storage process. B. SEM cross-

Figure 2 -

 2 Figure 2 -A. Overview of the combined ToF-SIMS / XPS analyses at the surface, in the middle

Figure 3 -Figure 4 -

 34 Figure 3 -Investigation of the Charge Storage Mechanism in the sputtered VN Films. A. Plots of

Figure 5 -

 5 Figure 5 -A. In situ AFM analysis of a MSC in 1M KOH electrolyte. B. Plots of the potential vs

  utmost gratitude. XAS experiment was performed on the ROCK beamline at SOLEIL synchrotron, which is benefiting from a public grant overseen by the French National Research Agency as part of the "Investissements d'Avenir" program (Reference: ANR-10-EQPX-45). The authors declare no conflict of interest. All the authors wish to thank Anne Duchene for the sketch-up. KR achieved the deposition of VN films and the fabrication of on-chip MSCs. DS, DD and CL were involved 5 in the in situ AFM analysis. KR, CD, AI, TB and CL were involved in the operando XAS. DT, MM, MH, PR and CL were involved in the TEM / EELS analysis of the VN films. KR, PS, NN and CL carried out the ToF SIMS / XPS analyses.

  VN PP-16µm in KOH

	Density (µWh.cm	VN ID-2 µm in KOH Graphene / CNT ID in Na 2 SO 4 CDC ID in H 2 SO 4	VN PP-7 µm in KOH
	Energy	J. P. K. This Lin Huang et al, et Nanoletters, al, Science, 351 (2016) 13 (2013) 72-78 691-695 Robert el al, Adv Mat Tech (2018) 1800036 work VN-16 µm This work VN-7 µm

and HAADF images of VN films. F. HAADF image of the VN film illustrating the two areas where EELS analysis is performed (blue square within the VN column, and pink square between two columns). G. Corresponding EELS spectra including both V-L3,2 edge and O-K edge.

Acknowledgments: This research benefitted from the financial support of the ANR within the DENSSCAPIO project (ANR-17-CE05-0015-02). The authors would also like to thank the ANR STORE-EX and the RS2E for their financial support. The RENATECH network receives our