Fausto Galetto
email: fausto.galetto@gmail.com

Appeal to the Scientific Community: let's take care of Quality of published papers

Keywords: Quality of Methods, Quality Education, Peer Review, Methods for Quality, Rational Manager, Quality Tetralogy, Intellectual Honesty, Reliability Integral Theory

They say that good papers are published only in "Peer Reviewed Trusted Journals (PRTJ)", while low quality papers are published in the "Predatory Publishing Journals". Here we use some cases to show that this is not true, because the quality of papers depends on the quality of the authors in the same manner that quality of teaching depends on the quality of professors. It seems that Peer Reviewers and Editors did not take care of the quality of published papers, because they missed Quality of Methods (Deming, Juran, Gell-Mann, Shewhart, Einstein, Galilei). This is very diffused in documents about Confidence Intervals and Control Charts [especially for Rare Events, where the data are assumed to follow the Weibull (or exponential) distribution]. Since generally the authors are professors it is important to see the two sides of the "publishing medal": authors and professors. Software (JMP, Minitab, SAS, …) get wrong Control Limits and do not find that processes are Out Of Control: this causes costs of dis-quality. The cases analysed here are from PRT Journals and teaching documents.

Introduction

In any activity we need to analyse information; information can be either given by words or by numbers (data provided by a measurement system). The analysis of information is done by suitable methods devised by competent scholars, working either in Universities or in Companies. Many times the methods are presented in papers published in Magazines and Journals or in books. Journals are broadly divided in two categories: 1) the Good and Reputed Journals and 2) the so-called "Predatory publishing" {Open Access Journals which publish papers and ask for a fee for that [named APC (Article Processing Charge) or a similar acronym]}.

The author, in his working life as Manager in Companies, as Professor in Universities and as Consultants, had the opportunity to read many wrong papers about data analysis.

For this reason, we titled this paper "Appeal to the Scientific Community: let's take care of Quality of published papers" because the people have the right of knowing the truth about the "Quality of published papers".

Unfortunately, the Universities, as said by Einstein «An Academic career poses a person in an embarrassing position, asking him to produce a great number of scientific publications…», ask the researchers for publications if they want to become professors; several times, the author asking the applicants (for professorship) "Why did you write such a statement…" got the answers either "My colleague wrote that,,," or "I found it in Wikipedia" or "I read it in that book…": in spite of their incompetence, they became professors!

We will show some fundamental ideas about the analysis of data collected in scientific experiments, based on the Scientific way of reasoning through Mathematics, Probability Theory and Statistics.

We start with the data in table 1, gathered in an experiment. A scholar must find the best from them. If the reader links to the three "forums" [1-3] iSigSigma, Academia.edu, Research Gate and looks at the discussions there (about statistical subjects) he can find a lot of people unable to correctly analyse the data in Table 1, writing wrong ideas on Probability and statistics Methods. They are not in line with the concepts provided in the documents [START_REF] Deming | Out of the Crisis[END_REF][START_REF] Deming | The new economics for industry, government, education[END_REF][START_REF] Shewhart | Economic Control of Quality of Manufactured Products[END_REF][START_REF] Shewhart | Statistical Method from the Viewpoint of Quality Control[END_REF][START_REF] Juran | Quality Control Handbook[END_REF][START_REF] Galetto | Quality in Higher Education Courses[END_REF][START_REF] Galetto | Hope for the Future: Overcoming the DEEP Ignorance on the CI (Confidence Intervals) and on the DOE (Design of Experiments[END_REF][START_REF] Dore | Introduzione al Calcolo delle Probabilità e alle sue applicazioni ingegneristiche[END_REF][START_REF] Mood | Introduction to the Theory of Statistics[END_REF][START_REF] Rao | Linear Statistical Inference and its Applications[END_REF][START_REF] Rozanov | Processus Aleatoire[END_REF][START_REF] Ryan | Statistical Methods for Quality Improvement[END_REF].

Suppose that a scholar ask himself the following questions:

(1) Do the two samples provide the same information about the process? (2) Do the two samples are distributed in the same way? (3) Do the sample 2 shows an improvement versus the sample 1? To answer the scholar either uses his intuition or uses a method. Since intuition can be fallacious he must use a sound method.

Let's see the steps he has to do: (i)

The data x ij (numbers, i=1, 2; j=1,2, …10) are to be considered the "determinations" of the Random Variables (RV) X ij (ii) Each RV X ij has a pdf (probability density function) which depends on k "parameters" , m=1, 2, …, k, which characterise the pdf (iii)

The "parameters" can be (a) either the "determinations" of the RV , distributed with a "known" pdf , or (b) "unknown" quantities (real numbers) and known type of pdf , or (c) pdf "completely unknown" (iv)

An "estimation function" is sought out to find the "best" value to be attributed to the parameter , for the cases (a) or (b) (v) While for the case (c), and for "Complete Samples" (as those in table 1), Probability and Statistics provide the ways to find "estimation functions" of the Mean (of the "Complete Samples"), of the Standard Deviation (of the "Complete Samples"), and other Moments (of the "Complete Samples"), … Case (c) is the easiest situation of computing the "estimation functions"

for "Complete Samples". In spite of that we find professors teaching wrong ideas. Notice the following wrong attached statement (excerpt 1) taken from a course on Quality Management, where Professors of Politecnico (of the Quality engineering Group) suggest Montgomery books to students. Any good student knows that the formula holds for any distribution and any sample size n: the Central Limit Theorem does not have any importance for that, BUT QEG professors do not know that!!! Excerpt 1 Wrong statement (from a course on Quality Management at Politecnico of Turin) [given by the QEG (Quality Engineering Group)] Remember: that formula holds for any distribution and any "Complete Samples" of sample size n.

For both the cases (a) and (b) we have a tool, based on the Likelihood Function (formula 1), for "Complete Samples"

(1) The "estimation function" of the "best" value to be attributed to the parameter , is different for the two cases.

For the case (a), let's see the figure 1, depicting the Bayesian method for estimation, because it is based on the Bayes' Theorem

Figure 1. The Bayesian method for estimation

In this case, the "parameter" is the "determination" of the RV , distributed with a "known" pdf , named "a priori (or Prior)" pdf, related to the scholar "a priori (or Prior)" knowledge (or experience). The test data D{x ij , i=1, 2; j=1,2, …10} in table 1 provide the Likelihood that is "mixed", via the Bayes' Theorem, with the Prior pdf: the "a posteriori (or Posterior)" pdf is computed; from that we can compute the Mean which estimates the mean value (a real number) of the Posterior pdf. From the Posterior) pdf we can compute two quantities (real numbers) and such that there is the "stated" probability , as in the formula (2)

(2)

The interval , named Credibility Interval, is a numerical interval which has a stated probability of comprising the RV , related to the "parameter" .

For example we could assume that the pdf of the data of table 1 is the exponential, where the parameter is the failure rate

(3) We can reparametrize (3) with and assume as the parameter.

To use the Bayesian estimation we must define either the "known" Prior pdf either with and or and ; if we, from Prior knowledge, use the Prior (with a specified value a, for the RV )

(4) we can compute the Mean of the Posterior pdf and the Credibility Intervals, both for Sample 1 and Sample 2.

We can then compare the means and the Credibility Intervals and take decisions.

It is clear that using another Prior pdf we get a different estimation and a different Credibility Interval. Therefore, two scholars have different estimations and different Credibility Intervals from the same data. On the other and, with the data of table 1 and without assuming any distribution we can compute the means and the standard deviations (sd) of both samples and decide only through our intuition. Engineering and Applied Sciences. Vol. 2, No. 3, 2017] invented by the author as the way to analyse both books and papers, because only very few people have been carefully considering Quality of the Methods: e. g., Deming,Juran,: professors, researcher, managers, scholars and students have been learning wrong ideas, in the Quality field: there is worldwide used book with many wrong concepts e.g., D. C. Montgomery falls in contradiction! He spreads wrong concept on Quality [START_REF] Montgomery | Introduction to Statistical Quality Control[END_REF].

The Theory of Confidence Intervals

This section is written to explain the method of approach to the problem of estimation especially designed for all cases in which the Prior distribution of the "parameter" to be estimated is not known: the parameter is then treated as an unknown constant and not as a RV.

Since we cannot use the Bayes Theorem we must find a new way for the estimation.

It is important that we do that because after almost one century from the first ideas on the CI (Confidence Intervals) they are not still understood [START_REF] Galetto | Quality in Higher Education Courses[END_REF][START_REF] Galetto | Hope for the Future: Overcoming the DEEP Ignorance on the CI (Confidence Intervals) and on the DOE (Design of Experiments[END_REF][START_REF] Dore | Introduzione al Calcolo delle Probabilità e alle sue applicazioni ingegneristiche[END_REF][START_REF] Mood | Introduction to the Theory of Statistics[END_REF][START_REF] Rao | Linear Statistical Inference and its Applications[END_REF]. It is dramatic seeing that many books and papers do not give the correct Theory of CIs!

The Scientific road to building the CIs (Confidence Intervals) can be found in [START_REF] Galetto | Hope for the Future: Overcoming the DEEP Ignorance on the CI (Confidence Intervals) and on the DOE (Design of Experiments[END_REF][START_REF] Dore | Introduzione al Calcolo delle Probabilità e alle sue applicazioni ingegneristiche[END_REF][START_REF] Mood | Introduction to the Theory of Statistics[END_REF][START_REF] Rao | Linear Statistical Inference and its Applications[END_REF][START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF]. Here we show the various steps.

To make the presentation very easily we consider only one "parameter" and the exponential pdf, with mean (3b) We consider the data of Sample 1 in the Table 1.

Here are the steps (related to the Sample 1): A. We name D={x 1j ; j=1,2, …10} the set of the data to be considered for the estimation of the parameter , with each RV X 1j following the pdf (probability density function) B. We write the Likelihood Function (formula 1), for the "Complete Sample 1" (1b) C. We find the Maximum of by setting (5) whose solution is the quantity [START_REF] Shewhart | Economic Control of Quality of Manufactured Products[END_REF] D.

is the determination of a RV T, sum of the RVs X 1j , (7) whose pdf can be derived, via Probability Theory [START_REF] Galetto | Hope for the Future: Overcoming the DEEP Ignorance on the CI (Confidence Intervals) and on the DOE (Design of Experiments[END_REF][START_REF] Dore | Introduzione al Calcolo delle Probabilità e alle sue applicazioni ingegneristiche[END_REF][START_REF] Mood | Introduction to the Theory of Statistics[END_REF][START_REF] Rao | Linear Statistical Inference and its Applications[END_REF][START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF], from that of the sum of the 10 RVs X 1j E. We write the Probability statement for the RV T which depends on the parameter (8) where L and U are two numbers and is a stated probability that the RV T is out of the probability interval L ------U [since the exponential distribution is often used for "life data" (Time To Failure)] T is named "Total Time on Test" F. From [START_REF] Juran | Quality Control Handbook[END_REF] we derive the equivalent Probability statement (9) where we see the random probability interval -----that covers (includes) the unknown "true" value of parameter ; see the figure 2 where the abscissa is the parameter, and the ordinate is the RV T G. We can define the two probability intervals L ------U and -----before any collection of the data D H. When we compute the number , named the "observed total time on test", the random interval -----becomes the "real" interval -------- "determination (of the Random Interval)" as it is shown in the figure 3: notice that the result holds also for Uncomplete Samples of n items and r failures (there are n-r ties) I. The "real" interval --------, "determination (of the Random Interval)", is named Confidence Interval (CI), and has the property that, in the long run, the ( )% of the CIs covers the unknown "true" value of parameter J. The probability that -------is either 1 or 0, because is not a RV We informed the authors and the Journals who published wrong papers; we wrote various letters to the Editors: they have been not published so far; Editors cannot acknowledge their errors. The same happened for Minitab: so people continue taking wrong decisions…

The "ocean full of errors by…" Dovoedo and Chakraborti, "Boxplot-based Phase I Control Charts for Time Between Events", QREI, Kumar, Rakitzis, Chakraborti, Singh (2022), "Statistical design of ATS-unbiased charts with runs rules for monitoring exponential time between events", CS-TM, Jones, Champ, "Phase I control charts for times between events", QREI, Fang, Khoo, Lee, "Synthetic-Type Control Charts for Time-Between-Events Monitoring", PLoS ONE, Kumar, Chakraborti, "Improved Phase I Control Charts for Monitoring Times Between Events" QREI, Dovoedo "Contribution to outlier detection methods: Some Theory and Applications", (found online, 2021, March), Liu, Xie, Sharma, "A Comparative Study of Exponential Time Between Event Charts", QT&QM, Frisén, "Properties and Use of the Shewhart Method and Followers", SA, Woodall "Controversies and Contradictions in Statistical Process Control", JQT, Kittlitz "Transforming the exponential for SPC applications". JQT, Schilling, Nelson "The effect of non-normality on the control limits of X charts", JQT, Woodall "The use of control charts in health-care and public health surveillance", JQT, Xie, Goh, Kuralmani, "Statistical Models and Control Charts for High-Quality Processes", (Boston, MA: Kluwer Academic Publisher, 2002), Xie, Goh, Ranjan, "Some effective control chart procedures for reliability monitoring", RE&SS, Xie, "Some Statistical Models for the Monitoring of High-Quality Processes", Boston, chapter 16 in the book Engineering Statistics (Pham Editor): Springer-Verlag, Zhang, Xie, M., Goh, "Economic design of exponential charts for time between events monitoring", IJPR, Zhang, Xie, Goh "Design of exponential control charts using a sequential sampling scheme", IIE Transactions, Zhang, Xie, Goh, Shamsuzzaman "Economic design of time-between-events control chart system", CIE, Santiago, Smith, "Control charts based on the Exponential Distribution", QE, Nasrullah, Aslam, "Design of an EWMA adaptive control chart using MDS sampling", JSMS, Balamurali, Aslam, "Variable batch-size attribute control chart", JSMS. On September 2022, the author looked (in the web) for other TBE papers and books to see their way of dealing with "Rare Events" Control Charts; he copied 77 pages of documents (several from Consultants) and downloaded 32 papers (Open Source). Several Journals asked from 15 $ to 60 $, to download a paper. The Open Source are: "Control Chart: Charts for monitoring and adjusting industrial processes", "TOOL #6 -XBar & R Charts", "Integrating Quality Control Charts with Maintenance", "A Brief Literature Review", "Paper SAS4040-2016, "Improving Health Care Quality with the RAREEVENTS Procedure Bucky Ransdell, SAS Institute Inc.", "Performance Criteria for Evaluation of Control Chart for Phase II Monitoring", "(Thesis) A Comparative Study of Control Charts for Monitoring Rare Events in Health Systems Using Monte Carlo Simulation", "A study on the application of control chart in healthcare", "Control Charts for Monitoring the Reliability of Multi-State Systems", "Part 7: Variables Control Charts2, "A Control Chart for Gamma Distribution using Multiple Dependent State Sampling", "A Variable Control Chart under the Truncated Life Test for a Weibull Distribution", "Plotting basic control charts: tutorial notes for healthcare practitioners", "Appendix 1: Control Charts for Variables Data -classical Shewhart control chart", TRUNCATED ZERO INFLATED BINOMIAL CONTROL CHART FOR MONITORING RARE HEALTH EVENTS", "Comparison of control charts for monitoring clinical performance using binary data", "A numberbetween-events control chart for monitoring finite horizon production processes", "Rare event research: is it worth it?", "Quality Improvement Charts: An implementation of statistical process control charts for R", "Control Chart Overview", "Statistical Process Control Monitoring Quality in Healthcare", "A Control Chart for Exponentially Distributed Characteristics Using Modified Multiple Dependent State Sampling", "Synthetic-Type Control Charts for Time-Between-Events Monitoring", "A systematic study on time between events control charts", "Lifestyle Management through System Analysis Monitor Progress", "Multivariate Time-Between-Events Monitoring -An overview and some (overlooked) underlying complexities", "A Comparison of Shewhart-Type Time-Between-Events Control Charts Based on the Renewal Process", "Control Charts for Monitoring Time-Between-Events-and-Amplitude Data", "How to Measure Customer Satisfaction Seven metrics you need to use in your research".

The "ocean full of errors by…" Dovoedo and Chakraborti, "Boxplot-based Phase I Control Charts for Time Between Events", QREI, Kumar, Rakitzis, Chakraborti, Singh (2022), "Statistical design of ATS-unbiased charts with runs rules for monitoring exponential time between events", CS-TM, Jones, Champ, "Phase I control charts for times between events", QREI, Fang, Khoo, Lee, "Synthetic-Type Control Charts for Time-Between-Events Monitoring", PLoS ONE, Kumar, Chakraborti, "Improved Phase I Control Charts for Monitoring Times Between Events" QREI, Dovoedo "Contribution to outlier detection methods: Some Theory and Applications", (found online, 2021, March), Liu, Xie, The case depicted in the figure 3 can be described as follows: the failure of electronic components while in use can be regarded as events of Poisson type with intensity 1/q which is to be determined from experiment. A convenient sample size n being chosen, n items are put into service simultaneously and kept in operation until exactly r items have failed.

Some If you go to the three forums [1-3] you find the same situation: scholars do not know the Theory.

The "NHSTP" (null hypothesis significance testing procedure)

This point is largely debated, with wrong ideas, as well. The road shown in the section 2 can be depicted as in the figure 4.

J. Juran, at the 1989 EOQC Conference in Vienna, highlighted the content of the paper [START_REF] Galetto | Quality of Quality Methods is important[END_REF] about the importance of the Quality of the methods for making quality: the paper shows the only good methods are crucial for suitable decision taking.

Since the data are unfortunately always variable we must consider all the uncertainties because they have consequences on our decisions: we face "decision-making under uncertainty".

That's why, before carrying out any testing we must think about the following points: I. We define the pdf (probability density function) followed by the RV X 1j (j to be determined), for the estimation of the parameter II. We state the so-called "Null Hypothesis" H 0 ={ 0} with a chosen risk  (risk of 1 st type) that H 0 is Rejected, while it is actually true, and an "Alternative Hypothesis" H 1 ={ } is wrongly considered to be true [the type of H 1 can have different forms as There are various drawbacks….. I mention only a FIRST Point:

H 1 ={ }, H 1 ={ }, H 1 ={ }] III.
 The confidence coefficient of a confidence interval derives from the procedure which generated it. It is therefore helpful to differentiate a procedure (CP) from a confidence interval: an X% confidence procedure is any procedure that generates intervals cover θ in X% of repeated samples, and a confidence interval is a specific interval generated by such a process. A confidence procedure is a random process; a confidence interval is observed and fixed. The statement  A confidence procedure is a random process is nonsense. It is the same type of error as  Statistical significance … is a sample statistic ………….

The above ideas are connected with a concept, wrongly understood by many people (in the three forums [1-3]), the p-value.

NOBODY can know the true values of the mean  and of the variance  2 of the Distribution of the data: one can only estimate the parameters  and the variance  2 from their Consider the area , which is a Random Variable because the estimator is Random Variable (written as S before). The RV  0 ------1 is uniformly distributed by definition.

The «Test Statistics» s, given the data D, is the "determination (=estimate)" of the estimator S, is here indicated by and the previous formula becomes the number  0 ------1 ( 12) that is named p-value: it is the probability of Rejection of the null hypothesis H 0, given the data D.

The number  0 ------1 tells us how much we can believe in H 0 , given the collected data D; all the "possible" numbers , which are the determinations of RV , are uniformly distributed. See figure 6: RS1 is the Random Sample of the RVs related to the Sample 1 (sample size n 1 , and g 1 failures). RS2 is the Random Sample of the RVs related to the Sample 2 (sample size n 2 , and g 2 failures). For the table 1, n 1 = g 1 =10 and n 2 = g 2 =10.

Many incompetent scholars make confusion between the RVs related to the Probability Statements and the Confidence Statements (confidence intervals and p-values).

Individual Control Charts (I-CC)

and Exponentially distributed data.

The Theory of Control Charts (CC) is shown in the Shewhart's books [START_REF] Shewhart | Economic Control of Quality of Manufactured Products[END_REF][START_REF] Shewhart | Statistical Method from the Viewpoint of Quality Control[END_REF] and very appreciated by Deming [START_REF] Deming | Out of the Crisis[END_REF][START_REF] Deming | The new economics for industry, government, education[END_REF] and Juran [START_REF] Juran | Quality Control Handbook[END_REF]. The CCs are the "thermometer for measuring the fever of a Process", using the Control Limits [CLs: LCL (Lower CL) and UCL( (Upper CL)], used to see if the Process is either "In Control (IC)" or "Out Of Control (OOC) [it has "fever"]". CCs are the tool for assessing the "health" of the process: CCs are a statistical tool for monitoring the "measurable output" of a Process. The "measurable output" (measures on the products provided by the products produced) can be viewed as a "Stochastic Process X(t)", ruled by a probability density for any set of n "Random Variables RV" X(t 1 ), X(t 2 ), …, X(t n ), considered at the "time instants" t 1 , t 2 , …, t n , of the Stochastic Process X(t)". In many applications the data plotted (on the CC) are the means , determinations of the RVs , i=1, 2, ..., n (n=number of the samples) computed from the data x ij , j=1, 2, ..., k (k=sample size); x ij are the determinations of the RVs at very close instants t ij , j=1, 2, ..., k; the RVs are assumed to follow a normal distribution because (Central Limit Theorem) they are the means of samples with sample size, k, each; usually k=5. For each RV , mean of the process (at time t i ), mean of RVs j=1, 2, ..., k, we assume here that it is distributed as : this is the assumption of W. A. Shewhart on page 278 of his book [START_REF] Shewhart | Economic Control of Quality of Manufactured Products[END_REF], and justified on page 289. The mean of all the RVs is indicated by and its determination is named "grand mean" and indicated by .

When the process is OOC (it has "fever") we say that it is operating in the presence of assignable causes of variation.

The Individual Control Charts (I-CC) have sample size k=1; see figure 7. The "grand mean" , in this case, becomes the mean . To compute the CLs (LCL and UCL) we are forced to use the differences ; we compute the n-1 ranges and then we can use the usual formulae, for the Normal distributed data [i=1, …, n-1 (n=total number of data)].

What do the scholar who do not have the right Theory? They transform the data in order to have the "transformed data" Normally distributed.

Before using any transformation, any scholar should see if it is suitable, because, as said by [START_REF] Deming | Out of the Crisis[END_REF][START_REF] Deming | The new economics for industry, government, education[END_REF], "Management need to grow-up their knowledge because experience alone, without theory, teaches nothing what to do to make Quality" and "The result is that hundreds of people are learning what is wrong. I make this statement on the basis of experience, seeing every day the devastating effects of incompetent teaching and faulty applications." and, moreover,

"It is necessary to understand the theory of what one wishes to do or to make."

To show how to compute the Control Limits for I-CC we use the following data about the time between failure of air conditioners on a Boeing 720 airplane: Had we chosen a higher CL we would have larger CIs. Since 1 is comprised in the CI, we can assume the exponential pdf, with 20% risk of being in error.

In this case we estimate the Mean Time To Failure MTTF=59.60.

To find the Control Limits, LCL and UCL, of the I-CC we need a suitable Theory.

We looked for it, by reading several documents [found in the literature and the Web…] and got the "ocean full of errors by …" (notice that one of the authors is very well known; he has more than 7000 Citations! Does that mean that he wrote good papers? Absolutely not!)]. All the papers in the above "ocean …" have the same problem: wrong CLs; all the authors confound the concepts, by stating that LCL and UCL (that actually are the Confidence Limit!) are the limits L and U of the Probability Interval.

The suitable theory is RIT [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF].

TBE data following Exponential distribution are with r=1

From

I make this statement on the basis of experience, seeing every day the devastating effects of incompetent teaching and faulty applications." and, moreover, "It is necessary to understand the theory of what one wishes to do or to make."

Why the authors in the "ocean full of errors by …" are so ignorant? Because they did not and still do not know the Theory.

They were (and are) "lead into temptation and delivered into evil" by the (inapplicable) formulae, that are applicable only for the normal data and not for exponential data, in spite of the wrong statements (excerpt 2) about the Peer Reviewers' incompetent statements "limits… typical in the vast literature…" and "The problem … exponential distribution is well-defined and solved". They use wrongly the Probability Interval L ------U as though it were the LCL ------UCL and put the estimates, either or 1/ , of the parameters in place of the parameters, q or =1/q. See the excerpt 2: "the temptation and the evil". Notice that an author ("ocean …") is Associated Editor. of … Now, the author is at risk. IF the Peer Reviewers (PRs) are taken from the "ocean …" they will not acknowledge the errors and could think the "strange statements (above)" and, hence, the paper would get the following evaluation: "Your manuscript is unsuitable for publication in …. I have attached comments at the bottom of this email. … Thank you for considering …. I hope the outcome will not discourage you from the submission of future manuscripts." "The associate editor (notice, perhaps the one with more than 7000 Citations!) has stated that the work lacks sufficient novelty statistically in terms of theory and methods."

Therefore, (1) the readers can know the wrong methods that have "sufficient novelty statistically in terms of theory and methods." (see the "ocean …", > 7000 Citations!) (2) but, on the contrary, they cannot know the rigth methods that prove how many incompetents published wrong papers, that diverted, are diverting and will divert people from learning scientific methods.

That's the reality we are confronting with… And nobody but F. Galetto seems to take care about it. See, e.g., .

Peer Reviewers and readers (and Editors, as well) should practice "metanoia" [START_REF] Deming | The new economics for industry, government, education[END_REF]

and remember his statement "The result is that hundreds of people are learning what is wrong. I make this statement on the basis of experience, seeing every day the devastating effects of incompetent teaching and faulty applications."

Now we see that Reliability Integral Theory (RIT) [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF][START_REF] Galetto | Quality of Quality Methods is important[END_REF] solves the problem of computing the Control Limits for Control Charts, especially for I-CC_TBE, exponentially distributed data.

Being the data exponentially distributed, also the ranges are exponentially distributed (Galetto books) and OOC. We see that actually the process is "Out Of Control".

All the wrong methods in the "ocean full of errors by …." (see the Excerpt 2, with 10 authors, and one with > 7000 Citations!) cannot find that actually the process is "Out Of Control".

Using the exponential pdf we can plot the I-CC as in figure 8 The figure 8 shows the Time Between Failures of the air conditioners and the LCL (symbol LCL_G_Exp), when the data are considered exponentially distributed: the Process is OOC (4 points below LCL).

Let q [the MTTF of any unit] the unknown parameter to be estimated and the "known" observed determination of the RV Total Time on Test . Let's fix the Confidence Level CL=1-; the Lower Limit of MTTF is q L and the Lower Limit of MTTF is q U : we have to solve the two equations ( 14) [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF], where the unknown variables are q and q , (see fig. 9) ( 14) is the reliability of a stand-by system [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF] ("associated to the reliability test, with exponential pdf") of n units for the interval 0 -----t, and MTTF unit = . It is also the Operating Curve [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF]. while is related to 1-/2 and 1. Thus, we have two lines, passing through the origin O [with linear scale, in figure 9 and 10]; putting q=q 0 the two lines intercept the vertical segment L ----U (probability interval), which has probability =1- that the "time to failure", Random Variable T, of any unit [vertical axis named "Total Time on Test" (for figure 9), because we consider all the data] is in the interval L ----U when q=q 0 . The angle depends on the values /2, 1-/2 and n (the number of data) [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF]. With the known quantity = [observed determination of the RV ], we can draw the horizontal line intersecting the two lines through the origin: the abscissas of intersections are the two numbers q L and q U , depending on the values /2, 1-/2 and n: q L and q U are the Lower limit and the Upper limit of the CI of the MTTF of each unit, with CL=1- [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF]. It is evident, for any intelligent person, that the two segments L ----U (vertical) and q L ----q U (horizontal) are two different intervals with clear different meaning and obvious different lengths q U -q L U-L! All the documents, known to the author, make this BIG ERROR: they confound the segment L ----U, a Probability segment, with the segment q L ----q U , which is a Confidence segment [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF]! See the "ocean full of …." and Excerpt 2 (10 authors).

RIT solves the case (TBE CC). We have to look at the figure 10 (similar to figure 9, but with different lines). Now the angular coefficient K are related to /2 and 1 (the single datum) while is related to 1-/2 and 1. As before we have two lines, passing through the origin O [with linear scale, in figure 10]; at q=q 0 the two lines intercept the vertical segment L ----U (probability interval), that has probability =1- that the "time to failure", Random Variable T, of any unit [vertical axis named "Time on Test", consider the single data]. The angle depends on the values /2, 1-/2 and the sample size 1 [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF].

Acting in figure 10 (as done for figure 9), with the known quantity "mean observed time to failure" = [observed determination of the RV ], we can draw the horizontal line intersecting the two lines through the origin: the abscissas of intersections are the two numbers LCL and UCL, depending on the two chosen values /2, 1-/2 and 1 (the single datum). As a matter of fact, in the I-CC, the CLs LCL and UCL must be consistent with the "individual" times to failures: we want to analyse if they are significantly different from the "true mean q", estimated by the "mean observed time to failure"

. Therefore the CLs are the values satisfying two equations, for any single unit, [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF] ("associated to the reliability test, with exponential pdf") of 1 unit for the interval 0 ----- (15) similar to the [START_REF] Rozanov | Processus Aleatoire[END_REF] with replaced by ; so we have 20 CIs [all equal], given and CL=1- [0.9973]; remember that in this case k=1 (sample size): I-CC! It is also the Operating Curve [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF].

All that (above) when =1. The same ideas, not the same formulae, can be used when the data are "Weibully" distributed.

Individual Control Charts (I-CC) and Weibully distributed data.

In the previous section we assumed that the shape parameter had the value =1, that is the pdf was exponential.

The same ideas, not the same formulae, can be used when the distribution of the data is Weibull (formula 13). Now we must estimate the two parameters and : with the data of Table 2, we find the estimates and ; both the estimates are determinations of the two estimators and , which have their own distribution to be found.

The variability of the two estimators and has an important effect on the Control Limits of the I-CC.

To find the Control Limits of the I-CC two roads can be followed: 1) we assume that the estimators has a "very small variability" (a very strong assumption!) and then we consider only the value , and 2) we use the distribution of .

The first road (case) is shown in the figure 11.

The estimated value

, "assumed as a constant parameter", moves down the LCL. It is very easy to compute it because the transformation transforms the Weibull pdf into the exponential pdf: so, the previous theory applies to the data and variables.

Figure 12. Surface of versus

The effect of the variability of the estimator (case 2) on the I-CC is very dramatic.

Since the distribution of the RV is not easily found we have to revert to simulations. Doing that the result is that the LCL is very near 0 and therefore can be assumed LCL=0. Consequently, there is no OOC in the Individual Control Chart when we consider the variability of the estimator of the shape parameter The Minitab and JMP software do not find that! Using the Theory in [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF] and simulations we have LCL=0: the figures 12 and 13 show "intuitively the reason. Other distributions, but the Normal one, can have the same problems.

Conclusion.

We recall some important ideas about the Control Charts and the Individual Control Charts (I-CC).

We are going to show some new cases about I-CC: we consider papers from the "ocean…"; we do not show here their data; we show only the right I-CC. Consider the figure 14 and compare with the figure 4.

This point is largely debated, with wrong ideas, as well. The road shown in the section 2 can be depicted as in the figure 4.

J. Juran, at the 1989 EOQC Conference in Vienna, highlighted the content of the paper [START_REF] Galetto | Quality of Quality Methods is important[END_REF] about the importance of the Quality of the methods for making quality: the paper shows the only good methods are crucial for suitable decision taking.

(i) For Control Charts the "Null Hypothesis" is H 0 ={ roc ss "In Con rol"} wi h a chos n risk of st type =0.003 that H 0 is Rejected, and we declare the process OOC, while it is actually IC, and an "Alternative Hypothesis" H 1 ={ roc ss "Ou Of Con rol"} is wrongly no foun h r ar OOCs with a stated probability  (risk of 2 nd type) (ii) We must define the "probabilistic model" (the pdf) followed by the RV X j , for finding the "Statistic of the CC" (iii) From the Theory we derive the statistic S (via the "elaboration formula", which is a RV depending on the pdf of the RVs X j ) and the "Control Limits LCL, UCL" that are the "Acceptance Region" [complementary to the Rejection Region, the critical region C (iv) The probability  of deciding that H 0 ={ roc ss "In Con rol"} is true (when actually it is OOC), with the probability 1- (the power) that we decide to decide that the Process is OOC, when it is OOC (v) When both the risks are fixed, before the test, we can compute the sample size n needed to satisfy both name D={x j ; j=1,2, …, n} the set of the data to be considered, (vi) Then we collect m subsequent empirical samples D i ={x ij ; i=1, 2, …, m; j=1, 2, …, k} ("Complete Samples") which allows us to Compute the LCL and UCL and to decide about H 0 (vii) We compute the sample quantity s, determination of the RV S; if s belongs to the Critical Region C, either s<LCL or s>UCL, we reject H 0 ={ roc ss "In Con rol"} an w claim ha i is OOC; otherwise we "accept (do not reject) H 0

Out of control kinds UCL LCL

Since the data are unfortunately always variable we must consider all the uncertainties because they have consequences on our decisions: we face "decision-making under uncertainty".

That's why, before carrying out any testing we must think about the following points:

The above points have dramatic consequences for Individual Control Charts, where k=1 and m<30.

We had the opportunity to use the software JMP (in Italian).

We analysed the case of table 2 and we got the proof that JMP does not know the true concepts; see the figure 15 and compare it with the figure 11… Notice that JMP does not consider the variability of the RV .

LCL and UCL are not in agreement with the Theory (fig. 14). Meditate… Use RIT: the n=30 TBE can be considered as the "transition times" (failure times, exponentially distributed) between states of a stand-by system of 30 units. We get the fig. 16 solving the two equations . Comparing the figures 16 and 17, it becomes very clear that the CC from "Improved Phase…" presents 5 errors about OOC.

Reader, could you think that "Improved Phase… " is scientific and this paper is not? How can the CC from "Improved Phase…" be good?

Simulations (five million!) show that only < 5% of the computations are correct… We agree with those authors that "Further work is necessary on the OOC performance of these charts": the further Work must be to STUDY (see Deming!). We ask the reader: do you think that these findings are not supported by Theory and Methods?

2 nd case: the paper "Control charts … Exponential Distribution", published in QE is no better.

The authors find the process IC: actually it is OOC (fig. 18) 3 rd case: the paper "Some effective … for reliability monitoring", published in RE&SS. Qualified authors Xie, Goh, Ranjan. Again WRONG Control Limits! See figure 19. 3 (where we used the same scale of Kumar et al.). Both the methods, "t1 Chart" and "ATS-unbiased t1 Chart", from the paper "Statistical design of ATS-unbiased …" provide wrong Control Limits. They say: "It can be observed that … detects a signal at the 67th point." The 67 th point is <0.63; obviously it is also <1.835 (the LCL of Galetto). A very strange conclusion is drawn: "… ATS unbiased t2-chart gives an OOC for the first time at the 36th point, while using the modified scheme… the chart detects an OOC, at the 30 th point." "Because the ATS-unbiased t1-chart … OOC at the 67th point whereas the ATS unbiased t2-chart … OOC at the 30th point, the example supports … that monitoring the times to every 2nd event (r>1) can speed up the detection of shifts in the process parameter." It is not clear (to us) why the authors write also: "ATS unbiased t2-chart gives an OOC for the first time at the 36th point, while using the modified scheme, the chart detects an OOC at the 30th point." IF there is an OOC at the "36th point" (for the non_modified scheme) and there is an OOC at the "30th point" (for the Modified Scheme) why it is NOT OOC the "22nd point"<"30th point"? The authors do not tell us. The Peer Reviewers and the editor did not find that! At this point, it should be clear that several Journals have been going on publishing wrong papers on I-CC_TBE [Individual Control Charts for TBE (Time Between Events)] data, exponentially distributed. Does, now, the reader think that the statement "The problem of monitoring TBE that follow an exponential distribution is well-defined and solved. I do not agree that "nobody could solve scientifically the cases" has to be considered a scientific idea? Absolutely not! This is due to lack of knowledge of the Sound Theory of the CC. The errors are in papers published by reputed Journals, written by reputed authors and analysed by reputed Peer Reviewers, who did not find the errors: moreover, they were and are read by reputed readers, who did not find the errors (see the "ocean full of errors …").

Nonetheless, they are wrong…. A true disaster. Their "formulae (wrong)" are used by the Minitab software [also JMP (seen before), SixPack, SAS, ...). [he users of such software take wrong decisions based on the "wrong formulae"… Worse, "the Software Management", informed of the errors did not take any Corrective Action: a very good attitude towards Quality! Those Journals publishing wrong papers on CC for "rare events" should, for future research about CC, accept the letters sent to their Editors and provide them to their Peer Reviewers, to avoid costly errors and decisions: the letters are not yet been published: the papers are wrong and obviously the Editors cannot acknowledge that. They did not used metanoia [START_REF] Deming | The new economics for industry, government, education[END_REF]. That is the big real problem: big errors of "well reputed" people make a lot of danger, and nobody (known to the author …), but the author (FG), takes care of teaching the students to use their own brain in order not to be poisoned by incompetents.

How many Statisticians, Professors, Certified Master Black Belts, practitioners, workers, students, all over the world, learned, are learning and will learn wrong methods and took and will take wrong decisions? If the reader considers that the author asked many [>>50] Statisticians and Certified Master Black Belts and Minitab users (you can find them in various forums such as ReasearchGate, iSixSigma, Academia.edu, Quality Digest, … and in several Universities) and nobody could solve scientifically the cases, he has the dimension of the problem. The author hopes that the Peer Reviewers of this paper have better knowledge than the discussants (in the various forums and in the "ocean full of errors …"…), otherwise he risks being passed off… .

In spite of all these proofs, the discussant who suggested the paper of J. Smith did not believe to the evidence (see the "ocean …"). He raised the problem that it could happen only by chance: he believed only in simulations (as do all who do not know Theory)! After ten million of simulations F. Galetto got that T Charts (Minitab, JMP and in all wrong papers) were wrong 93.3% of the times! We think that it should be enough…

The author, many times, with his documents , tried to compel several scholars to be scientific (from Galetto 1998 to Galetto 2022, in the References): he did not have success. Only Juran appreciated the author's ideas when he mentioned the paper "Quality of methods for quality is important" at the plenary session of EOQC Conference, Vienna (Galetto 1989). He always asked his students to use their own Intelligence, in order to avoid being poisoned by incompetents. He helped them with his papers presented at the HEI (Higher Education Institutions) Conferences since 1998. We saw that data need to be analysed with suitable methods devised on the basis of Scientific Theory and not on methods in fashion, in order to generate the correct CC. RIT [START_REF] Galetto | Affidabilità Teoria e Metodi di calcolo[END_REF][START_REF] Galetto | Affidabilità Prove di affidabilità: distribuzione incognita, distribuzione esponenziale[END_REF][START_REF] Galetto | Qualità. Alcuni metodi statistici da Manager[END_REF][START_REF] Galetto | Gestione Manageriale della Affidabilità[END_REF][START_REF] Galetto | Manutenzione e Affidabilità[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Reliability and Maintenance, Scientific Methods, Practical Approach[END_REF][START_REF] Galetto | Affidabilità per la manutenzione Manutenzione per la disponibilità[END_REF][START_REF] Galetto | Statistical Process Management[END_REF] is able to deal with many distributions and then usable for many types of data and make Quality Decisions about Quality matters. We showed various cases (from books and papers) where errors were present due to the lack of knowledge of a Sound Theory of Control Charts and of RIT. In order to show the several wrong ideas and methods related to financial and business considerations about quality in several books (not given in the references) we would need at least 80 more pages in this paper: we, obviously, cannot do that.

Therefore we ask the readers to look at some of the author's documents.

Figure 2 .

 2 Figure 2. The two Probability Intervals connected to the RV T (Total Time on Test) Many scholars do not know the Theory; you find them in the forums [1-3] and in many papers, in good and respected Journals, as the ones in the following "Ocean full of errors by…".

Figure 3 .

 3 Figure 3. The Confidence Interval --------and the Probability Interval --------[for the RV T (Total Time on Test)]

Figure 5 .

 5 Figure 5. Deming's ideas about wrong scholars The wrong ideas are presented in the paper (THEORETICAL REVIEW) written by five authors (R. Morey, R. Hoekstra, J. Rouder, M. Lee, Eric-Jan Wagenmakers) The fallacy of placing confidence in confidence intervals, published in Psychon Bull Rev (2016) 23:103-123.There are various drawbacks….. I mention only a FIRST Point: The confidence coefficient of a confidence interval derives from the procedure which generated it. It is therefore helpful to differentiate a procedure (CP) from a confidence interval: an X% confidence procedure is any procedure that generates intervals cover θ in X% of repeated samples, and a confidence interval is a specific interval generated by such a process. A confidence procedure is a random process; a confidence interval is observed and fixed. The statement  A confidence procedure is a random process is nonsense. It is the same type of error as  Statistical significance … is a sample statistic ………….The above ideas are connected with a concept, wrongly understood by many people (in the three forums [1-3]), the p-value.NOBODY can know the true values of the mean  and of the variance  2 of the Distribution of the data: one can only estimate the parameters  and the variance  2 from their

  are Random Variables!!!]. For easiness we consider the previous case of a single parameter ; we indicate with the ESTIMATOR and with the the density (pdf) of the estimator [which is a RV!].

Figure 6 .

 6 Figure 6. The process of generation of the p-value [symbols f(t)= , , ]

  Statistical Process Control Applied at Level Crossing Incidents, by O. Abdallah et al. International Journal of Sciences: Basic and Applied Research, 2023. Excerpt 2. Typical wrong formulae picked from the "ocean full of errors…" (10 authors, and one with > 7000 Citations!) The Deming statements are in order for excerpt 2: "Management need to grow-up their knowledge because experience alone, without theory, teaches nothing what to do to make Quality" and "The result is that hundreds of people are learning what is wrong.

Figure 8 .

 8 Figure 8. Individual Control Chart of the Time Between Failures of the air conditioners. Notice that k=1 (sample size)

Figure 9 .Figure 10 .

 910 Figure 9. Confidence Interval of the MTTF, and

Figure 11 .

 11 Figure 11. Individual Control Chart of the Time Between Failures of the air conditioners, considering either the values 1 or 0.85 for the parameter . Notice that k=1 (sample size). See also the section Conclusion.

Figure 13 .

 13 Figure 13. Curves of versus (abscissa) and We think we have shown the problems arising with I-CC for Weibull distributed data.Other distributions, but the Normal one, can have the same problems.

Figure 14 .Figure 15 .

 1415 Figure 14. The flow-chart of steps for building control chart

Figure 16 .Figure 17 .

 1617 Figure 16. [Excerpt] Control Chart from "Improved Phase… for Monitoring TBE" Figure 17. Control Chart, by RIT, for "Improved Phase… for Monitoring TBE" data; vertical axis logarithmic; UCL is >100.

Figure 18 .Figure 19 .

 1819 Figure 18. Control Chart of Minitab authors' paper data (Urinary); vertical axe logarithmic. RIT used (F. Galetto) Figure 19. Control Chart of Xie et al. TBF data; vertical axe logarithmic. RIT used (F. Galetto)

Figure 20 .

 20 Figure 20. Necessity

Figure 21 .Figure 22 .

 2122 Figure 21. Intelligence vs "common sense"The author (figures 20, 21) has been always fond of Quality in his activity; for that reason, he wrote several papers and books showing scientific methods versus many wrong methods and presented them in several national and International Conferences: he wanted to diffuse Quality (from Galetto 1989 to Galetto 2022, in the References). The truth sets you free!

Table 1 .

 1 Data gathered in an experiment: two samples of size 10. Higher values are better.

	Sample 1 286 948 536 124 816 729	4 143 431 8
	Sample 2 2837 596 81 227 603 492 1199 1214 2831 96

  Journals that have wrong methods for computing the Confidence Interval are Journal of Quality Technology,

	Kluwer Academic Publisher, Reliability Engineering &
	System Safety, International Journal of Production
	Research, IIE Transactions, Computers and Industrial
	Engineering, Quality and Reliability Engineering
	International, Quality Engineering, International Journal of
	Production Research, Computers and Industrial
	Engineering, …

Table 2 .

 2 Time between failures of air conditioners on a Boeing 720 airplane. Higher values are better.

		RS1=T 1 , T 2 ,…, T g1 ,…, T n1 
		RS2=T' 1 , T' 2 ,…, T' g2 ,…, T' n2 
		Random
		Variable
	DATA	p-value (number)	H 0
			23 261 87 7 120 14 62 47 225 71
			246 21 42 30	5 12 120 11	3 14
			71 11 14 11 16 90	1 16 52 95
			The data are not "Normally Distributed"; therefore we
			cannot use the Shewhart Theory.
			Fitting a Weibull pdf to the data of Table 2
				(13)
			we find the estimates
				with Confidence Interval	and
				, with Confidence Level CL=80%,
				with Confidence Interval
			and	, with Confidence Level CL=80%.

  A very good result for a Peer Reviewed paper! The two Peer Reviewers did not know the Theory. "It is necessary to understand the theory of what one wishes to do or to make."[Deming] 4 th case: the paper "Statistical design of ATS-unbiased … time between events", we find a new wrong case copied from Santiago and Smith (2013): the CLs are wrong.According to the Kumar et al. computations, the CLs are: LCL=31.36 and UCL=1943.22, quite different from those of Santiago&Smith. The cause is not explained by the authors… It is interesting what we find with RIT. See Table

Table 3 .

 3 Comparison of results from the paper "Statistical design of ATS…." and RIT

	Type of	LCL	UCL	Comment
	Method
	N. Kumar et al.	0.63	2093.69 Both LCL and UCL
	"t1 Chart"		lower	than	the
			Scientific ones
	N. Kumar et al.	31.36 1943.22 LCL 17 times higher
	"ATS-unbiased		than Scientific and
	t1 Chart…"		UCL 24% of the
			Scientific ones
	F. Galetto RIT 1.835 7940.01 Scientific

TRUTH is ALWAYS the TRUTH even though NO ONE believes it.

Idiocy Ignorance Incompetence

a LIE is ALWAYS a LIE even if EVERYONE believes it.

Galileo Galilei Galileo Galilei