scholarly journals STATISTICAL PERFORMANCE OF X ̅ AND R CONTROL CHARTS FOR SKEWED DISTRIBUTION - CASE STUDY

2018 ◽  
Vol 6 ◽  
pp. 1050-1055
Author(s):  
Izabela D. Czabak-Górska ◽  
Marcin Lorenc
Keyword(s):  
Control Charts ◽  
Type I Error ◽  
Average Run Length ◽  
Measurement Data ◽  
Correction Method ◽  
Point Of View ◽  
Skewed Distribution ◽  
Type I ◽  
Control Limits

The purpose of the article is to determine the Type I error and Average Run Length values for charts   and R, for which control limits have been determined based on the Skewness Correction method (SC method), with an unknown probability distribution of the qualitative feature being tested. The study also used the Monte Carlo Simulation, in which two sampling methods were used to obtain random input scenarios - matching theoretical distributions (selected skewed distributions) and bootstrap resampling based on a manufacturing company’s measurement data. The presented article is a continuation of Czabak-Górska's (2016) research. The purpose of the article was to determine Type I error value and ARL type A for chart   and R, for which the control limits were determined based on the skewness correction method. For this purpose, measurement data from a company producing car seat frames. Presented case study showed that the chart determined using the skewness correction method works better for the data described by the gamma or log-normal distribution. This, in turn, may suggest that appropriate distribution was selected for the presented data, thanks to which it is possible to determine the course and nature of the process, which is important from the point of view of its further analysis, e.g. in terms of the process capability.

scholarly journals On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Johnson A. Adewara ◽  
Kayode S. Adekeye ◽  
Olubisi L. Aako
Keyword(s):  
Control Chart ◽  
Coverage Probability ◽  
Control Charts ◽  
Average Run Length ◽  
Real Life ◽  
Correction Method ◽  
Gompertz Distribution ◽  
Real Life Data ◽  
Control Limits ◽  
Two Parameter

In this paper, two methods of control chart were proposed to monitor the process based on the two-parameter Gompertz distribution. The proposed methods are the Gompertz Shewhart approach and Gompertz skewness correction method. A simulation study was conducted to compare the performance of the proposed chart with that of the skewness correction approach for various sample sizes. Furthermore, real-life data on thickness of paint on refrigerators which are nonnormal data that have attributes of a Gompertz distribution were used to illustrate the proposed control chart. The coverage probability (CP), control limit interval (CLI), and average run length (ARL) were used to measure the performance of the two methods. It was found that the Gompertz exact method where the control limits are calculated through the percentiles of the underline distribution has the highest coverage probability, while the Gompertz Shewhart approach and Gompertz skewness correction method have the least CLI and ARL. Hence, the two-parameter Gompertz-based methods would detect out-of-control faster for Gompertz-based X¯ charts.

Designing variable control charts under failure censoring reliability tests with replacement

2020 ◽  
Vol 42 (15) ◽  
pp. 3002-3011
Author(s):  
Hasan Rasay ◽  
Hossein Arshad
Keyword(s):  
Control Charts ◽  
Type I Error ◽  
Average Run Length ◽  
Quality Characteristic ◽  
Erlang Distribution ◽  
Type I ◽  
Chi Square ◽  
Variable Control ◽  
Specific Distribution ◽  
The One

There exist many processes where the quality characteristic does not follow a normal distribution, and the conditions for the application of central limit theorem are not satisfied; for example, because collecting data in a subgroup is impossible or the distribution is highly skewed. Thus, researchers have developed the control charts according to the specific distribution that models the quality characteristic. In this paper, some control charts are designed to monitor an exponentially distributed lifetime. The life testing is conducted according to the failure censoring while during the test; once observing a failure item, it is replaced by a new one so that the total number of items inspected during the test remains constant. Under the condition of the test, it is discussed that the elapsed time until observing the r’th failure has Erlang distribution. According to the relation of Erlang and chi-square distributions, the chart limits are computed to satisfy a specified value of type I error. Examples are presented and the curves of average run length are derived for the one-sided and two-sided control charts. Also, a comparative study is conducted to show the performance and superiority of the proposed control charts.

scholarly journals X̅ and R control charts based on marshall-olkin inverse log-logistic distribution for positive skewed data

2020 ◽  
Vol 1 (1) ◽  
pp. 9-16
Author(s):  
O. L. Aako ◽  
J. A. Adewara ◽  
K. S Adekeye ◽  
E. B. Nkemnole
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Logistic Distribution ◽  
Skewed Data ◽  
Process Data ◽  
And Performance ◽  
Set Up ◽  
Control Limits ◽  
Normally Distributed

The fundamental assumption of variable control charts is that the data are normally distributed and spread randomly about the mean. Process data are not always normally distributed, hence there is need to set up appropriate control charts that gives accurate control limits to monitor processes that are skewed. In this study Shewhart-type control charts for monitoring positively skewed data that are assumed to be from Marshall-Olkin Inverse Loglogistic Distribution (MOILLD) was developed. Average Run Length (ARL) and Control Limits Interval (CLI) were adopted to assess the stability and performance of the MOILLD control chart. The results obtained were compared with Classical Shewhart (CS) and Skewness Correction (SC) control charts using the ARL and CLI. It was discovered that the control charts based on MOILLD performed better and are more stable compare to CS and SC control charts. It is therefore recommended that for positively skewed data, a Marshall-Olkin Inverse Loglogistic Distribution based control chart will be more appropriate.

scholarly journals Evaluasi Kinerja Bagan Kendali Fm Pada Proses Short-Run

2018 ◽  
Vol 17 (1) ◽  
Author(s):  
Darmanto Darmanto
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Job Shop ◽  
Average Run Length ◽  
Just In Time ◽  
Multivariate Normal ◽  
Sensitivity Level ◽  
Short Run ◽  
Control Limits ◽  
Vector Shift

<p><em>The manufacturing production process that is currently trend is short-run. Short-run process is a job shop and a just in-time. These causes the process parameters to be unknown due to unavailability of data and generally a small amount of product. The control chart is one of the control charts which  designed for the short run. The procedure of the control chart follows the concept of succesive difference and under the assumption of the multivariate Normal distribution. The sensitivity level of a control chart is evaluated based on the average run length (ARL) value. In this study, the ARL value was calculated based on the shift simulation of the average vector by recording the first m-point out of the control limits. The average vector shift simulation of the target () is performed simultaneously with the properties of a positive shift (=+ δ). Variations of data size and many variables in this study were m = 20, 50 and p = 2, 4, 8, respectively. Each scheme (a combination of δ, m and p) is iterated 250,000 times. The simulation results show that for all schemes when both parameters are known ARL<sub>0 </sub>≈ 370. But, when parameters are unknown, ARL<sub>1</sub> turn to smaller. This conclusion also implied when the number of p and n are increased, it reduce the sensitivity of the control chart.</em></p>

Analyzing Group Data

2021 ◽  
pp. 121-142
Author(s):  
Charles Auerbach
Keyword(s):  
Control Charts ◽  
Type I Error ◽  
Statistical Significance ◽  
Data Sets ◽  
Type I ◽  
Chi Square ◽  
Statistical Process ◽  
Incorrect Decision ◽  
Group Data ◽  
Statistical Process Control Charts

This chapter covers tests of statistical significance that can be used to compare data across phases. These are used to determine whether observed outcomes are likely the result of an intervention or, more likely, the result of chance. The purpose of a statistical test is to determine how likely it is that the analyst is making an incorrect decision by rejecting the null hypothesis and accepting the alternative one. A number of tests of significance are presented in this chapter: statistical process control charts (SPCs), proportion/frequency, chi-square, the conservative dual criteria (CDC), robust conservative dual criteria (RCDC), the t test, and analysis of variance (ANOVA). How and when to use each of these are also discussed. The method for transforming autocorrelated data and merging data sets is discussed. Once new data sets are created using the Append() function, they can be tested for Type I error using the techniques discussed in the chapter.

scholarly journals Control charts for skewed distributions

2012 ◽  
Vol 9 (2) ◽  
Author(s):  
Derya Karagöz ◽  
Canan Hamurkaroğlu
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Control Charts ◽  
Type I ◽  
Skewed Distributions ◽  
Simulation Results ◽  
Standard Deviations ◽  
Control Limits

In this paper the control limits of \(\bar{X}\) and \(R\) control charts for skewed distributions are obtained by considering the classic, the weighted variance (\(\mathit{WV}\)), the weighted standard deviations (\(\mathit{WSD}\)) and the skewness correction (\(\mathit{SC}\)) methods. These methods are compared by using Monte Carlo simulation. Type I risk probabilities of these control charts are compared with respect to different subgroup sizes for skewed distributions which are Weibull, gamma and lognormal. Simulation results show that Type I risk of \(\mathit{SC}\) method is less than that of other methods. When the distribution is approximately symmetric, then the Type I risks of Shewhart, \(\mathit{WV}\) , \(\mathit{WSD}\), and \(\mathit{SC}\) \(\bar{X}\) charts are comparable, while the \(\mathit{SC}\) \(R\) chart has a noticeable smaller Type I risk.

Transformasi Terhadap Min bagi Menguji Taburan Terpencong

2012 ◽  
Author(s):  
Nor Haniza Sarmin ◽  
Md Hanafiah Md Zin ◽  
Rasidah Hussin
Keyword(s):  
Key Words ◽  
Simulation Study ◽  
Bias Correction ◽  
Type I Error ◽  
Small Sample Size ◽  
Small Sample ◽  
Skewed Distribution ◽  
Type I ◽  
Skewed Distributions ◽  
Chi Square

Suatu transformasi terhadap min dilakukan menggunakan penganggar pembetulan kepincangan bagi mendapatkan statistik untuk menguji min hipotesis taburan terpencong. Penghasilan statistik ini melibatkan pengubahsuaian pemboleh ubah . Kajian simulasi yang dijalankan terhadap taburan yang terpencong iaitu taburan eksponen, kuasa dua khi dan Weibull ke atas Kebarangkalian Ralat Jenis I menunjukkan bahawa statistik t3 sesuai untuk ujian satu hujung sebelah kiri dan saiz sampel yang kecil (n=5). Kata kunci: Min; statistik; taburan terpencong; penganggar pembetulan kepincangan; kebarangkalian Ralat Jenis I A transformation of mean has been done using a bias correction estimator to produce a statistic for mean hypothesis of skewed distributions. The statistic found involves a modification of the variable . A simulation study that has been done on some skewed distributions i.e. esponential, chi-square and Weibull on the Type I Error shows that t3 is suitable for the left-tailed test and a small sample size (n=5). Key words: Mean; statistic; skewed distribution; bias correction estimator; Type I Error

Comparison Between the Economic-Statistical Design of Double and Triple Sampling X ¯ \bar{X} Control Charts

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Azamsadat Iziy ◽  
Bahram Sadeghpour Gildeh ◽  
Ehsan Monabbati
Keyword(s):  
Optimal Control ◽  
Quality Control ◽  
Control Chart ◽  
Control Charts ◽  
Statistical Design ◽  
Sampling Interval ◽  
Point Of View ◽  
Double Sampling ◽  
Control Limits

AbstractControl charts have been established as major tools for quality control and improvement in industry. Therefore, it is always required to consider an appropriate design of a control chart from an economical point of view before using the chart. The economic design of a control chart refers to the determination of three optimal control chart parameters: sample size, the sampling interval, and the control limits coefficient. In this article, the double sampling (DS)

Using Monte Carlo Software to Teach Abstract Statistical Concepts: A Case Study

2005 ◽  
Vol 32 (3) ◽  
pp. 193-195 ◽  
Author(s):  
Holly Raffle ◽  
Gordon P. Brooks
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Type I Error ◽  
Computer Software ◽  
Course Evaluation ◽  
Error Rates ◽  
Type I ◽  
Statistics Course ◽  
Instructor's Manual

Violations of assumptions, inflated Type I error rates, and robustness are important concepts for students to learn in an introductory statistics course. However, these abstract ideas can be difficult for students to understand. Monte Carlo simulation methods can provide a concrete way for students to learn abstract statistical concepts. This article describes the MC4G computer software (Brooks, 2004) and the accompanying instructor's manual (Raffle, 2004). It also provides a case study that includes both assessment and course evaluation data supporting the effectiveness of Monte Carlo simulation exercises in a graduate-level statistics course.

scholarly journals Monitoring the Variability in the Process Using Neutrosophic Statistical Interval Method

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 562 ◽  
Author(s):  
Muhammad Aslam ◽  
Nasrullah Khan ◽  
Muhammad Khan
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Interval Methods ◽  
Interval Method ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
Imprecise Observations ◽  
Better Than

Existing variance control charts are designed under the assumptions that no uncertain, fuzzy and imprecise observations or parameters are in the population or the sample. Neutrosophic statistics, which is the extension of classical statistics, has been widely used when there is uncertainty in the data. In this paper, we will originally design S 2 control chart under the neutrosophic interval methods. The complete structure of the neutrosophic S 2 control chart will be given. The necessary measures of neutrosophic S 2 will be given. The neutrosophic coefficient of S 2 control chart will be determined through the neutrosophic algorithm. Some tables are given for practical use. The efficiency of the proposed control chart is shown over the S 2 control chart designed under the classical statistics in neutrosophic average run length (NARL). A real example is also added to illustrate the proposed control chart. From the comparison in the simulation study and case study, it is concluded that the proposed control chart performs better than the existing control chart under uncertainty.

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