Reply to “open problem of fuzzy confidence interval for fuzzy process capability index”

2013 ◽  
Vol 24 (1) ◽  
pp. 1-3 ◽  
Author(s):  
Wen-Chuan Lee ◽  
Jong-Wuu Wu
Keyword(s):  
Confidence Interval ◽  
Open Problem ◽  
Process Capability ◽  
Process Capability Index ◽  
Capability Index ◽  
Fuzzy Process ◽  
Fuzzy Process Capability

scholarly journals Measuring Loss-Based Process Capability IndexLeand Its GenerationLe′′with Fuzzy Numbers

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mohammad Abdolshah
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Numbers ◽  
Process Capability ◽  
Process Capability Index ◽  
Process Capability Indices ◽  
Capability Index ◽  
Fuzzy Process ◽  
Capability Indices ◽  
Fuzzy Process Capability ◽  
The Membership Function

Loss-based process capability indices are appropriate and realistic tools in order to measure the process capability. Among them, indexLeand its generationLe′′are well-known loss-based process capability indices, whose concepts are based on the worth (the opposite concept of loss). Sometimes, in order to calculateLeandLe′′there are some uncertainties in observations, so fuzzy logic can be employed to manage the uncertainties. This paper investigates fuzzification of process capability indexL~eand its generationL~e′′. In order to find the membership function of process capability indicesL~eandL~e′′, theα-cuts of fuzzy observation were employed. Then with an example of fuzzy process capability index,L~eandL~e′′were calculated and compared. Results showed that fuzzyL~e′′was more sensitive compared withL~eand was increased while the target departs (asymmetric tolerance). This example also showed that, with departure from the target, variation of fuzzyL~e′′and consequently its fuzziness were increased.

scholarly journals Measuring process capability index C pmk with fuzzy data and compare it with other fuzzy process capability indices

2011 ◽  
Vol 38 (6) ◽  
pp. 6452-6457 ◽  
Author(s):  
Mohammad Abdolshah ◽  
Rosnah Mohd. Yusuff ◽  
Tang Sai Hong ◽  
Md. Yusof B. Ismail ◽  
Aghdas Naimi Sadigh
Keyword(s):  
Process Capability ◽  
Process Capability Index ◽  
Process Capability Indices ◽  
Fuzzy Data ◽  
Measuring Process ◽  
Capability Index ◽  
Fuzzy Process ◽  
Capability Indices ◽  
Fuzzy Process Capability

scholarly journals Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 484 ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Mohammed Albassam ◽  
Muhammad Aslam
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Process Capability ◽  
Real Data ◽  
Process Capability Index ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Confidence Intervals ◽  
Capability Index ◽  
Coverage Probabilities ◽  
Percentile Bootstrap

This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) for Weibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index Cpkw over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.

scholarly journals The Capability Index when Some Assumptions are not Satisfied: Analysis and Empirical Comparisons

2020 ◽  
Vol 34 (3) ◽  
pp. 639
Author(s):  
Pablo José Moya Fernández ◽  
Juan Francisco Muñoz Rosas ◽  
Encarnación Álvarez Verdejo
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Process Capability ◽  
Process Capability Index ◽  
Sample Standard Deviation ◽  
Quality Requirements ◽  
Capability Index ◽  
Usual Estimator ◽  
Process Standard Deviation

The process capability index (PCI) evaluates the ability of a process to produce items with certain quality requirements. The PCI depends on the process standard deviation, which is usually unknown and estimated by using the sample standard deviation. The construction of confidence intervals for the PCI is also an important topic. The usual estimator of the PCI and its corresponding confidence interval are based on various assumptions, such as normality, the fact that the process is under control, or samples selected from infinite populations. The main aim of this paper is to investigate the empirical properties of estimators of the PCI, and analyze numerically the effect on confidence intervals when such assumptions are not satisfied, since these situations may arise in practice.

scholarly journals Confidence interval for the process capability index based on the bootstrap-t confidence interval for the standard deviation

2014 ◽  
Vol 11 (2) ◽  
Author(s):  
Wararit Panichkitkosolkul
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Coverage Probability ◽  
Process Capability ◽  
Process Capability Index ◽  
Skewed Distributions ◽  
Monte Carlo Simulation Study ◽  
Nominal Level ◽  
R Language ◽  
Capability Index

This paper proposes a confidence interval for the process capability index based on the bootstrap-t confidence interval for the standard deviation. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence interval with the existing confidence interval based on the confidence interval for the standard deviation. Simulation results show that the proposed confidence interval performs well in terms of coverage probability in case of more skewed distributions. On the other hand, the existing confidence interval has a coverage probability close to the nominal level for symmetrical or less skewed distributions. The code to estimate the confidence interval in R language is provided.

The Nonparametric Confidence Interval for the Process Capability Index C*pmk

2013 ◽  
Vol 404 ◽  
pp. 520-525 ◽  
Author(s):  
Shu Fei Wu
Keyword(s):  
Confidence Interval ◽  
Coverage Probability ◽  
Process Capability ◽  
Process Capability Index ◽  
The Other ◽  
Interval Estimate ◽  
Jackknife Method ◽  
Capability Index ◽  
Simulation Results ◽  
Bootstrap Interval

The process capability index which is a generalization of is defined by the use of the idea of Chan et al. [ for asymmetric tolerance. In this paper, we proposed a Jackknife confidence interval for and compare its coverage probability with the other three Efron and Tibshiranis [ bootstrap interval estimate techniques. The simulation results show that the Jackknife method has higher chance of reaching the nominal confidence coefficient for all cases considered in this paper. Therefore this method is recommended for used. One numerical example to demonstrate the construction of confidence interval for the process capability index is also given in this paper.

scholarly journals Performance of a Robust Confidence Interval for the Process Capability Index Cp based on the Modified Trimmed Standard Deviation Under Non-Normal Distributions

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Process Capability ◽  
Process Capability Index ◽  
Robust Estimator ◽  
Average Width ◽  
Normal Distributions ◽  
Capability Index ◽  
Simulation Results ◽  
Interval Estimator

In this paper, a robust interval estimator for the classical process capability index (Cp) based on the modified trimmed standard deviation (MTSD = ST ∗ ) is considered under both normal and non-normal distributions. The performance of the newly proposed process capability index interval estimator over the existing method is compared using a simulation study. As a performance criterion, we consider both simulated coverage probability and average width. Simulation results evident that the proposed confidence interval based on the robust estimator performed well for most of cases. For illustration purposes, two real-life data from industry are analyzed which supported our simulation results to some extent. As a result, the proposed method can be recommend to be used by the practitioners in various fields of industry, engineering and physical sciences.

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