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.

Bootstrap Confidence Intervals of the Modified Process Capability Index for Weibull distribution

2017 ◽  
Vol 42 (11) ◽  
pp. 4565-4573 ◽  
Author(s):  
Muhammad Kashif ◽  
Muhammad Aslam ◽  
G. Srinivasa Rao ◽  
Ali Hussein AL-Marshadi ◽  
Chi-Hyuck Jun
Keyword(s):  
Weibull Distribution ◽  
Confidence Intervals ◽  
Process Capability ◽  
Process Capability Index ◽  
Bootstrap Confidence Intervals ◽  
Capability Index

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.

Improved bootstrap confidence intervals for the process capability index Cpk

2018 ◽  
Vol 49 (10) ◽  
pp. 2583-2603 ◽  
Author(s):  
Chanseok Park ◽  
Sanku Dey ◽  
Linhan Ouyang ◽  
Jai-Hyun Byun ◽  
Mark Leeds
Keyword(s):  
Confidence Intervals ◽  
Process Capability ◽  
Process Capability Index ◽  
Bootstrap Confidence Intervals ◽  
Capability Index

scholarly journals Evaluation of Modified Non-Normal Process Capability Index and Its Bootstrap Confidence Intervals

IEEE Access ◽  
2017 ◽  
Vol 5 ◽  
pp. 12135-12142 ◽  
Author(s):  
Muhammad Kashif ◽  
Muhammad Aslam ◽  
Ali Hussein Al-Marshadi ◽  
Chi-Hyuck Jun ◽  
Muhammad Imran Khan
Keyword(s):  
Confidence Intervals ◽  
Process Capability ◽  
Process Capability Index ◽  
Normal Process ◽  
Bootstrap Confidence Intervals ◽  
Capability Index
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