Confidence Intervals for the Common Process Capability Index Cp of Normal Distributions

2022 ◽  
Vol 11 (1) ◽  
pp. 175-187
Keyword(s):  
Confidence Intervals ◽  
Process Capability ◽  
Process Capability Index ◽  
Normal Distributions ◽  
Capability Index ◽  
Common Process ◽  
The Common

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 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.

Some new methods for comparing the capability of two processes using process capability index Cpm

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Michael Perakis
Keyword(s):  
Confidence Intervals ◽  
Practical Implication ◽  
Simulated Data ◽  
Process Capability ◽  
Process Capability Index ◽  
Small Samples ◽  
Content Type ◽  
Capability Index ◽  
New Methods ◽  
Practical Implications

PurposeThe purpose of the paper is the construction of confidence intervals for the ratio of the values of process capability index Cpm for two processes. These confidence intervals can be used for comparing the capability of any pair of competitive processes.Design/methodology/approachTwo methods for constructing confidence intervals for the ratio of the values of process capability index Cpm for two processes are proposed. The suggested techniques are based on a two-step approximation of the doubly non-central F distribution. Their performance is tested via simulation.FindingsThe performance of the suggested techniques seems to be rather satisfactory even for small samples, as illustrated through the use of simulated data.Practical implicationsThe practical implication of the suggested techniques is that they can be implemented in real-world applications, since they can be used for comparing the capability of any pair of competitive processes.Originality/valueThe paper presents two new methods for constructing confidence intervals for the ratio of the values of process capability index Cpm for two processes.

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