Bootstrap Confidence Interval of the Difference Between Two Process Capability Indices

2003 ◽  
Vol 21 (4) ◽  
pp. 249-256 ◽  
Author(s):  
L.I. Tong ◽  
J.P. Chen
Keyword(s):  
Confidence Interval ◽  
Process Capability ◽  
Process Capability Indices ◽  
Bootstrap Confidence Interval ◽  
Capability Indices ◽  
The Difference

Bootstrap test for process capability indices

2017 ◽  
Vol 34 (7) ◽  
pp. 925-939
Author(s):  
Bahram Sadeghpour Gildeh ◽  
Sedigheh Rahimpour ◽  
Fatemeh Ghanbarpour Gravi
Keyword(s):  
Hypothesis Test ◽  
Bootstrap Method ◽  
Process Capability ◽  
Statistical Hypothesis ◽  
Process Capability Indices ◽  
Content Type ◽  
Statistical Hypothesis Test ◽  
Test Of Hypotheses ◽  
Capability Indices ◽  
The Difference

Purpose The purpose of this paper is to construct a statistical hypotheses test for process capability indices and compare the pairs of them with a fixed sample size. Design/methodology/approach Since the sampling distribution of the estimators of pairs of two process capability indices (PCIs) is very complex, an exact statistical hypothesis test for them cannot be constructed. Therefore, the authors have proposed a bootstrap method to construct the hypothesis test for them on the basis of p-value. Findings The authors have shown that by increasing n, the bootstrap method has better output relative to other methods and it can be easily implemented. The authors have also demonstrated that sometimes an exact hypotheses test cannot be constructed and need some assumptions. Originality/value In the present paper, several methods to test of hypotheses about the difference between two process capability indices have been compared.

scholarly journals Process Quality Evaluation Model with Taguchi Cost Loss Index

2021 ◽  
Vol 11 (21) ◽  
pp. 10182
Author(s):  
Chiao-Tzu Huang ◽  
Kuei-Kuei Lai
Keyword(s):  
Confidence Interval ◽  
Quality Evaluation ◽  
Evaluation Model ◽  
Process Capability ◽  
Process Quality ◽  
Statistical Testing ◽  
Process Capability Indices ◽  
Capability Indices ◽  
Loss Index ◽  
Quality Evaluation Model

Process Capability Indices (PCIs) are not only a good communication tools between sales departments and customers but also convenient tools for internal engineers to evaluate and analyze process capabilities of products. Many statisticians and process engineers are dedicated to research on process capability indices, among which the Taguchi cost loss index can reflect both the process yield and process cost loss at the same time. Therefore, in this study the Taguchi cost loss index was used to propose a novel process quality evaluation model. After the process was stabilized, a process capability evaluation was carried out. This study used Boole’s inequality and DeMorgan’s theorem to derive the (1 – α) ×100% confidence region of (δ,γ2) based on control chart data. The study adopted the mathematical programming method to find the (1 – α) ×100% confidence interval of the Taguchi cost loss index then employed a (1 – α) ×100% confidence interval to perform statistical testing and to determine whether the process needed improvement.

New multivariate process capability indices for measuring the performance of multivariate processes subject to non-normal distributions

2015 ◽  
Vol 33 (1) ◽  
pp. 42-61 ◽  
Author(s):  
Jeh-Nan Pan ◽  
Chung-I Li ◽  
Wei-Chen Shih
Keyword(s):  
Process Capability ◽  
Process Capability Indices ◽  
Process Data ◽  
Multivariate Process ◽  
Multivariate Processes ◽  
Content Type ◽  
Normal Distributions ◽  
Normality Assumption ◽  
Capability Indices ◽  
Multivariate Manufacturing

Purpose – In the past few years, several capability indices have been developed for evaluating the performance of multivariate manufacturing processes under the normality assumption. However, this assumption may not be true in most practical situations. Thus, the purpose of this paper is to develop new capability indices for evaluating the performance of multivariate processes subject to non-normal distributions. Design/methodology/approach – In this paper, the authors propose three non-normal multivariate process capability indices (MPCIs) RNMC p , RNMC pm and RNMC pu by relieving the normality assumption. Using the two normal MPCIs proposed by Pan and Lee, a weighted standard deviation method (WSD) is used to modify the NMC p and NMC pm indices for the-nominal-the-best case. Then the WSD method is applied to modify the multivariate ND index established by Niverthi and Dey for the-smaller-the-better case. Findings – A simulation study compares the performance of the various multivariate indices. Simulation results show that the actual non-conforming rates can be correctly reflected by the proposed capability indices. The numerical example further demonstrates that the actual quality performance of a non-normal multivariate process can properly reflected by the proposed capability indices. Practical implications – Process capability index is an important SPC tool for measuring the process performance. If the non-normal process data are mistreated as a normal one, it will result in an improper decision and thereby lead to an unnecessary quality loss. The new indices can provide practicing managers and engineers with a better decision-making tool for correctly measuring the performance for any multivariate process or environmental system. Originality/value – Once the existing multivariate quality/environmental problems and their Key Performance Indicators are identified, one may apply the new capability indices to evaluate the performance of various multivariate processes subject to non-normal distributions.

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