Bootstrap Confidence Intervals of the Difference between Two Process Capability Indices for Half Logistic Distribution

Wararit Panichkitkosolkul

Abstract


The process capability indices are important numerical measures in statistical quality control. Well-known process capability indices are constructed under the process distribution is normal. Unfortunately, this situation is rather not realistic. This paper focuses on the half logistic distribution. The bootstrap confidence intervals for the difference between two process capability indices for the mentioned distribution are proposed. The bootstrap confidence intervals considered in this paper consist of the standard bootstrap confidence interval, the percentile bootstrap confidence interval and the bias-corrected percentile bootstrap confidence interval. A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the bootstrap confidence intervals. Simulation results showed that the estimated coverage probabilities of the standard bootstrap confidence interval get closer to the nominal confidence level than those of the other bootstrap confidence intervals.


Keywords


Process capability index, Bootstrap confidence interval, Half logistic distribution

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DOI: http://dx.doi.org/10.18187/pjsor.v8i4.455

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Title

Bootstrap Confidence Intervals of the Difference between Two Process Capability Indices for Half Logistic Distribution

Keywords

Process capability index, Bootstrap confidence interval, Half logistic distribution

Description

The process capability indices are important numerical measures in statistical quality control. Well-known process capability indices are constructed under the process distribution is normal. Unfortunately, this situation is rather not realistic. This paper focuses on the half logistic distribution. The bootstrap confidence intervals for the difference between two process capability indices for the mentioned distribution are proposed. The bootstrap confidence intervals considered in this paper consist of the standard bootstrap confidence interval, the percentile bootstrap confidence interval and the bias-corrected percentile bootstrap confidence interval. A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the bootstrap confidence intervals. Simulation results showed that the estimated coverage probabilities of the standard bootstrap confidence interval get closer to the nominal confidence level than those of the other bootstrap confidence intervals.


Date

2012-11-08

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 8 No. 4. 2012



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810