Generalized Confidence Intervals for Comparing the Capability of Two Processes

Abstract

The issue of selecting suppliers or assessing the impact of process improvement has already been investigated based on several process capability indices. However, the statistical test for comparing the capability of two suppliers or processes based on the C _pmk index has not been developed due to the complexity of the sampling distribution. In this article, we apply the concept of generalized pivotal quantities to derive the generalized confidence intervals (GCI) for the capability ratio and the capability difference between two given suppliers or processes. A simulation study is conducted to investigate the performance of the proposed methods and compare them with the coverage rates and the average width of confidence intervals. The numerical results indicate that the GCI method on the ratio is quite satisfactory for comparing the capability of two suppliers or processes since the attained coverage rates of the confidence interval are very close to the nominal confidence level.

Keywords:

• Coverage rate
• Generalized confidence intervals
• Supplier selection

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62P30

Acknowledgments

The earlier version of this article was presented at the 3rd Asian International Workshop on Advanced Reliability Modeling (AIWARM 2008). This work was partially supported by the National Science Council of Taiwan under grant no. NSC 96-2221-E-035-014 and NSC 97-2221-E-035-059-MY2.

Notes

*Indicate the value of coverage rate different from 0.95 at a significant level of 0.01.