On the generalized process capability under simple and mixture models

Abstract

Process capability (PC) indices measure the ability of a process of interest to meet the desired specifications under certain restrictions. There are a variety of capability indices available in literature for different interest variables such as weights, lengths, thickness, and the life time of items among many others. The goal of this article is to study the generalized capability indices from the Bayesian view point under different symmetric and asymmetric loss functions for the simple and mixture of generalized lifetime models. For our study purposes, we have covered a simple and two component mixture of Maxwell distribution as a special case of the generalized class of models. A comparative discussion of the PC with the mixture models under Laplace and inverse Rayleigh are also included. Bayesian point estimation of maintenance performance of the system is also part of the study (considering the Maxwell failure lifetime model and the repair time model). A real-life example is also included to illustrate the procedural details of the proposed method.

Keywords:

• Bayesian estimation
• informative and non-informative priors
• Maxwell distribution
• posterior risk
• process capability indices
• relative risk
• sensitivity analysis
• system availability
• squared error and precautionary loss functions

2010 AMS Classifications:

• 62F15
• 62N01
• 62N02

Acknowledgements

We thank the learned referees and the Editor of the Journal of Applied Statistics, for careful reading and helpful comments that improved our manuscript. The author Muhammad Riaz is indebted to King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia for providing excellent research facilities.

Notes

1. Supplementary Content may be viewed online at http://dx.doi.org/10.1080/02664763.2013.856386