Comparisons of frequentist and Bayesian inferences for interval estimation on process yield

Abstract

Process yield has been a standard metric for measuring the capability and performance of manufacturing processes. Process capability index Spk, a concise unit-less gauge with yield-sensitive functionality, communicates succinctly the genuine process yield for normally distributed processes. However, in frequentist statistics, the exact sampling distribution of Spk’s natural estimator is intractable. Various frequentist approaches have attempted to address its wide-scale accuracy in statistical inference. Among them, the approach of generalized confidence interval (GCI) has been demonstrated superiority. In this paper, we incorporate Markov chain Monte Carlo (MCMC) algorithms to introduce a Bayesian-type approach. Extensive simulations in comparison of accuracy and precision performances between the Spk’s frequentist and Bayesian inferences are conducted. Concerning coverage rates and average interval widths of the inferential criteria, Spk’s Bayesian MCMC credibility intervals perform better than frequentist GCIs in most cases, particularly, the cases with only a few samples of information acquired from the manufacturing process.

Keywords:

• Process performance evaluation
• generalised confidence intervals
• Markov chain Monte Carlo
• statistical inference criteria
• coverage rate
• quality assurance

Acknowledgements

The authors would like to thank the Associate Editor and two anonymous referees for their insightful comments and careful readings, which significantly improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the Ministry of Science and Technology of Taiwan under grant numbers MOST 104-2221-E-151-018-MY3 and MOST 107-2221-E-992-064-MY3.