BAYES ESTIMATION OF CAPABILITY INDEX USING THREE-PARAMETER WEIBULL DISTRIBUTION

Abstract

The process capability index is an important tool used in quality control and process improvement. Generally, the index is estimated under the assumption of a normal distribution, although some other distributions are also recommended in the literature. This paper instead considers a three-parameter Weibull distribution and obtains an estimate of the process capability index under the Bayesian framework. Bayesian development is based on the use of non-informative priors and the posterior sample-based inferences are drawn using an important Markov Chain Monte Carlo technique, namely, the Gibbs sampler algorithm. Finally, a numerical illustration based on two real datasets is provided. © 2024 Gnedenko Forum. All rights reserved.