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Objective Bayesian inference for the capability index of the Gamma distribution
Author(s) -
de Almeida Marcello Henrique,
Ramos Pedro Luiz,
Rao Gadde Srinivasa,
Moala Fernando Antonio
Publication year - 2021
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2854
Subject(s) - markov chain monte carlo , bayesian probability , statistics , prior probability , posterior probability , inverse gamma distribution , bayesian linear regression , estimator , gamma distribution , mathematics , bayesian inference , computer science , inverse chi squared distribution , bayes estimator , bayesian hierarchical modeling , generalized gamma distribution , distribution fitting , probability distribution
The Gamma distribution has been applied in research in several areas of knowledge, due to its good flexibility and adaptability nature. Process capacity indices like C p kare widely used when the measurements related to the data follow a normal distribution. This article aims to estimate the C p kindex for nonnormal data using the Gamma distribution. We discuss maximum likelihood estimation and a Bayesian analysis through the Gamma distribution using an objective prior, known as a matching prior that can return Bayesian estimates with good properties for the C p k . A comparative study is made between classical and Bayesian estimation. The proposed Bayesian approach is considered with the Markov chain Monte Carlo method to generate samples of the posterior distribution. A simulation study is carried out to verify whether the posterior distribution presents good results when compared with the classical approach in terms of the mean relative errors and the mean square errors, which are the two commonly used metrics to evaluate the parameter estimators. Based on the real dataset, Bayesian estimates and credibility intervals for unknown parameters and the prior distribution are achieved to verify if the process is under control.