학술논문
Parametric inference on partially accelerated life testing for the inverted Kumaraswamy distribution based on Type-II progressive censoring data
Document Type
Academic Journal
Source
Mathematical Biosciences and Engineering. February 2023, Vol. 20 Issue 2, p1674, 21 p.
Subject
Language
English
Abstract
1. Introduction As a result of significant advancements in high technology, today's products are becoming more and more reliable, and product lifetimes are increasing. A product's failure may take a [...]
This article discusses the problem of estimation with step stress partially accelerated life tests using Type-II progressively censored samples. The lifetime of items under use condition follows the two-parameters inverted Kumaraswamy distribution. The maximum likelihood estimates for the unknown parameters are computed numerically. Using the property of asymptotic distributions for maximum likelihood estimation, we constructed asymptotic interval estimates. The Bayes procedure is used to calculate estimates of the unknown parameters from symmetrical and asymmetric loss functions. The Bayes estimates cannot be obtained explicitly, therefor the Lindley's approximation and the Markov chain Monte Carlo technique are used to obtaining the Bayes estimates. Furthermore, the highest posterior density credible intervals for the unknown parameters are calculated. An example is presented to illustrate the methods of inference. Finally, a numerical example of March precipitation (in inches) in Minneapolis failure times in the real world is provided to illustrate how the approaches will perform in practice. Keywords: step-stress partially accelerated life test; Type-II progressive censoring; inverted Kumaraswamy distribution; maximum likelihood method; Bayesian inference; Lindley's approximation; Markov chain Monte Carlo; Monte Carlo simulation
This article discusses the problem of estimation with step stress partially accelerated life tests using Type-II progressively censored samples. The lifetime of items under use condition follows the two-parameters inverted Kumaraswamy distribution. The maximum likelihood estimates for the unknown parameters are computed numerically. Using the property of asymptotic distributions for maximum likelihood estimation, we constructed asymptotic interval estimates. The Bayes procedure is used to calculate estimates of the unknown parameters from symmetrical and asymmetric loss functions. The Bayes estimates cannot be obtained explicitly, therefor the Lindley's approximation and the Markov chain Monte Carlo technique are used to obtaining the Bayes estimates. Furthermore, the highest posterior density credible intervals for the unknown parameters are calculated. An example is presented to illustrate the methods of inference. Finally, a numerical example of March precipitation (in inches) in Minneapolis failure times in the real world is provided to illustrate how the approaches will perform in practice. Keywords: step-stress partially accelerated life test; Type-II progressive censoring; inverted Kumaraswamy distribution; maximum likelihood method; Bayesian inference; Lindley's approximation; Markov chain Monte Carlo; Monte Carlo simulation