Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

Abstract

The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) samples, which are obtained from the doubly truncated three-parameter BurrXII distribution. Because computational difficulty occurs for maximum likelihood estimation method, two Bayesian procedures are suggested to estimate model parameters and lifetime quantiles under the normal use condition. A Markov Chain Monte Carlo approach using the Metropolis–Hastings algorithm via Gibbs sampling is built to obtain Bayes estimators of the model parameters and to construct credible intervals. The proposed Bayesian estimation procedures are simple for practical use, and the obtained Bayes estimates are reliable for evaluating the reliability of lifetime products based on ALT samples. Monte Carlo simulations were conducted to evaluate the performance of these two Bayesian estimation procedures. Simulation results show that the second Bayesian estimation procedure outperforms the first Bayesian estimation procedure in terms of bias and mean squared error when users do not have sufficient knowledge to set up hyperparameters in the prior distributions. Finally, a numerical example about oil-well pumps is used for illustration.

Warranty costs analysis under accelerated life test for power Ishita distribution with type-I censored data

“…For constant stress ALT (see; Xin et al (2020), Balakrishnan and Ling (2014), Wang and Shi (2017) and Yang (1994)).…”

“…Uj, j=1,2,...,k are the k levels of high stress and also predict that the usual use situation satisfying Uu<U1<U2<⋯<Uk.njth items are set on investigation, and the testing ends once the quantity of failures reaches mj from these n j observed items at each stress level. For constant stress ALT (see; Xin et al . (2020), Balakrishnan and Ling (2014), Wang and Shi (2017) and Yang (1994)).…”

Reliability analysis of exponentiated Poisson‐exponential constant stress accelerated life test model

“…18 Further, Zhao et al 19 studied Burr-XII distribution based on type-I progressively hybrid censored samples using CSALT. Xin et al 20 investigated the MLE method and two Bayesian estimation procedures based on CSALT using doubly truncated three-parameter Burr-XII distribution.…”