Reliability analysis of Birnbaum–Saunders model based on progressive type-II censoring

ABSTRACT

The reliability $R=P(Y<X)$ is derived based on progressively Type-II censored samples, when X and Y are independent Birnbaum–Saunders distributions with the same shape parameter but different scale parameters, and all of these parameters are unknown. The maximum likelihood estimate of R is derived and the approximate variance is constructed by combining delta and Monte Carlo (MC) methods. Then, Bayesian inference is performed to derive R and to predict the times to failure of the items censored in multiple stages of progressively type-II data with two Markov Chain MC (MCMC) algorithms. One algorithm is the hybrid Metropolis-Gibbs methodology, which considers the censored data to be unknown parameters along with model parameters and includes them in MCMC sampler to obtain parameter estimation. In the other algorithm, the unknown parameters are considered in the Metropolis methodology to construct Bayesian estimation and then to predict censored observations. Two illustrative examples are finally provided to examine the performance of the proposed methods.

KEYWORDS:

• Birnbaum–Saunders distribution
• reliability
• progressive type-II censoring
• MCMC technique

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The paper is supported by the National Natural Science Foundation of China [grant numbers 11461051, 81860605, 11861049], Natural Science Foundation of Inner Mongolia [grant number 2017MS0101].