A novel random-effect Birnbaum-Saunders distribution for reliability assessment considering accelerated mechanism equivalence

Birnbaum-Saunders (B-S) distribution has been widely used in reliability assessment of products. However, the basic B-S distribution fails in characterizing the variation of damage caused by different units. In this paper, a novel random-effect B-S distribution which considers the unit heterogeneity is proposed. First, the novel distribution incorporates the inverse gamma distribution into the shape parameter of B-S distribution, and statistical inferences of the novel distribution are thoroughly investigated. Then, an extension of the proposed B-S distribution is developed to handle accelerated life test (ALT) data. In order to ensure the validity of ALTs, a coefficient of variation hypothesis test method employing the necessary condition for mechanism equivalence of the proposed distribution is executed. To estimate the parameters of the novel B-S distribution with explanatory variables, a two-step algorithm combining analogue least square and expectation maximization (ALS-EM) is proposed based on the data with constant coefficients of variation. A simulation is conducted to verify the effectiveness of the proposed ALS-EM method. Finally, two actual engineering cases are utilized to show the advantages of the random-effect B-S distribution in terms of goodness-of-fit and reliability assessment precision.