Time to failure due to fatigue is one of the common quality characteristics in material engineering applications. In this article, acceptance sampling plans are developed for the Birnbaum–Saunders distribution percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer's risk. The operating characteristic values (and curves) of the sampling plans as well as the producer's risk are presented. The R package named spbsq is developed to implement the developed sampling plans. Two examples with real data sets are also given as illustration.

Let X and Y have two-parameter Burr XII distributions. The maximum-likelihood estimator of δ=P(X<Y) is studied under the progressively first failure-censored samples. Three confidence intervals of δ are constructed by using an asymptotic distribution of the maximum-likelihood estimator of δ and two bootstrapping procedures, respectively. Some computational results from intensive simulations are presented. An illustrative example is provided to demonstrate the application of the proposed method.

The lumen degradation of light emitting diodes subject to increasing stress loading is investigated by using a cumulative damage model. The cumulative damage process is taken as a Wiener diffusion process with a drift which depends on two stress loadings. General statistical inferences on the parameters and percentiles of the light emitting diode lifetime distribution are presented based on the cumulative damage measurements, collected from a two-variable constant-stress loading accelerated degradation test. Approximate lower s-confidence bounds of the light emitting diode lighting lifetime percentiles are given using the Fisher information of the maximum-likelihood estimators, and Bonferroni's inequality. The application of the proposed method is illustrated by a lumen cumulative damage data set of high power light emitting diodes.

Bayesian estimation for population parameter under progressive type-I interval censoring is studied via Markov Chain Monte Carlo (MCMC) simulation. Two competitive statistical models, generalized exponential and Weibull distributions for modeling a real data set containing 112 patients with plasma cell myeloma, are studied for illustration. In model selection, a novel Bayesian procedure which involves a mixture model is proposed. Then the mix proportion is estimated through MCMC and used as the model selection criterion.

The cumulative damage of highly reliable products that subject to multiple loading stresses is investigated under Wiener process. Optimal strategies on the constant-stress accelerated degradation test plan are established to reach a compromised decision between the experiment budget and the estimation precision on the reliability inference. An algorithm is provided to search an optimal strategy for the accelerated degradation test. An example of light emitting diodes is used for illustrating the application of the proposed method.