Order restricted Bayesian inference for exponential simple step-stress model

ABSTRACT

A step-stress model has received a considerable amount of attention in recent years. In the usual step-stress experiment, a stress level is allowed to increase at each step to get rapid failure of the experimental units. The expected lifetime of the experimental unit is shortened as the stress level increases. Although extensive amount of work has been done on step-stress models, not enough attention has been paid to analyze step-stress models incorporating this information. We consider a simple step-stress model and provide Bayesian inference of the unknown parameters under cumulative exposure model assumption. It is assumed that the lifetime of the experimental units are exponentially distributed with different scale parameters at different stress levels. It is further assumed that the stress level increases at each step, hence the expected lifetime decreases. We try to incorporate this restriction using the prior assumptions. It is observed that different censoring schemes can be incorporated very easily under a general setup. Monte Carlo simulations have been performed to see the effectiveness of the proposed method, and two datasets have been analyzed for illustrative purposes.

KEYWORDS:

• Cumulative exposure model
• Hybrid censoring scheme
• Maximum likelihood estimator
• Posterior analysis
• Prior distribution
• Progressive censoring scheme
• Step-stress life-tests
• Type-I and Type-II censoring schemes

Mathematics Subject Classification:

• Primary 62E15
• Secondary 62H10