A Bayesian Approach for Predicting Functional Reliability of One-Shot Devices

Accelerated life tests (ALTs) have been used to assess reliability of one-shot devices in a short time. Due to destructive characteristics of one-shot devices, lifetime data of the devices is incomplete and enough number of failures or even no failures may be not secured in ALT. In such situations, Baysian methods incorporating prior information into the parameters provides useful inference on the reliability of one-shot devices. In this paper, we propose a modeling approach to predict functional reliability of pin pullers as a kind of one-shot devices, mainly in a Bayesian framework. We introduce three different priors to the parameters of the Weibull distribution or reliability function. Sress-strength relationships of key components in pin pullers are employed to the scale and shape parameters via three prior densities. The proposed methods are illustrated with a variety of simulation studies. The simulation works are performed using the Gibbs sampling technique to generate MCMC samples to obtain Bayesian estimates of the Weibull parameters. The Bayesian estimates from the three priors tend to approach to true parameter values as sample size increases.