A bayes analysis and comparison of weibull and lognormal based accelerated test models with actual lifetimes unknown

Abstract

The paper considers an accelerated test situation where the actual lifetimes of the items are not directly observable rather their status are known in the form of binary outcomes. By assuming two widely entertained models, namely the Weibull and the lognormal distributions, for the actual lifetimes, the paper provides full Bayesian analysis of the entertained models when both scale and shape parameters of the models are allowed to vary over the covariates involved in the study, thus giving rise to corresponding accelerated test models. The Bayes implementation is based on sample based approaches, namely the Metropolis algorithm and the Gibbs sampler using proper priors of the parameters where the prior elicitation is based on the expert testimonies. The situation involving missing items where actual status is also unknown is additionally entertained using the same modelling assumption. A comparison between the two entertained models is carried out using some standard Bayesian model comparison tools. Finally, numerical illustration is provided based on a given set of current status data and some relevant findings are reported. © 2020 Seventh Sense Research Group. All rights reserved.