A Bayes ranking of survival distributions using accelerated or correlated data

The high reliability of modern components requires accelerated testing to compare or predict survival or failure rates in the use condition. If the testing of highly reliable components is done in the use condition, the times to failure are too long to observe. Therefore, it is often required to compare or predict mean times to failure in the use condition when the only available data are from a highly accelerated condition. Comparison of failure rates in this situation is possible using frequentist methods but estimation of the individual failure rates is not. Using Bayes methods, both comparison and prediction results are easily possible and computable. The accelerated model in this paper is similar to the model used in health-related research when the data are from a paired experiment. This use of the model to compare and predict survival rates using paired data is also handled easily by the Bayes approach. Let the two failure rates be λ₁, λ ₂; the results are presented as the posterior probability 𝒫r{λ₁<c·λ₂|data}, 0<c⩽1. The predictions are the posterior means, E{λ₁ |data}, E{λ₂|data}