Does distribution choice matter in practical reliability analysis?

Abstract

We present some examples and results on the extent to which the choice of reliability distribution affects estimation of specific properties of failure distributions; we focus here on the probability of failure within a warranty period, but briefly consider estimating a percentile of the distribution. We show that the effect of choosing the correct distribution is often quite small, with similar estimates obtainable from other candidate distributions. Similar conclusions apply when the list of candidate distributions does not include the true underlying distribution — the penalty for not selecting the ‘best’ candidate is often quite small. We establish a framework for simulation experiments for quantifying these penalties; elements in the framework allow us to simulate data with many of the features commonly observed in warranty data. We illustrate the framework by modelling three typical scenarios encountered in the analysis of warranty data; the corresponding simulation results provide further details on the extent to which the choice of distribution matters in this particular reliability setting.