The time of 'guessing' your failure time distribution is over!

Abstract

Each statistical analysis of reliability data starts with the choice of the underlying distribution of failure times. This choice is of great importance because all conclusions drawn from this analysis will depend on it. Lifetime predictions can vary orders of magnitude depending on the distribution used. Most researchers choose the underlying distribution of failure times rather unfounded: because of "historical" reasons, because everybody uses it,… We developed a method which offers reliability engineers an objective tool for making the distinction between the two most widely used distributions, the lognormal and the Weibull, using a statistical well-founded technique. Essentially, the method comes down to constructing both the lognormal and the Weibull probability plot of the data set under consideration. For each plot, the Pearson's correlation coefficient is calculated. It is shown that the ratio of these two correlation coefficients is a pivotal quantity. Hence, it can serve as a test statistic.