Factorial Experiments in Life Testing

This paper discusses procedures for analyzing factorial experiments, where the experiment deals with the life testing of components or equipment. These procedures assume an underlying general distribution of “times-to-failure”, of which the exponential, Weibull, and extreme value distributions are special cases. Statistical tests and confidence procedures are outlined, and an example illustrating the procedure for life-test results of glass capacitors is included. Small sample approximations, which are adequate for practical applications, are given for the proposed procedures. This is shown empirically by generating thousands of life-test experiments on an electronic computer. An empirical sampling investigation is given of the robustness of the proposed procedures. From the sampling results, it is concluded that these techniques are sensitive (non-robust) to departures from the original assumptions on the probability distribution of failure-times. An investigation is also given of a transformation which appears to give robust results. These same techniques carry over exactly to the situation where one is analyzing an array of variance estimates from an underlying normal population.