Non-parametric predictive comparison of success-failure data in reliability

Abstract

Suppose a technical unit is required to perform a particular task in the future, and that several different types of the unit are available. The unit could be a system or a component, the different types might be different designs or units made by different producers. Units of each type have been tested, and the result of each test of a unit is success or failure to perform the task required. It is assumed that the available test data consist of the number of tests of units per type together with the numbers of successes in these tests. In this paper comparison of different types of units on the basis of such success-failure data is considered, where it is explicitly assumed that interest is in the future performance of m ≥1 units per type. Both pairwise and multiple comparisons of such different types of units are presented, with the overall idea of selecting the particular type of unit that is likely to lead to fewest failures in the m future tasks. The use of upper and lower probabilities makes it possible to work in a non-parametric statistical framework which requires only few modelling assumptions. The influence of the value of m on the inferences is studied. In addition, special attention is given to cases where for some types of units few, or even zero, failures were observed during testing.