Component importance measures for complex repairable system

In recent years, the system signature has been recognized as an important tool to quantify the reliability of systems consist of independent and identically distributed (iid) or exchangeable components with respect the random failure times. System signature separates the system structure from the component probabilistic failure distribution. However, when it is adopted to solve a complex system with more than one component type, it requires the computation of the probabilities of all possible different ordering statistics of each component failure lifetime distributions, which is often an intractable procedure

Maximum group sizes for simultaneous testing in high potential risk scenarios

When tests are performed in scenarios such as reliability demonstration, two extreme possibilities are to perform all required tests simultaneously or to test all units sequentially. From the perspective of time for testing, the former is typically preferred, but in high potential risk scenarios, for example in the case of possibly disastrous results if a tested unit fails, it is better to have the opportunity to stop testing after a failure occurs. An analogon appears in medical testing, with patients being the ‘units’, if new medication is to be tested to confirm its functionality while possibly severe (side) effects are not yet known. There is a wide range of test scenarios in between these two extremes, with groups of units being tested simultaneously. This article discusses such scenarios in a basic setting, assuming that the total number of required tests has been set, for example based on other criteria or legislation. A new criterion for guidance on suitable test group sizes is presented. Throughout, the aim is for high reliability, with testing stopped in case any unit fails, following which the units will not be approved. Any consecutive actions, such as improvement of the units or dismissing them, are not part of the main considerations in this article. While in practice the development of complex models and decision approaches may appear to be required, a straightforward argument is presented, which leads to results that can be widely applied and easily communicated

Nonparametric predictive comparison of lifetime data under progressive censoring

In reliability and lifetime testing, comparison of two groups of data is a common problem. In some lifetime experiments, making a quick and efficient decision is desirable in order to save time and costs. To this end, a progressive censoring scheme can be useful, with censoring occurring at different stages [2]. This paper presents a nonparametric predictive inference (NPI) approach to compare two groups, say X and Y, when one (or both) is (are) progressively censored. NPI can easily be applied to different types of progressive censoring schemes. NPI is a statistical method based on Hill’s assumption A (n) [1], with inferences strongly based on data and with uncertainty quantified via lower and upper probabilities. These inferences consider the event that the lifetime of a future unit from Y is greater tha