Repairable systems reliability trend tests and evaluation

Abstract

Repairable systems reliability trend tests are reviewed, extensively tested and compared to evaluate their effectiveness over diverse data patterns. A repairable system is often modeled as a counting failure process. For a counting failure process, successive inter-arrival failure times will tend to become larger (smaller) for an improving (deteriorating) system. During testing and development of new systems, reliability trend analysis is needed to evaluate the progress of the design development and improvement process. Often a program of testing and modification, followed by more testing and modification, is required to achieve a desired system reliability goal. Reliability trend tests can be an important part of this program. The objective of system reliability trend tests is to determine whether and how the pattern of failures is significantly changing with time. This paper reviews the following four trend tests: (1) Crow/AMSAA Test, (2) PCNT (pair-wise comparison nonparametric test), (3) Laplace Test, and (4) Lewis-Robinson Test. These tests are extensively tested, evaluated and compared for diverse repairable system reliability trends. Particular emphasis focused on comparisons with low sample sizes. Simulation models for trend tests are presented and discussed; and simulation results are summarized and compared. Based on these comparisons, it is concluded that the Crow/AMSAA test is the most robust trend test.

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“…Crow-AMSAA test accepts trend behavior of the repair time/ lifetime datasets if 2 is the score of chi-square distribution, and 1−α is the confidence interval. β can be estimated using Equation 1 where T i is cumulative time-between-failures till the i th failure [30]. …”

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“…β can be estimated using Equation (1) where T i is cumulative time-between-failures till ith failure [33]:…”

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“…Assuming that the observation starts at t = 0, then, t in is the nth failure arrival time. More discussions about the trend test and analysis are available in [9] and [28]. When the Crow/AMSAA model is appropriate for predicting the surfaced failure mode intensity, (1) can be rewritten aŝ…”