Nonparametric Significance Tests for Imperfect Repair

Given the failure history for K >= 2 independent and identical repairable systems, a nonparametric procedure is presented to test the null hypothesis of minimal repair (MR) against the alternative of imperfect repair. The main idea is that, under non-harmful (harmful) repair, systems that failed later (earlier) are more reliable than those that have failed (later). This fact allows one, at any moment in time, to rank the systems from more to less reliable and, hence, to define a vector that counts how many times the system ranked r failed. When all the systems are time-truncated at the same time T, it is shown that, under the null hypothesis of MR, the vector of counts follows a multinomial distribution with class probabilities p(r) = K-1 for r = 1, ... , K. The test proceeds by computing a chi-bar squared test statistic similar to the one used to test one-sided alternatives in the multinomial setup, which allows us to compute p-values using either asymptotic theory or a straightforward Monte Carlo simulation using the null multinomial distribution. Extension to the case of different truncation times is also discussed. The procedure is applied to two real datasets regarding equipment used in the mining industry.