Estimating the delay-time distribution of faults in repairable machinery from failure data

This paper considers a repairable machine that may fail or suffer breakdown many times during the course of its service lifetime,a nd is inspected for visible faults at intervals. The delay-time concept of Christer & Waller provides a means of modelling the behaviour of the sysem, and predicting such useful quantities as reliability and cost, under various putative inspection regimes. Hitherto, model parameters have been estimated mainly from subjective data. In this paper, the authors show that it is both theoretically and practically possible to estimate model parameters, and make useful predictions, purely from objective data, i.e. the history of breakdown times and the findings of inspections. Model parameters are fitted by the method of maximum likelihood, and selection of the ‘best’ model made using the Akaike information criterion. Initially, Monte-Carlo studies were made, and showed that the procedure did enable unbiased and asymptotically accurate estimates of model parameters to be recovered from data. Manual records of inspections and failures of a sample of hospital infusion pumps were then analysed, and values of model parameters estimated. Tests of fit were derived and carried out. Finally, the reliability of infusion-pump components under different inspection intervals was derived from the delay-time model, with 95% confidence limits, as a demonstration that the method does indeed provide a practical tool for optimizing inspection policies. The practical details of the relevant computations are given in some detail throughout, to enable other workers to follow the present procedure.