Identification and Treatment of Extreme Inter-Failure Times from a Fleet of Repairable Systems

Inter-failure time data collected from a fleet of repairable systems often contain extremely small or/and large observations. The extremely small observations probably result from poor maintenance or/and manufacturing quality while the extremely large observations are probably because one or more failure events have not been recorded. The reliability of a repairable system is usually modelled by a failure point process model. The model can be biased if handling the extreme observations as regular ones and the prediction made from the fitted model can be inaccurate. Thus, for a given dataset, two issues must be adequately addressed: (a) to determine whether or not the dataset contains extreme observations and to identify them if yes, and (b) to treat them properly. This paper aims to address these two issues. A mixture-based approach is proposed to address the first issue. The normal, lognormal and Weibull QQ plots are built using the data between the lower and upper quartiles. For the data outside the quartiles, the extreme observations are identified based on the absolute deviations between the actual and theoretical observations obtained from the best fitted model. A new treatment technique is proposed to address the second issue. The proposed technique modifies the failure number of each extreme observation from 1 to a real number. The reliability model is built based on the revised data. Two real-world examples are included to illustrate the proposed methods and their appropriateness.