Distinguishing Heterogeneity From Decreasing Hazard Rates

Different copies of a repairable machine, or units, may exhibit different failure rates. If this heterogeneity is ignored, a statistical model of the time until failure may reveal a spurious decreasing hazard rate. Such a model results in incorrect inferences concerning the risk following repair. This paper develops a statistical model that accommodates both heterogeneity across units and decreasing hazard rates. The model is best suited for a fairly large number of units with relatively few failures apiece. The times to failure for each unit are assumed to be Weibull, and the Weibull scale parameter is allowed to vary randomly across units under a Gamma distribution. The model is illustrated using data on U.S. Navy radars.