Distinguishing Heterogeneity From Decreasing Hazard Rates

Abstract

Different copies of a repairable machine, or units, often exhibit different failure rates. If this heterogeneity is ignored, a statistical model of the time until failure may estimate a spurious decreasing hazard rate, resulting in incorrect inferences concerning the risk following repair. This article develops a renewal-proces model that accommodates both heterogeneity across units and decreasing hazard rates. Failure times for each unit are assumed Weibull, and the Weibull scale parameter is assumed to vary across units according to a gamma distribution. The model is illustrated using both Proschan's air-conditioner data and data on a U.S. Navy radar.

KEY WORDS:

• Overdispersion
• Reliability
• Renewal process
• Repairable systems
• Repeated measures
• Weibull distribution