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A Criterion for Burn-in That Balances Mean Residual Life and Residual Variance

Department of Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Department of Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Department of Statistics, West Virginia University, Morgantown, West Virginia 26506-6330, and Department of Statistics, Panjab University, Chandigarh 160014, India
hwb{at}stat.pitt.edu
ths{at}stat.pitt.edu
hsingh{at}student.stat.wvu.edu

Optimum burn-in times have been determined for a variety of criteria such as mean residual life and conditional survival. In this paper we consider a residual coefficient of variation that balances mean residual life with residual variance. To study this quantity, we develop a general result concerning the preservation ofbathtub distributions. Using this result, we give a condition so that the residual coefficient of variation is bathtub-shaped. Furthermore, we show that it attains its optimum value at a time that occurs after the mean residual life function attains its optimum value, but not necessarily before the change point of the failure rate function.

Subject classifications: Reliability: burn-in, bathtub curves (life distributions).
History: Received September 1998; revision received July 2000; accepted September 2000.