Abstract
The lifetime of a system is measured in two principal time scales, L and H. We consider a family of time scales of type Ta=(1−a) · L+a · H, for which the lifetime is T=(1−a) L+aH, a∈[0, 1], where L and H are the lifetimes in the principal time scales. The optimal time scale, by the definition, provides the minimal value of the coefficient of variation of system lifetime. We consider the age replacement model in time scale Ta and develop a nonparametric numerical procedure for finding the optimal weighting parameter a* that provides the smallest value of the corresponding cost function. This procedure is applied to fatigue test data, and it is demonstrated that the best time scale with respect to the age replacement cost function is very close to the optimal time scale. The same is true for a modified age replacement scheme in which the replacement age equals the p-quantile of system lifetime.
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