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On the Use of Imprecise Probabilities in Reliability
 Quality and Reliability Engineering International
, 2004
"... Theory of imprecise probability generalizes classical probability theory, by assigning to each event an interval instead of a single number. In this paper, we briefly discuss this generalization and some recently suggested applications of imprecise probabilities in reliability. We also comment on ..."
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Theory of imprecise probability generalizes classical probability theory, by assigning to each event an interval instead of a single number. In this paper, we briefly discuss this generalization and some recently suggested applications of imprecise probabilities in reliability. We also comment on challenges for research and applications.
Nonparametric adaptive age replacement with a onecycle criterion
"... Age replacement of technical units has received much attention in the reliability literature over the last four decades. Mostly, the failure time distribution for the units is assumed to be known, and minimal costs per unit of time is used as optimality criterion, where renewal reward theory simplif ..."
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Age replacement of technical units has received much attention in the reliability literature over the last four decades. Mostly, the failure time distribution for the units is assumed to be known, and minimal costs per unit of time is used as optimality criterion, where renewal reward theory simplifies the mathematics involved but requires the assumption that the same process and replacement strategy continues over a very large (‘infinite’) period of time. Recently, there has been increasing attention to adaptive strategies for age replacement, taking into account the information from the process. Although renewal reward theory can still be used to provide an intuitively and mathematically attractive optimality criterion, it is more logical to use minimal costs per unit of time over a single cycle as optimality criterion for adaptive age replacement. In this paper, we first show that in the classical age replacement setting, with known failure time distribution with increasing hazard rate, the onecycle criterion leads to earlier replacement than the renewal reward criterion. Thereafter, we present adaptive age replacement with a onecycle criterion within the nonparametric predictive inferential framework. We study the performance of this approach via simulations, which are also used for comparisons with the use of the renewal reward criterion within the same statistical framework. Key words: Age replacement; nonparametric predictive inference; onecycle optimality criterion; renewal reward theorem. 1 1
On optimality criteria for age replacement
"... Age replacement is a wellknown topic in the literature of Operational Research and Reliability. Traditionally, the probability distribution of a unit’s failure time is assumed to be known, and the cost criterion is derived via the renewal reward theorem, which implicitly assumes that the same preve ..."
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Age replacement is a wellknown topic in the literature of Operational Research and Reliability. Traditionally, the probability distribution of a unit’s failure time is assumed to be known, and the cost criterion is derived via the renewal reward theorem, which implicitly assumes that the same preventive replacement strategy will be used over a very long period of time. As an alternative, one can use a onecycle criterion, aiming at minimisation of costs per unit of time only over the period that one unit is in place. We discuss these two criteria, and we also consider possible alternatives. Recently, we have presented a nonparametric predictive approach to age replacement, which is based on rather minimal assumptions for the failure time distributions, and provides full flexibility to the information from the process. We summarize the main conclusions from this research, where we also considered both the renewal criterion and the onecycle criterion. We discuss further aspects related to age replacement, highlighting several interesting topics for future research. Key words: Age replacement, nonparametric predictive inference, optimality criteria 1.