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Sequential Estimation of Optimal Age Replacement Policies

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Master's thesis

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Under an age replacement policy a system is replaced at a fixed age phi or at failure whichever comes first. If the cost of replacing the system before failure is less than the cost of replacing it at failure, this type of maintenance policy can lead to considerable savings. An often used criterion for finding an optimal replacement age phi, is to minimize the long run expected cost per unit time of a policy with replacement age phi. This cost function clearly depends on the underlying distribution of the system lifetimes. When this distribution is unknown, the cost function and hence phi need to be estimated. In this thesis, we study the large and small sample properties of a procedure which estimates phi. In particular, we study sequential maximum likelihood estimators of phi which are updated at each replacement based on the replacement history of the system so far. In this sequential procedure each system is subject to the age replacement policy with estimated phi based on all data gathered so far. This type of procedure should control the actual cost per unit time while gathering data needed to estimate phi. This thesis contains a detailed description of the sequential estimation procedure when the underlying system life times have a Weibull distribution and a Gamma distribution. Monte-Carlo methods are then used to study the behavior of the estimated optimal age replacement times and more importantly the actual costs per unit time for different sample sizes, costs and choices of the underlying Weibull and Gamma distributions.

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  • Economics and Cost Analysis

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