Summary
Replacement models deal with the problem of finding the optimal random time for a preventive replacement of a technical system. A large class of such models has been considered in the literature recently. In this paper a unifying approach to the replacement problem is given regarding it as an optimal stopping problem. The generalization allows to weaken a necessary monotonicity condition and to consider different information levels. Measuring information in this context leads to discussing the problem in general terms of stochastic process theory. An example shows how to get explicit solutions and how the information level influences the optimal replacement policy.
Zusammenfassung
Ersetzungsmodelle beschreiben im Rahmen der Zuverlässigkeitstheorie das Problem, einen optimalen Zeitpunkt für die vorbeugende Ersetzung eines technischen Systems festzulegen. Eine große Vielfalt solcher Modelle ist in letzter Zeit in der Literatur zu finden. Ziel dieser Arbeit ist es, einen einheitlichen Zugang zu dem Ersetzungsproblem anzugeben, indem dieses Problem als Problem des optimalen Stoppens aufgefaßt wird. Die Verallgemeinerung vorhandener Modelle erlaubt es, eine notwendige Monotoniebedingung abzuschwächen und unterschiedliche Informationsniveaus zu betrachten. An einem Beispiel wird gezeigt, wie sich explizite Lösungen des Ersetzungsproblems gewinnen lassen und wie sich das Informationsniveau auf die optimale Ersetzungsstrategie auswirkt.
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Jensen, U. A general replacement model. ZOR - Methods and Models of Operations Research 34, 423–439 (1990). https://doi.org/10.1007/BF01421549
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DOI: https://doi.org/10.1007/BF01421549