Preventive maintenance and the interval availability distribution of an unreliable production system

Traditionally, the optimal preventive maintenance interval for an unreliable production system has been determined by maximizing its limiting availability. Nowadays, it is widely recognized that this performance measure does not always provide relevant information for practical purposes. This is particularly true for order-driven manufacturing systems, in which due date performance has become a more important, and even a competitive factor. Under these circumstances, the so-called interval availability distribution is often seen as a more appropriate performance measure. Surprisingly enough, the relation between preventive maintenance and interval availability has received little attention in the existing literature. In this article, a series of mathematical models and optimization techniques is presented, with which the optimal preventive maintenance interval can be determined from an interval availability point of view, rather than from a limiting availability perspective. Computational results for a class of representative test problems indicate that significant improvements of up to 30% in the guaranteed interval availability can be obtained, by increasing preventive maintenance frequencies somewhere between 10 and 70%

On a number theoretic property of optimal maintenance grouping

In this paper we consider the problem of preventive maintenance of a failure prone system, for which a number of maintenance actions has to be executed on a regular basis. For each action i the frequency is prescribed. Between consecutive actions of type i there is an integer interspacing of T(i) time units. The set-up costs are activity dependent. The set-up structure is supposed to be tree-like and additive over the set-up nodes involved in the action or group of actions. Hence, for different activities with common setup nodes joint execution leads to set-up costs reduction. The question is how the actions should be arranged in time in order to exploit this set-up costs reduction effect maximally. It is shown that the time averaged set-up costs are minimal if a main peak clustering property is satisfied: all maintenance actions are combined at one moment in time. Intuitively, this property is appealing, but it asks for some interesting and non-trivial applications of number theory and inductive reasoning, to prove it