A well known preventive replacement policy is the block replacement policy (BRP). In such a policy the item undergoes a planned replacement at a sequence of equally spaced time points independent of failure history. The main advantage of a BRP i s its simplicity, because under this policy it is unnecessary to keep detailed records about times of failures or ages of items. The main drawback of a BRP is that at planned replacement times we may be replacing practically new items. In this paper we study a modified BRP which is free of this drawback. We calculate the expected cost of following a modified BRP for lifetime distributions possessing a special structure and illustrate it for the case of an Erlang distribution.A numerical comparison is made between a modified BRP and a standard BRP for the special case of a two stage Erlang distribution.
A broad class of production-inventory systems is studied in which a number of producing machines are susceptible to failure following which they must be repaired to make them operative again. The machines' production can also be stopped deliberately due to stocking capacity limitations or any other relevant considerations. The interplay between the processes involved, namely, production, demand, and failure/repair or reliability, in conjunction with the shutdown policy used, determine the inventory accumulation process and possible shortages. We first obtain the stationary distribution of the inventory process for different assumptions on the random behavior of the production, demand, and reliability processes. By employing level-crossing techniques, a mathematical analysis is carried out for a “core” model, which then serves the role of the nucleus for the study of a wide range of models. We compute performance measures that characterize the operation of the production-inventory system with respect to its service-level to customers, expected inventory stocked, machines' utilization, repairmen utilization, and so on. A numerical illustration is provided which shows the effect of machine breakdowns on service and inventory levels.
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