Abstract
This paper tries to trace our research history briefly from Barlow and Proschan to attain general replacement models. We begin with a random age replacement policy that is planned at a random time Y and call it as random replacement. When the distribution of Y becomes a degenerate distribution placing unit mass at T, age replacement is formulated. We obtain the general formulas for optimum replacement times. We next suppose the unit works for a job with random works, and replacement policies with N cycles are discussed. As follows, we combine age and random replacement models and discuss replacement first, replacement last, replacement overtime, replacement overtime first and replacement overtime last. By formulating the distributions of replacement times with n variables, general replacement models with n replacement times are obtained.
Highlights
Most basic model in maintenance theory is age replacement, in which we plan to replace an operating unit before failure at an optimum time T∗ to minimize the expected replacement cost rate
Our objective is to find optimum preventive replacement times to minimize the expected cost rates
The so called replacement that is planned at time T and random replacement planned at random time Y have been introduced
Summary
Most basic model in maintenance theory is age replacement, in which we plan to replace an operating unit before failure at an optimum time T∗ to minimize the expected replacement cost rate. 3. Age and Random Replacement Models Suppose that an operating unit is replaced at a random time Y(0 < Y ≤ ∞) or at failure, whichever occurs first. Suppose the unit is replaced at time T or at failure, whichever occurs first We call this policy as age replacement, and the expected cost rate is. Suppose that the unit is replaced at cycle N or at failure, whichever occurs first We call this policy as random replacement, and the expected cost rate is (Nakagawa, 2014). Optimum policy to minimize CF(T, N) is (TF∗ = T∗, NF∗ = ∞), where T∗ is given in (3) This shows that when the costs of preventive replacement are the equal, age replacement is more economical than the random policy.
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