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A cost relationship between age and block replacement policies
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- Journal:
- Journal of Applied Probability / Volume 25 / Issue 4 / December 1988
- Published online by Cambridge University Press:
- 14 July 2016, pp. 789-796
- Print publication:
- December 1988
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- Article
- Export citation
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The general cost structure of a unit on line is assumed to be governed by a stochastic process
, where R(t) denotes the operating cost on [0, t)and ζ denotes the time of an unscheduled (or unplanned) replacement by a new unit at a cost c1. For an age replacement maintenance policy, scheduled (or planned) replacements occur whenever an operating unit reaches age T, whereas in the block replacement case, scheduled replacements occur every T units of time. Such scheduled replacements cost c2. The expected long-run cost per unit time can then be expressed in the form A(T)/Ε [min(ζ, T)] and B(T)/T respectively. Our main result shows that 
where U is the associated renewal function generated by ζ.
, where 
where 