یک طرح برای تعمیر و نگهداری پیش گویانه

An operating system contains a replaceable unit whose wear (i.e. accumulated amount of damage) can be observed over time. When the wear reaches a certain level the unit is no longer able to function satisfactorily and needs to be replaced. Although units are produced to the same nominal specification there is still some random variation among them in their wear rates. This will be expressed by incorporating a random effect, or frailty term, in the model for individual degradation. There are costs for observing the wear on a unit, for replacing a unit, and for allowing a unit to fail before being replaced. When the last cost is comparatively large replacement before failure is preferable. For some standard examples of wear processes the lifetime distributions are obtained and the cost consequences of particular maintenance schemes are investigated.

The scheme investigated in this paper is fairly basic but the calculations can be quite involved and the computations can be quite demanding. Elaborations naturally suggest themselves, such as making a second inspection at or before time R instead of automatic replacement. The analysis of such schemes will follow the lines of the present one, but with more complicated expressions to evaluate. Although the focus has been on deriving analytic expressions in the present paper, simulation will be a useful general tool for such problems. We have assumed throughout that the various parameters and distributions are known. This will be the case when sufficient experience of the behaviour of the units has been accumulated. In principle, the extra layer of uncertainty of having these estimated from development data could be accommodated, but at the cost of substantially increased computational complexity. We have defined the future replacement time in terms of the estimated time at which the wear will reach a specified level, yC. Clearly, there are alternative definitions. One such is to equate P(T > R∣Y1 = y1) to a specified value of α; the closer α is to 1, the less likely a premature failure. This requires calculations analogous to those above. Finally, the calculations here demonstrate, as others have done, that condition-based maintenance schemes can offer very substantial cost savings over simple age-replacement and failure-replacement policies. It should also be noted that the expected cost per unit time varies rather slowly with respect to t1 and yC in the region of the minimum. Consequently, one can be flexible in the choice of inspection time, making such condition-based schemes more convenient to implement.