TABLE OF CONTENTS In the ordinary block replacement policy (OBRP), a unit is replaced at predetermined time intervals k T p ( k = 1, 2, 3, ), and at failure by a new one with an identical times-to-failure distribution. The total preventive maintenance cost for a period T p, or for one replacement period only, for the OBRP, is given by
where
| C p = | planned replacement cost, |
| C c = | corrective, or failure, replacement cost, |
and
| H o ( T p) = | expected, or mean, number of failures in a period (0, T p), |
defined as the ordinary renewal function (ORF) [1, pp. 45-46]. By definition of an ORF
where
and
f(T) is the times-to-failure pdf of the unit. Assuming an infinite time span, or life, of the equipment, the average cost per unit time of operation is given by
A unit has a gamma times-to-failure pdf with ? = 2 and ? = 200 hr. The unit is preventively maintained under the ordinary block replacement policy. The planned replacement cost is $10. The corrective replacement cost is $50. Find the minimum total preventive cost per unit time of operation for the OBRP and the optimum replacement time.
With ? = 2, the gamma pdf becomes
and its Laplace transform is
The Laplace transform of H o( T) is
or
and...
