Optimal replacement of improving and deteriorating repairablesystems

System improvement and deterioration are defined in terms of partial orderings between life distributions. The effects of ageing of `the distribution of time to first failure' on improvement and deterioration of a repairable system subject to minimal repairs, are investigated. Under various types of life distributions we derive explicitly the times at which the system should be condemned (replaced by a new one) to minimize the total cost of maintenance and replacement in terms of parameters of the distribution and of the cost function