Two types of preventive maintenance policies are considered. A policy is defined to be optimum if it maximizes “limiting efficiency,” i.e., fractional amount of up-time over long intervals. Elementary renewal theory is used to obtain optimum policies. The optimum policies are determined, in each case, as unique solutions of certain integral equations depending on the failure distribution. It is shown that both solutions are also minimum cost solutions when the proper identifications are made. The two optimum policies are compared under certain restrictions.

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This paper considers an electronic system that upon failure is repaired Only two states—the “on” state and the “off” state—are distinguished. The time-to-failure and the time-to-repair are random variables with general distribution functions. The purpose of the paper is to make available, in single unified treatment, mathematical information that is relevant for a reliability analysis of a one-unit system. The following questions are answered (a) What is the probability that the system will be on at any given time t? (b) What is the probability that it will be on t hours or more during a given time interval (0, T)? (c) What is the expected fractional amount of time that it will be on during (0, T)? (d) What is the probability distribution of the number of failures during a given time interval? (e) What is the expected number of failures during a given time interval?. In particular, it is noted that “down” time is approximately normally distributed for large time intervals. The special cases of exponential failure with exponential and constant repair are given as examples.

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