This paper considers a 2-dissimilar unit warm standby system. The failure rates are constant but the repair rates need not be constant. We shall say that a major breakdown occurs in the system when both unit fail. The system fails if one unit under repair is not repaired within a fixed time measured from the instant at which major breakdown occurs, or if the number of major breakdowns during the mission period exceeds a fixed number. As a special case, this number is allowed to be infinite". The Laplace transform of the reliability and the mean time to system failure (MTSF) are derived. The special case of constant failure and repair rates is treated. We present the asymptotic results which describe the performance of system with short mean repair time. Also the case when allowed down time is negligible, compared to the mission time, is discussed.

Optimum inspection schedule is discussed to maximize the availability for a two-unit parallel redundant system when a failure of unit is detected only by actual inspection. The stationary availability is derived by applying Piecewise Markov Process under the assumption that a failure distribution is exponential and other distributions are arbitrary.

In this paper we derive several results on the dependent 2-unit system with single repair facility. The dependency means that it is allowed for the two units to fail at the same time. First, for the dependent 2-unit warm standby system, we obtain the following results: Laplace transform of the system reliability by using the conditional transform, limit theorems for the system reliability and mean time to the system failure (MTSF), distribution of the number of repairs completed during (0, t] and Laplace transform of the system reliability and MTSF in the case that the repair facility is capable of only n repairs. Second we discuss on the effects of repair policies to the availability of the dependent 2-unit hot standby system.