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MIL-HDBK-338B SECTION 5: RELIABILITY/MAINTAINABILITY/AVAILABILITY THEORY 5.6.2.4 Exponential Approximation In general, the repair time density function is lognormally distributed. In practice, however, the standard deviation of the logarithms of repair times (o///Mct) is not usually known and must be estimated in order to compute the probability of repair for any value of repair time. A value of G = 0.55 has been suggested by some prediction procedures, based on maintenance experience data accumulated on equipment. In the absence of justifiable estimates of G, it is practicable to use the exponential distribution as an approximation of the lognormal. Figure 5.6-6 compares the exponential function with several lognormal functions of different standard deviations. All functions in the figure are normalized to a common Mct at M ctj/ Met = 1.0. The exponential approximation is, in general, conservative over the region shown. Probability of repair in time t in the exponential case is given by M(t) - 1 - e_t/ M ct = l - e"M-t where: M(t) = probability of repair in a specified time t M = known mean corrective maintenance time This approximation will be used in the next section on availability theory because it allows for a relatively simple description of the basic concepts without becoming overwhelmed by the mathematics involved. 5.7 Availability Theory The concept of availability was originally developed for repairable systems that are required to operate continuously, i.e., round the clock, and are at any random point in time either operating or "down" because of failure and are being worked upon so as to restore their operation in minimum time. In this original concept a system is considered to be in only two possible states -operating or in repair - and availability is defined as the probability that a system is operating satisfactorily at any random point in time t, when subject to a sequence of "up" and "down" cycles which constitute an alternating renewal process (Ref. [35]). In other words, availability is a combination of reliability and maintainability parameters. 5-70

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