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By Craig C. Sherbrooke

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Furthermore, the lower-indenture items, such as computer chips, are more likely to be common items, that is, used in several different “parents”. For these reasons, there is an incentive to stock the lowerindenture items rather than their higher-indenture “parents”. On the other hand, when an item fails, it takes time and expertise to diagnose and replace the lower-indenture items that are responsible. It may take specialized test equipment, and it may require sending the item to the depot or next-higher echelon.

Each point on the optimal system availabilitycost curve corresponds to a set of stockage policies - a stock level for every item. 2 Mean and Variance Let X be a random variable and Pr{X = x} designate the probability that the random variable X takes on a specific value x from some unspecified probability distribution. A requirement for a probability distribution is that Pr{X = x} is non-negative for any x and the sum of probabilities over all x equals one. In this book we shall be concerned primarily with probability distributions where X is a discrete random variable taking on values 0, 1, 2...

If there is only one aircraft or end item, the availability is the percent of time that the aircraft is operational. As in the item measures of performance, we will be interested in the expected value of availability in the steady-state where it does not vary. In Chapter 6 we will consider an application to the space station, where resupply is periodic and availability declines between resupply missions. Even though the availability is different at each time t in the cycle, the availability we calculate for a specific value of t is an expected availability in the sense that it is the percent of cycles where the station is not down for spares at time t.