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9 Reliability

9 Reliability - 1 Reliability Problem Consider a prototype...

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1 Reliability Problem Consider a prototype reliability problem where n components in series define the reliability of a system. It is possible to install multiple units of a given component which results in a corresponding increase in that component's reliability. The problem then is to determine how many units of each of the n components should be installed so as to maximize the total system reliability subject to a budget constraint. Component reliability is given by a matrix of reliability's as a function of the number of units of each component (limited to m ). In addition, we have a cost matrix which has arguments of the component and number of units assigned by component. The problem is to maximize the reliability subject to a budget constraint. The mathematical formulation of this problem is: max R = r [ i , x i ] i = 1 n subject to c i = 1 n [ i , x i ] t x i {1 , " , m }, for i {1, " , n }, where r [ i,j ] and c [ i,j ] are the reliability and the cost, respectively, of j units of component i and t is the total budget available to allocate among the n components. The bracket notation is used here since we are defining these data via matrices as opposed to general functions.

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9 Reliability - 1 Reliability Problem Consider a prototype...

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