The Use of Lac-rangian Multipliers for Optimum Reliability Allocation

Research Perfoxnned by Robert Davison Under The Supervision of Pr, *<« J« HoHlchols —»■—«— II I II ■ IIH I III« I I! Ill« This paper develops a method to allocate reliability to system elements where a system reliability requirement must be met or a total cost constraint is imposed« Parallel and serially arranged elements are considered with each element's probability density function of time to failure being approximated by the two parameter Weibull distribution. The problem is approached as a minimization of total system cost or system unreliability and Lagrange multipliers prove to be useful as a solution technique, A cost function is developed to relate the cost of and element to the reliability level achieved in that element. Both the elements cost function and reliability expression must be continuous variables. Numerical examples are shown for each allocation model«