the number of redundancies but also the reliability of each Ching-Lai Hwang component. This is a mixed integer nonlinear programming Way Kuo problem.
In general, problems of this type are difficult to solve by the normal system optimization techniques, for example, Key Words-Optimum system reliability, Mixed integer pro- Lagrange multipliers [3], sequential unconstrained minimi- gramming, Redundancy.
zation technique (SUMT), or generalized reduced gradient ReaderAids-technique [7] because these techniques do not provide integer Purpose: Widen state of the art solutions. The available integer programming techniques do Special math needed for explanations & results: Probability, Optimiza-not guarantee an optimal solution. Hence a technique that tion techniques provides an integer solution as well as the optimal level of Results useful to: Reliability theoreticians component reliability is required. The suggested procedure is Abstract-The usual constrained reliability optimization problem one such technique.
is extended to include determining the optimal level of component A series system with active component redundancy is con- reliability and the number of redundancies in each stage. With cost, sidered in this study. A combination of the well-known weight, and volume constraints, the problem is one in which the com- Hooke and Jeeves pattern search [2] and the suggested ponent reliability is a variable, and the optimal trade-off between heuristic approach by Aggarwal et al., [1] is proposed as a adding components and improving individual component reliability is determined. This is a mixed integer nonlinear programming problem in which the system reliability is to be maximized as a function of com-procedure is simple and efficient; a component reliability is ponent reliability level and the number of components used at each assumed and the optimal number of redundancies is determined stage. The model is illustrated with three general non linear constraints by the heuristic technique. A sequential search routine for imposed on the system. The Hooke and Jeeves pattern search tech-maximizing the overall system reliability is carried out by nique in combination with the heuristic approach by Aggarwal et al, is using the Hooke and Jeeves pattern search.
used to solve the problem. The Hooke and Jeeves pattern search tech- nique is a sequential search routine for maximizing the system reliability, RS(R, X). The argument in the Hooke and Jeeves pattern search is the Notation component reliability, R, which is varied according to exploratory 'kn ee a rs c pm se n [6] F.A. Tiliman, C.L. Hwang, L.T. Fan, S.A. Balbale, "Systems re- Hooke and Jeeves pattern search optimizes the component liability subject to multiple nonlinear constraints", IEEE Trans.
reliability level. This procedure seems to be very efficient in