Way Kuo

An annotated overview of system-reliability optimization

This paper provides: an overview of the methods that have been developed since 1977 for solving various reliability optimization problems; applications of these methods to various types of design problems; and heuristics, metaheuristic algorithms, exact methods, reliability-redundancy allocation, multi-objective optimization and assignment of interchangeable components in reliability systems. Like other applications, exact solutions for reliability optimization problems are not necessarily desirable because exact solutions are difficult to obtain, and even when they are available, their utility is marginal. A majority of the work in this area is devoted to developing heuristic and metaheuristic algorithms for solving optimal redundancy-allocation problems.

Recent Advances in Optimal Reliability Allocation

Reliability has become a greater concern in recent years, because high-tech industrial processes with ever increasing levels of sophistication comprise most engineering systems today. To keep pace with this rapidly developing field, this paper provides a broad overview of recent research on reliability optimization problems and their solution methodologies. In particular, we address issues related to: 1) universal generating-function-based optimal multistate system design; 2) percentile life employed as a system performance measure; 3) multiobjective optimization of reliability systems, especially with uncertain component-reliability estimations; and 4) innovation and improvement in traditional reliability optimization problems, such as fault-tolerance mechanism and cold-standby redundancy-involved system design. New developments in optimization techniques are also emphasized in this paper, especially the methods of ant colony optimization and hybrid optimization. We believe that the interesting problems that are reviewed here are deserving of more attention in the literature. To that end, this paper concludes with a discussion of future challenges related to reliability optimization

Determining Component Reliability and Redundancy for Optimum System Reliability

The usual constrained reliability optimization problem is extended to include determining the optimal level of component reliability and the number of redundancies in each stage. With cost, weight, and volume constraints, the problem is one in which the component reliability is a variable, and the optimal trade-off between 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 component reliability level and the number of components used at each stage. The model is illustrated with three general non linear constraints imposed on the system. The Hooke and Jeeves pattern search technique in combination with the heuristic approach by Aggarwal et al, is used to solve the problem. The Hooke and Jeeves pattern search technique is a sequential search routine for maximizing the system reliability, RS (R, X). The argument in the Hooke and Jeeves pattern search is the component reliability, R, which is varied according to exploratory moves and pattern moves until the maximum of RS (R, X) is obtained. The heuristic approach is applied to each value of the component reliability, R, to obtain the optimal number of redundancies, X, which maximizes RS (R, X) for the stated R.

Reliability optimization of coherent systems

This paper presents a search method based on lexicographic order, and an upper bound on the objective function, for solving redundancy allocation problems in coherent systems. Such problems generally belong to the class of nonlinear integer programming problems with separable constraints and nondecreasing functions. For illustration, 3 types of problems are solved using our method. Numerical investigation shows the performance of the method for large problems.

Optimal allocation of minimal & perfect repairs under resource constraints

The effect of a repair of a complex system can usually be approximated by the following two types: minimal repair for which the system is restored to its functioning state with minimum effort, or perfect repair for which the system is replaced or repaired to a good-as-new state. When both types of repair are possible, an important problem is to determine the repair policy; that is, the type of repair which should be carried out after a failure. In this paper, an optimal allocation problem is studied for a monotonic failure rate repairable system under some resource constraints. In the first model, the numbers of minimal & perfect repairs are fixed, and the optimal repair policy maximizing the expected system lifetime is studied. In the second model, the total amount of repair resource is fixed, and the costs of each minimal & perfect repair are assumed to be known. The optimal allocation algorithm is derived in this case. Two numerical examples are shown to illustrate the procedures.

Reliability for Sparsely Connected Consecutive-

We introduce the system of consecutive failures with sparse d which is a natural extension of consecutive-k systems. Then a series of generalizations of consecutive-k systems are discussed, such as consecutive-k-out-n:F systems with sparse d, M consecutive-k-out-of-n:F systems with sparse d, and (n, f, k) :F systems with sparse d. We present the formulation for the system reliability of these generalized consecutive-k systems with various component settings in terms of the finite Markov chain imbedding idea, along with two numerical examples.

k

A tree heuristic is presented for solving the general redundancy allocation problem in reliability optimization. The tree heuristic can obtain several local optima by branching off the main searching path when some criterions are satisfied. Then, the best local optima is selected for the final solution. The tree heuristic is a simple, efficient, iterative heuristic for any integer nonlinear programming problems with increasing constraint functions. Iterative heuristics are normally trapped in a local optimum. However, the tree heuristic can overcome local optima by branching the solution path. The experiments show that the proposed heuristic is very efficient in terms of solution quality, and computation time.

Systems

A system of N statistically identical machines is modeled using renewal theory through a unique architecture and state space. The model is very useful in evaluating flexible manufacturing systems (FMS) in particular. Each machine consists of multiple part types that are subject to individual failure. A multiple stage repair process composed of integrable sojourn time distributions requires access to spare parts to repair down machines. A performability measure is used to gauge system effectiveness for this partially degradable system, and an example is given.

Multi-path heuristic for redundancy allocation: the tree heuristic

System burn-in can get rid of many residual defects left from component and subsystem burn-in since incompatibility exists not only among components but also among different subsystems and at the system level. Even if system, subsystem, and component burn-in are performed, the system reliability often does not achieve the requirement. In this case, redundancy is a good way to increase system reliability when improving component reliability is expensive. This paper proposes a nonlinear model to: estimate the optimal burn-in times for all levels, and determine the optimal amount of redundancy for each subsystem. For illustration, a bridge system configuration is considered; however, the model can be easily applied to other system configurations. Since there are few studies on system, subsystem, and component incompatibility, reasonable values are assigned for the compatibility factors at each level. >

Performability of systems based on renewal process models

This paper is split into three sections. In section 1, Kuo believes that incompatibility exists among components and can justify an interdependence of component unreliability and system size. In section 2, Fu and Lou show how to compute the reliability of C(k,n) through a numerical example and use of a given theorem. In section 3, Hwang further elaborates his concerns. >