This paper is a state-of-art review of the literature related to optimal system reliability with redundancy. The literature is classified as follows. Optimal system reliability models with redundancy Series Parallel Series-parallel Parallel-series Standby Complex (nonseries, nonparallel) Optimization techniques for obtaining optimal system configuration Integer programming Dynamic programming Maximum principle Linear programming Geometric programming Sequential unconstrained minimization technique (SUMT) Modified sequential simplex pattern search Lagrange multipliers and Kuhn-Tucker conditions Generalized Lagrangian function Generalized reduced gradient (GRG) Heuristic approaches Parametric approaches Pseudo-Boolean programming Miscellaneous

Optimization Techniques for System Reliability with RedundancyߞA Review

List of Figures. Preface. 1. Introduction. 2. Computation of Reliability. 3. Design of Optimal Consecutive Systems. 4. The Lifetime Distribution. 5. Asymptotic Analysis. 6. Window Systems. 7. The Network Model. 8. Consecutive-2 Graphs. 9. Some Related Systems. 10. Applications. References. Index.

Reliabilities of Consecutive-k Systems

This paper presents a method for finding the terminal-pair reliability expression of a general network. First, the system success function S is found, beginning from the connection matrix for the logic diagram of the network. Second, using the concept of Exclusive operator, S is changed to its equivalent S (disjoint) form, and the reliability expression has been derived. The method has the advantage of not requiring step by step testing for disjointness. Examples illustrate the method.

An Efficient Method for Reliability Evaluation of a General Network

An exact and an approximate method for calculating the probability of occurrence of the output event from priority-AND (sequential) failure logic is given. The approximate method can be used during fault-tree analysis without modification to existing quantitative evaluation techniques. Assumptions made include s-independent, exponentially distributed, non-repairable basic events as input to the priority-AND failure logic.

https://ieeexplore.ieee.org/iel5/24/5220005/05220025.pdf

OntheQuantitative Analysis ofPriority-AND Failure Logic

This paper proposes a modification of the Aggarwal et al. algorithm for reliability optimization by introducing a new heuristic criterion for selecting the subsystem where redundancy is to be added. This criterion accounts for the relative decrement in unreliability versus the largest of the relative increments in resources. The method applies to multiple separable constraint problems (which need not be linear) and to systems which may be complex or series. The method is simple, fast, and easily programmed. The results are compared with those of the Aggarwal et al. algorithm and are better in many problems.

An Improved Algorithm for Reliability Optimization

Purpose: Present a derivation Special math needed for derivations: Probability Special math needed to use the results: Same Results useful to: Reliability theoreticians Summary & Conclusions - A software release problem based on 4 software-reliability growth models (SRGMs) with random lifecycle length is studied. Test of the software system is terminated after time T, and released (sold) to the user at a price. The price of the software system and three cost components are considered and average total profit is used as a criterion. The optimal values of release times are shown to be finite and unique. Hence, the optimal solutions can be obtained numerically by, for example, a bisection method. Numerical example indicates that the optimal releasetime increases as: 1) the error rate in each model decreases, and 2) the difference between the error fiiing cost during test phase and that during operational phase increases. The case of unknown model parameters is considered only for Jelinski-Moranda model because a Bayes model is not available for other SRGMs. The release decision depends on testing time; but other stopping rules, for example, based on number of corrected errors, can be considered.

http://ieeexplore.ieee.org/iel1/24/2019/00055877.pdf

Optimum Software Release Policy with Random Life Cycle

OntheAnalysis ofFault Trees

http://ieeexplore.ieee.org/iel1/24/5924/00229502.pdf

A Sampling Scheme for Estimating the Reliability of a Series System

2.PROBLEMFORMULATIONANDSOLUTION Abstract-An algorithm foroptimumallocation ofredundancies in Notation ageneral system ispresented. Themethodisapplicable toproblems having anynumber ofconstraints which neednotbelinear. Forselect-qj unreliability ofasingle unitofsubsystem-i. ingthesubsystem whereredundancy istobeadded, aheuristic criter-n ionisintroduced which takes into account therelative increment in n reliability versus increments inconstraints. Themethod isapplicable inthecomputation, ni>1I foranysystem configuration where subsystems arecomposed ofidenti-Qi unreliability ofsubsystem-i. calparallel elements. Thealgorithm issimple, requires little computation k total numberofsubsystems. effort, andiseasily programmed foracomputer. Anexample ofanon- QS systemunreliability. series system illustrates theprocedure. s KeyWords-Redundancy, Algorithm, Optimization, Heuristic, Non-gli resource-j consumed insubsystem-i. linear constraints. Agi(ni) increment inresource-j atsubsystem-i forincreasing

Redundancy Optimization inGeneral Systems

Frequency andDuration Concepts inSystem Reliability Evaluation

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