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

[1]  V. K. Koumousis,et al.  Competitive genetic algorithms with application to reliability optimal design , 2003 .

[2]  HsiangLEE,et al.  COMPARISON OF MAX—MIN APPROACH AND NN METHOD FOR RELIABILITY OPTIMIZATION OF SERIES—PARALLEL SYSTEM , 2003 .

[3]  G. Levitin,et al.  Multi-state system reliabilit y , 2003 .

[4]  Mitsuo Gen,et al.  A Method of Fuzzy Multi-objective Nonlinear Programming with GUB Structure by Hybrid Genetic Algorithm , 2003 .

[5]  Lirong Cui,et al.  Optimal allocation of minimal & perfect repairs under resource constraints , 2004, IEEE Transactions on Reliability.

[6]  Kondo Hloindo Adjallah,et al.  Availability allocation to repairable systems with genetic algorithms: a multi-objective formulation , 2003, Reliab. Eng. Syst. Saf..

[7]  Hong Seo Ryoo.  Robust Metaheuristic Algorithm for Redundancy Optimization in Large-Scale Complex Systems , 2005, Ann. Oper. Res..

[8]  Way Kuo,et al.  An annotated overview of system-reliability optimization , 2000, IEEE Trans. Reliab..

[9]  Baoding Liu,et al.  Redundancy optimization problems with uncertainty of combining randomness and fuzziness , 2004, Eur. J. Oper. Res..

[10]  Gregory Levitin,et al.  Optimal multilevel protection in series-parallel systems , 2003, Reliab. Eng. Syst. Saf..

[11]  Chung-Chi Hsieh,et al.  Reliability and cost optimization in distributed computing systems , 2003, Comput. Oper. Res..

[12]  Yash P. Aneja,et al.  Minimal-cost system reliability with discrete-choice sets for components , 2004, IEEE Transactions on Reliability.

[13]  Mitsuo Gen,et al.  Reliability optimal design problem with interval coefficients using hybrid genetic algorithms , 1998 .

[14]  Baoding Liu,et al.  Stochastic programming models for general redundancy-optimization problems , 2003, IEEE Trans. Reliab..

[15]  K. O. Kim,et al.  Optimal allocation of s-identical, multi-functional spares in a series system , 1999 .

[16]  Mitsuo Gen,et al.  Reliability Optimization Design for Complex Systems by Hybrid GA with Fuzzy Logic Control and Local Search , 2002, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[17]  Gregory Levitin.  Consecutive k-out-of-r-from-n system with multiple failure criteria , 2004, IEEE Transactions on Reliability.

[18]  Way Kuo,et al.  Reliability optimization of coherent systems , 2000, IEEE Trans. Reliab..

[19]  Mustapha Nourelfath,et al.  Ant system for reliability optimization of a series system with multiple-choice and budget constraints , 2005, Reliab. Eng. Syst. Saf..

[20]  Hoang Pham,et al.  Weighted voting systems , 1999 .

[21]  Yi-Chih Hsieh,et al.  A linear approximation for redundant reliability problems with multiple component choices , 2003 .

[22]  Gregory Levitin,et al.  Survivability maximization for vulnerable multi-state systems with bridge topology , 2000, Reliab. Eng. Syst. Saf..

[23]  Way Kuo,et al.  Structure importance of consecutive-k-out-of-n systems , 1999, Oper. Res. Lett..

[24]  Alice E. Smith,et al.  Optimal Design of Reliable Computer Networks: A Comparison of Metaheuristics , 2003, J. Heuristics.

[25]  Ming Jian Zuo,et al.  Generalized multi-state k-out-of-n: G systems , 2000, IEEE Trans. Reliab..

[26]  Gregory Levitin,et al.  Optimal separation of elements in vulnerable multi-state systems , 2001, Reliab. Eng. Syst. Saf..

[27]  David W. Coit,et al.  Maximization of System Reliability with a Choice of Redundancy Strategies , 2003 .

[28]  Gregory Levitin,et al.  Reliability optimization for weighted voting system , 2001, Reliab. Eng. Syst. Saf..

[29]  Chengbin Chu,et al.  A new dynamic programming method for reliability & redundancy allocation in a parallel-series system , 2005, IEEE Transactions on Reliability.

[30]  Gregory Levitin,et al.  A new approach to solving problems of multi‐state system reliability optimization , 2001 .

[31]  Mitsuo Gen,et al.  Reliability optimization design using hybrid NN-GA with fuzzy logic controller , 2001 .

[32]  Hoang Pham,et al.  Optimal design of k-out-of-n:G subsystems subjected to imperfect fault-coverage , 2004, IEEE Transactions on Reliability.

[33]  D. Coit.  Cold-standby redundancy optimization for nonrepairable systems , 2001 .

[34]  Gregory Levitin,et al.  Structure optimization of multi-state system with time redundancy , 2000, Reliab. Eng. Syst. Saf..

[35]  Samuel Kotz,et al.  On the Effect of Redundancy for Systems with Dependent Components , 2003 .

[36]  Kyungmee O. Kim,et al.  Maximization of a percentile life of a series system through component redundancy allocation , 2001 .

[37]  Stephen Wolfram,et al.  Cellular automata as models of complexity , 1984, Nature.

[38]  A. J. Miller,et al.  A cellular evolutionary approach applied to reliability optimization of complex systems , 2000, Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (Cat. No.00CH37055).

[39]  Luca Podofillini,et al.  Optimal design of reliable network systems in presence of uncertainty , 2005, IEEE Transactions on Reliability.

[40]  Michał Kleiber,et al.  Study on discrete optimization techniques in reliability-based optimization of truss structures , 2001 .

[41]  Mohamed Djerdjour,et al.  An enumerative algorithm framework for a class of nonlinear integer programming problems , 1997 .

[42]  Tongdan Jin,et al.  Variance of system-reliability estimates with arbitrarily repeated components , 2001, IEEE Trans. Reliab..

[43]  Gregory Levitin,et al.  Optimizing survivability of vulnerable series-parallel multi-state systems , 2003, Reliab. Eng. Syst. Saf..

[44]  Luca Podofillini,et al.  Optimal reliability/availability of uncertain systems via multi-objective genetic algorithms , 2004, IEEE Transactions on Reliability.

[45]  D. Elmakis,et al.  Redundancy optimization for series-parallel multi-state systems , 1998 .

[46]  Corso Elvezia,et al.  Ant colonies for the traveling salesman problem , 1997 .

[47]  K. B. Misra,et al.  On Optimal Reliability Design: A Review , 1975 .

[48]  Gregory Levitin,et al.  Optimizing survivability of multi-state systems with multi-level protection by multi-processor genetic algorithm , 2003, Reliab. Eng. Syst. Saf..

[49]  Gregory Levitin,et al.  Evaluating correct classification probability for weighted voting classifiers with plurality voting , 2002, Eur. J. Oper. Res..

[50]  Suprasad V. Amari,et al.  Optimal reliability of systems subject to imperfect fault-coverage , 1999 .

[51]  Maw-Sheng Chern,et al.  On the computational complexity of reliability redundancy allocation in a series system , 1992, Oper. Res. Lett..

[52]  Peter Xiaoping Liu,et al.  Using neural network function approximation for optimal design of continuous-state parallel-series systems , 2003, Comput. Oper. Res..

[53]  Hans-Jürgen Zimmermann,et al.  Fuzzy global optimization of complex system reliability , 2000, IEEE Trans. Fuzzy Syst..

[54]  C. S. Sung,et al.  Reliability optimization of a series system with multiple-choice and budget constraints , 2000, Eur. J. Oper. Res..

[55]  Joon-Eon Yang,et al.  Application of genetic algorithm for reliability allocation in nuclear power plants , 1999 .

[56]  Gregory Levitin,et al.  Optimal allocation of multi-state retransmitters in acyclic transmission networks , 2002, Reliab. Eng. Syst. Saf..

[57]  Kyungmee O. Kim,et al.  Percentile Life and Reliability As Performance Measures in Optimal System Design , 2003 .

[58]  M. Zuo,et al.  Optimal Reliability Modeling: Principles and Applications , 2002 .

[59]  Enrico Zio,et al.  System design optimization by genetic algorithms , 2000, Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (Cat. No.00CH37055).

[60]  Elias P. Zafiropoulos,et al.  Reliability and cost optimization of electronic devices considering the component failure rate uncertainty , 2004, Reliab. Eng. Syst. Saf..

[61]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[62]  Alice E. Smith,et al.  An ant colony optimization algorithm for the redundancy allocation problem (RAP) , 2004, IEEE Transactions on Reliability.

[63]  Way Kuo,et al.  Multi-Path Approach for Reliability-Redundancy Allocation Using a Scaling Method , 2005, J. Heuristics.

[64]  Yves Dutuit,et al.  A combined approach to solve the redundancy optimization problem for multi-state systems under repair policies , 2004, Reliab. Eng. Syst. Saf..

[65]  Chung-Chi Hsieh.  Optimal task allocation and hardware redundancy policies in distributed computing systems , 2003, Eur. J. Oper. Res..

[66]  David W. Coit,et al.  Reliability optimization of series-parallel systems using a genetic algorithm , 1996, IEEE Trans. Reliab..

[67]  Gregory Levitin.  Reliability evaluation for acyclic transmission networks of multi-state elements with delays , 2003, IEEE Trans. Reliab..

[68]  Ta-Cheng Chen,et al.  An efficient heuristic for series-parallel redundant reliability problems , 2005, Comput. Oper. Res..

[69]  Jezdimir Knezevic,et al.  Availability based spare optimization using renewal process , 1998 .

[70]  Way Kuo,et al.  Reliability redundancy allocation: An improved realization for nonconvex nonlinear programming problems , 2006, Eur. J. Oper. Res..

[71]  Gregory Levitin,et al.  Optimal allocation of multistate elements in a linear consecutively-connected system , 2003, IEEE Trans. Reliab..

[72]  Yansong Ren,et al.  Design of reliable systems using static and dynamic fault trees , 1998 .

[73]  Y. Hsieh,et al.  Genetic algorithms for reliability design problems , 1998 .

[74]  Vanderlei da Costa Bueno,et al.  Minimal standby redundancy allocation in a k , 2005, Eur. J. Oper. Res..

[75]  G. Levitin,et al.  Structure optimization of power system with bridge topology , 1998 .

[76]  B. Suman.  Simulated annealing-based multiobjective algorithms and their application for system reliability , 2003 .

[77]  Chengbin Chu,et al.  Reliability allocation through cost minimization , 2003, IEEE Trans. Reliab..

[78]  Gregory Levitin.  Reliability of multi-state systems with two failure-modes , 2003, IEEE Trans. Reliab..

[79]  Mitsuo Gen,et al.  Reliability Optimization Design Using a Hybridized Genetic Algorithm with a Neural-Network Technique , 2001 .

[80]  John D. Andrews,et al.  A branching search approach to safety system design optimisation , 2005, Reliab. Eng. Syst. Saf..

[81]  S. P. Levitan,et al.  Reliability optimization models for embedded systems with multiple applications , 2004, IEEE Transactions on Reliability.

[82]  Gregory Levitin,et al.  Reliability evaluation for acyclic consecutively connected networks with multistate elements , 2001, Reliab. Eng. Syst. Saf..

[83]  Michael R. Lyu,et al.  Optimal allocation of test resources for software reliability growth modeling in software development , 2002, IEEE Trans. Reliab..

[84]  Gregory Levitin,et al.  Optimal structure of fault-tolerant software systems , 2005, Reliab. Eng. Syst. Saf..

[85]  Kamel Rekab,et al.  A branch and bound algorithm for designing reliable systems at a minimum cost , 2001, Appl. Math. Comput..

[86]  E. Polak,et al.  Reliability-based optimal design using sample average approximations , 2004 .

[87]  N. Sancho,et al.  A hybrid ‘dynamic programming/depth-first search’ algorithm, with an application to redundancy allocation , 2001 .

[88]  Way Kuo,et al.  Reliability Optimization with the Lagrange-Multiplier and Branch-and-Bound Technique , 1987, IEEE Transactions on Reliability.

[89]  Alice E. Smith,et al.  Redundancy allocation to maximize a lower percentile of the system time-to-failure distribution , 1998 .

[90]  Way Kuo,et al.  A Note on Heuristic Methods in Optimal System Reliability , 1978, IEEE Transactions on Reliability.

[91]  Takeaki Taguchi,et al.  Optimal design problem of system reliability with interval coefficient using improved genetic algorithms , 1999 .

[92]  Gregory Levitin,et al.  Importance and sensitivity analysis of multi-state systems using the universal generating function method , 1999 .

[93]  Alice E. Smith,et al.  Efficiently Solving the Redundancy Allocation Problem Using Tabu Search , 2003 .

[94]  C. Hwang,et al.  Optimization Techniques for System Reliability with RedundancyߞA Review , 1977, IEEE Transactions on Reliability.

[95]  M. Raghavachari,et al.  Optimal allocation of interchangeable components in a series-parallel system , 1998 .

[96]  Ta-Cheng Chen,et al.  Immune algorithms-based approach for redundant reliability problems with multiple component choices , 2005, Comput. Ind..

[97]  Gregory Levitin,et al.  A universal generating function approach for the analysis of multi-state systems with dependent elements , 2004, Reliab. Eng. Syst. Saf..

[98]  V. K. Jayaraman,et al.  Ant algorithm for single and multiobjective reliability optimization problems , 2002 .

[99]  Manuel López-Ibáñez,et al.  Ant colony optimization , 2010, GECCO '10.

[100]  Gregory Levitin,et al.  Optimal series-parallel topology of multi-state system with two failure modes , 2002, Reliab. Eng. Syst. Saf..

[101]  Way Kuo,et al.  Reliability, Yield, And Stress Burn-In , 1998 .

[102]  David W. Coit,et al.  Redundancy allocation for series-parallel systems using a max-min approach , 2004 .

[103]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[104]  Gregory Levitin,et al.  Optimal allocation of multi-state elements in linear consecutively connected systems with vulnerable nodes , 2003, Eur. J. Oper. Res..

[105]  Chengbin Chu,et al.  Reliability allocation problem in a series-parallel system , 2005, Reliab. Eng. Syst. Saf..

[106]  Tongdan Jin,et al.  System optimization with component reliability estimation uncertainty: a multi-criteria approach , 2004, IEEE Transactions on Reliability.

[107]  Vadlamani Ravi.  Optimization of Complex System Reliability by a Modified Great Deluge Algorithm , 2004, Asia Pac. J. Oper. Res..

[108]  Gregory Levitin,et al.  Linear multi-state sliding-window systems , 2003, IEEE Trans. Reliab..

[109]  G. Levitin,et al.  Structure optimization of multi-state system with two failure modes , 2001, Reliab. Eng. Syst. Saf..

[110]  Gregory Levitin.  Redundancy optimization for multi-state system with fixed resource-requirements and unreliable sources , 2001, IEEE Trans. Reliab..

[111]  M. Dorigo,et al.  The Ant Colony Optimization MetaHeuristic 1 , 1999 .

[112]  Sung Chang Sup,et al.  Branch-and-bound redundancy optimization for a series system with multiple-choice constraints , 1999 .

[113]  Gregory Levitin,et al.  Uneven allocation of elements in linear multi-state sliding window system , 2005, Eur. J. Oper. Res..

[114]  Krishna B. Misra,et al.  An algorithm to solve integer programming problems: An efficient tool for reliability design , 1991 .

[115]  Way Kuo,et al.  Multi-path heuristic for redundancy allocation: the tree heuristic , 2006, IEEE Transactions on Reliability.

[116]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[117]  Won Young Yun,et al.  Multi-level redundancy optimization in series systems , 2004, Comput. Ind. Eng..

[118]  David W. Coit,et al.  A heuristic for solving the redundancy allocation problem for multi-state series-parallel systems , 2004, Reliab. Eng. Syst. Saf..

[119]  Enrico Zio,et al.  Multiobjective optimization by genetic algorithms: application to safety systems , 2001, Reliab. Eng. Syst. Saf..

[120]  David W. Coit,et al.  Genetic algorithm to maximize a lower-bound for system time-to-failure with uncertain component Weibull parameters , 2002 .

[121]  Gregory Levitin,et al.  Joint redundancy and maintenance optimization for multistate series–parallel systems , 1999 .

[122]  Mitsuo Gen,et al.  Fuzzy multiple objective optimal system design by hybrid genetic algorithm , 2003, Appl. Soft Comput..

[123]  Y. Massim,et al.  Optimal Design and Reliability Evaluation of Multi-State Series-Parallel Power Systems , 2005 .

[124]  Way Kuo,et al.  Reliability Importance and Invariant Optimal Allocation , 2002, J. Heuristics.

[125]  Yuji Nakagawa,et al.  Surrogate Constraints Algorithm for Reliability Optimization Problems with Two Constraints , 1981, IEEE Transactions on Reliability.

[126]  Mitsuo Gen,et al.  GA-based reliability design: state-of-the-art survey , 1999 .

[127]  E. Polak,et al.  Reliability-Based Optimal Design of Series Structural Systems , 2001 .

[128]  José E. Valdés,et al.  Active-redundancy allocation in systems , 2004, IEEE Transactions on Reliability.

[129]  A. Saidane,et al.  Optimal Reliability Design: Fundamentals and Applications , 2001 .

[130]  Gregory Levitin,et al.  Optimal allocation of elements in a linear multi-state sliding window system , 2002, Reliab. Eng. Syst. Saf..

[131]  Gregory Levitin.  Reliability and performance analysis of hardware-software systems with fault-tolerant software components , 2006, Reliab. Eng. Syst. Saf..