Recent advances in system reliability optimization driven by importance measures

Abstract

System reliability optimization problems have been widely discussed to maximize system reliability with resource constraints. Birnbaum importance is a well-known method for evaluating the effect of component reliability on system reliability. Many importance measures (IMs) are extended for binary, multistate, and continuous systems from different aspects based on the Birnbaum importance. Recently, these IMs have been applied in allocating limited resources to the component to maximize system performance. Therefore, the significance of Birnbaum importance is illustrated from the perspective of probability principle and gradient geometrical sense. Furthermore, the equations of various extended IMs are provided subsequently. The rules for simple optimization problems are summarized to enhance system reliability by using ranking or heuristic methods based on IMs. The importance-based optimization algorithms for complex or large-scale systems are generalized to obtain remarkable solutions by using IM-based local search or simplification methods. Furthermore, a general framework driven by IM is developed to solve optimization problems. Finally, some challenges in system reliability optimization that need to be solved in the future are presented.

Keywords

importance measure / system performance / reliability optimization / optimization rules / optimization algorithms

References

[1] Abouei Ardakan M, Zeinal Hamadani A (2014). Reliability-redundancy allocation problem with cold-standby redundancy strategy. Simulation Modelling Practice and Theory, 42: 107–118

[2] Abouei Ardakan M, Rezvan M T (2018). Multi-objective optimization of reliability-redundancy allocation problem with cold-standby strategy using NSGA-II. Reliability Engineering & System Safety, 172: 225–238

[3] Aliee H, Vitzethum S, Glaß M, Teich J, Borgonovo E (2016). Guiding Genetic Algorithms using importance measures for reliable design of embedded systems. In: Proceedings of International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems. Storrs, CT: IEEE, 53–56

[4] Arora S, Singh S, Yetilmezsoy K (2018). A modified butterfly optimization algorithm for mechanical design optimization problems. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(1): 21

[5] Aven T, Jensen U (2000). Stochastic Models in Reliability. 2nd ed. New York: Springer

[6] Barabady J, Kumar U (2007). Availability allocation through importance measures. International Journal of Quality & Reliability Management, 24(6): 643–657

[7] Barlow R E, Proschan F (1975). Importance of system components and fault tree events. Stochastic Processes and Their Applications, 3(2): 153–173

[8] Baroud H, Barker K (2018). A Bayesian kernel approach to modeling resilience-based network component importance. Reliability Engineering & System Safety, 170: 10–19

[9] Baxter L A (1984). Continuum structures I. Journal of Applied Probability, 21(4): 802–815

[10] Baxter L A (1986). Continuum structures II. Mathematical Proceedings of the Cambridge Philosophical Society, 99(2): 331–338

[11] Bhattacharya D, Roychowdhury S (2014). Redundancy allocation using component-importance measures for maximizing system reliability. American Journal of Mathematical and Management Sciences, 33(1): 36–54

[12] Bhattacharya D, Roychowdhury S (2016). Bayesian importance measure-based approach for optimal redundancy assignment. American Journal of Mathematical and Management Sciences, 35(4): 335–344

[13] Birnbaum Z W (1969). On the importance of different components in a multicomponent system. Multivariate Analysis, II: 581–592

[14] Boland P J, El-Neweihi E, Proschan F (1988). Active redundancy allocation in coherent systems. Probability in the Engineering and Informational Sciences, 2(3): 343–353

[15] Borgonovo E, Aliee H, Glaß M, Teich J (2016). A new time-independent reliability importance measure. European Journal of Operational Research, 254(2): 427–442

[16] Bretas A S, Cabral R J, Leborgne R C, Ferreira G D, Morales J A (2018). Multi-objective MILP model for distribution systems reliability optimization: A lightning protection system design approach. International Journal of Electrical Power & Energy Systems, 98: 256–268

[17] Cai Z Q, Si S B, Liu Y, Zhao J B (2018). Maintenance optimization of continuous state systems based on performance improvement. IEEE Transactions on Reliability, 67(2): 651–665

[18] Cai Z Q, Si S B, Sun S D, Li C T (2016). Optimization of linear consecutive-k-out-of-n system with a Birnbaum importance-based genetic algorithm. Reliability Engineering & System Safety, 152: 248–258

[19] Čepin M (2019). Evaluation of the power system reliability if a nuclear power plant is replaced with wind power plants. Reliability Engineering & System Safety, 185: 455–464

[20] Chakri A, Yang X S, Khelif R, Benouaret M (2018). Reliability-based design optimization using the directional bat algorithm. Neural Computing & Applications, 30(8): 2381–2402

[21] Chern M S (1992). On the computational complexity of reliability redundancy allocation in a series system. Operations Research Letters, 11(5): 309–315

[22] Coit D W, Smith A E (1996). Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Transactions on Reliability, 45(2): 254–260

[23] Coit D W, Zio E (2019). The evolution of system reliability optimization. Reliability Engineering & System Safety, 192: 106259

[24] Compare M, Bellani L, Zio E (2019). Optimal allocation of prognostics and health management capabilities to improve the reliability of a power transmission network. Reliability Engineering & System Safety, 184: 164–180

[25] Compare M, Bellora M, Zio E (2017). Aggregation of importance measures for decision making in reliability engineering. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 231(3): 242–254

[26] da Costa Bueno V (2005). Minimal standby redundancy allocation in a k-out-of-n: F system of dependent components. European Journal of Operational Research, 165(3): 786–793

[27] Derman C, Lieberman G J, Ross S M (1974). Optimal allocations in the construction of k-out-of-n reliability systems. Management Science, 21(3): 241–250

[28] Du Y J, Si S B, Jin T D (2019). Reliability importance measures for network based on failure counting process. IEEE Transactions on Reliability, 68(1): 267–279

[29] Dui H Y, Chen L W, Wu S M (2017a). Generalized integrated importance measure for system performance evaluation: Application to a propeller plane system. Maintenance and Reliability, 19(2): 279–286

[30] Dui H Y, Li S M, Xing L D, Liu H L (2019). System performance-based joint importance analysis guided maintenance for repairable systems. Reliability Engineering & System Safety, 186: 162–175

[31] Dui H Y, Si S B, Sun S D, Cai Z Q (2013). Gradient computations and geometrical meaning of importance measures. Quality Technology & Quantitative Management, 10(3): 305–318

[32] Dui H Y, Si S B, Wu S M, Yam R C M (2017b). An importance measure for multistate systems with external factors. Reliability Engineering & System Safety, 167: 49–57

[33] Dui H Y, Si S B, Yam R C M (2017c). A cost-based integrated importance measure of system components for preventive maintenance. Reliability Engineering & System Safety, 168: 98–104

[34] Dui H Y, Si S B, Yam R C M (2018). Importance measures for optimal structure in linear consecutive-k-out-of-n systems. Reliability Engineering & System Safety, 169: 339–350

[35] Espiritu J F, Coit D W, Prakash U (2007). Component criticality importance measures for the power industry. Electric Power Systems Research, 77(5–6): 407–420

[36] Fang C, Marle F, Xie M (2017). Applying importance measures to risk analysis in engineering project using a risk network model. IEEE Systems Journal, 11(3): 1548–1556

[37] Fang Y, Pedroni N, Zio E (2016). Resilience-based component importance measures for critical infrastructure network systems. IEEE Transactions on Reliability, 65(2): 502–512

[38] Fu Y, Yuan T, Zhu X (2019a). Importance-measure based methods for component reassignment problem of degrading components. Reliability Engineering & System Safety, 190: 106501

[39] Fu Y, Yuan T, Zhu X (2019b). Optimum periodic component reallocation and system replacement maintenance. IEEE Transactions on Reliability, 68(2): 753–763

[40] Garg H, Sharma S P (2013). Multi-objective reliability-redundancy allocation problem using particle swarm optimization. Computers & Industrial Engineering, 64(1): 247–255

[41] Ghambari S, Rahati A (2018). An improved artificial bee colony algorithm and its application to reliability optimization problems. Applied Soft Computing, 62: 736–767

[42] Gopal K, Aggarwal K K, Gupta J S (1980). A new method for solving reliability optimization problem. IEEE Transactions on Reliability, R-29(1): 36–37

[43] Griffith W S (1980). Multistate reliability models. Journal of Applied Probability, 17(3): 735–744

[44] Gupta S, Bhattacharya J, Barabady J, Kumar U (2013). Cost-effective importance measure: A new approach for resource prioritization in a production plant. International Journal of Quality & Reliability Management, 30(4): 379–386

[45] He X, Yuan Y (2019). A framework of identifying critical water distribution pipelines from recovery resilience. Water Resources Management, 33(11): 3691–3706

[46] Hilber P, Bertling L (2004). Monetary importance of component reliability in electrical networks for maintenance optimization. In: Proceedings of International Conference on Probabilistic Methods Applied to Power Systems. Ames, IA: IEEE, 150–155

[47] Jiang T, Liu Y, Zheng Y X (2019). Optimal loading strategy for multi-state systems: Cumulative performance perspective. Applied Mathematical Modelling, 74: 199–216

[48] Kim C, Baxter L A (1987). Reliability importance for continuum structure functions. Journal of Applied Probability, 24(3): 779–785

[49] Knight C R (1991). Four decades of reliability progress. In: Proceedings of Annual Reliability and Maintainability Symposium. Orlando, FL: IEEE, 156–160

[50] Kulturel-Konak S, Smith A E, Coit D W (2003). Efficiently solving the redundancy allocation problem using tabu search. IIE Transactions, 35(6): 515–526

[51] Kuo W, Lin H H, Xu Z K, Zhang W X (1987). Reliability optimization with the Lagrange-multiplier and branch-and-bound technique. IEEE Transactions on Reliability, R-36(5): 624–630

[52] Kuo W, Prasad V R (2000). An annotated overview of system-reliability optimization. IEEE Transactions on Reliability, 49(2): 176–187

[53] Kuo W, Zhu X (2012). Importance Measures in Reliability, Risk and Optimization: Principles and Applications. 1st ed. Chichester: John Wiley & Sons

[54] Levitin G, Finkelstein M, Dai Y (2017a). Redundancy optimization for series-parallel phased-mission systems exposed to random shocks. Reliability Engineering & System Safety, 167: 554–560

[55] Levitin G, Xing L, Amari S V (2012). Recursive algorithm for reliability evaluation of non-repairable phased-mission systems with binary elements. IEEE Transactions on Reliability, 61(2): 533–542

[56] Levitin G, Xing L, Dai Y (2017b). Optimization of component allocation/distribution and sequencing in warm standby series-parallel systems. IEEE Transactions on Reliability, 66(4): 980–988

[57] Levitin G, Xing L, Dai Y (2017c). Reliability versus expected mission cost and uncompleted work in heterogeneous warm standby multiphase systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(3): 462–473

[58] Li R Y, Wang J F, Liao H T, Huang N (2015). A new method for reliability allocation of avionics connected via an airborne network. Journal of Network and Computer Applications, 48: 14–21

[59] Li X Y, Huang H Z, Li Y F (2018). Reliability analysis of phased-mission system with non-exponential and partially repairable components. Reliability Engineering & System Safety, 175: 119–127

[60] Liang Y C, Smith A E (2004). An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Transactions on Reliability, 53(3): 417–423

[61] Lin F H, Kuo W (2002). Reliability importance and invariant optimal allocation. Journal of Heuristics, 8(2): 155–171

[62] Lin M S, Chen D J (1997). The computational complexity of the reliability problem on distributed systems. Information Processing Letters, 64(3): 143–147

[63] Lin S, Fang X, Lin F, Yang Z, Wang X (2018). Reliability of rail transit traction drive system: A review. Microelectronics and Reliability, 88–90: 1281–1285

[64] Liu S Y, She R, Fan P Y, Letaief K B (2018). Non-parametric message importance measure: Storage code design and transmission planning for big data. IEEE Transactions on Communications, 66(11): 5181–5196

[65] Marseguerra M, Zio E, Podofillini L, Coit D W (2005). Optimal design of reliable network systems in presence of uncertainty. IEEE Transactions on Reliability, 54(2): 243–253

[66] Mettas A (2000). Reliability allocation and optimization for complex systems. In: Proceedings of Annual Reliability and Maintainability Symposium. International Symposium on Product Quality and Integrity. Los Angeles, CA: IEEE, 216–221

[67] Mi J H, Li Y F, Peng W, Huang H Z (2018). Reliability analysis of complex multi-state system with common cause failure based on evidential networks. Reliability Engineering & System Safety, 174: 71–81

[68] Mohamad F, Teh J (2018). Impacts of energy storage system on power system reliability: A systematic review. Energies, 11(7): 1749

[69] Nguyen K A, Do P, Grall A (2017). Joint predictive maintenance and inventory strategy for multi-component systems using Birnbaum’s structural importance. Reliability Engineering & System Safety, 168: 249–261

[70] Onishi J, Kimura S, James R J W, Nakagawa Y (2007). Solving the redundancy allocation problem with a mix of components using the improved surrogate constraint method. IEEE Transactions on Reliability, 56(1): 94–101

[71] Pant S, Anand D, Kishor A, Singh S B (2015). A particle swarm algorithm for optimization of complex system reliability. International Journal of Performability Engineering, 11(1): 33–42

[72] Papastavridis S (1987). The most important component in a consecutive-k-out-of-n: F system. IEEE Transactions on Reliability, R-36(2): 266–268

[73] Peng R, Zhai Q Q, Xing L D, Yang J (2016). Reliability analysis and optimal structure of series-parallel phased-mission systems subject to fault-level coverage. IIE Transactions, 48(8): 736–746

[74] Prasad V R, Kuo W (2000). Reliability optimization of coherent systems. IEEE Transactions on Reliability, 49(3): 323–330

[75] Qiu S Q, Sallak M, Schön W, Ming H X G (2018). Extended LK heuristics for the optimization of linear consecutive-k-out-of-n: F systems considering parametric uncertainty and model uncertainty. Reliability Engineering & System Safety, 175: 51–61

[76] Ramirez-Marquez J E, Coit D W (2004). A heuristic for solving the redundancy allocation problem for multi-state series-parallel systems. Reliability Engineering & System Safety, 83(3): 341–349

[77] Ramirez-Marquez J E, Coit D W (2007). Multi-state component criticality analysis for reliability improvement in multi-state systems. Reliability Engineering & System Safety, 92(12): 1608–1619

[78] Ramirez-Marquez J E, Rocco C M, Gebre B A, Coit D W, Tortorella M (2006). New insights on multi-state component criticality and importance. Reliability Engineering & System Safety, 91(8): 894–904

[79] Rausand M, Høyland A (2003). System Reliability Theory: Models, Statistical Methods and Applications. 2nd ed. Hoboken: John Wiley & Sons

[80] Roychowdhury S, Bhattacharya D (2019). Performance improvement of a multi-state coherent system using component importance measure. American Journal of Mathematical and Management Sciences, 38(3): 312–324

[81] Shen J, Cui L (2015). Reliability and Birnbaum importance for sparsely connected circular consecutive-k systems. IEEE Transactions on Reliability, 64(4): 1140–1157

[82] Shen J, Cui L, Du S (2015). Birnbaum importance for linear consecutive-k-out-of-n systems with sparse d. IEEE Transactions on Reliability, 64(1): 359–375

[83] Shen K, Xie M (1990). On the increase of system reliability by parallel redundancy. IEEE Transactions on Reliability, 39(5): 607–611

[84] Shojaei M, Mahani A (2019). Efficient reliability-redundancy allocation with uniform importance measure in presence of correlated failure. International Journal of Computers and Applications, 41(5): 378–391

[85] Si S B, Dui H Y, Cai Z Q, Sun S D (2012a). The integrated importance measure of multi-state coherent systems for maintenance processes. IEEE Transactions on Reliability, 61(2): 266–273

[86] Si S B, Dui H Y, Cai Z Q, Sun S D, Zhang Y F (2012b). Joint integrated importance measure for multi-state transition systems. Communications in Statistics—Theory and Methods, 41(21): 3846–3862

[87] Si S B, Dui H Y, Zhao X B, Zhang S G, Sun S D (2012c). Integrated importance measure of component states based on loss of system performance. IEEE Transactions on Reliability, 61(1): 192–202

[88] Si S B, Levitin G, Dui H Y, Sun S D (2013). Component state-based integrated importance measure for multi-state systems. Reliability Engineering & System Safety, 116: 75–83

[89] Si S B, Levitin G, Dui H Y, Sun S D (2014). Importance analysis for reconfigurable systems. Reliability Engineering & System Safety, 126: 72–80

[90] Si S B, Liu M L, Jiang Z Y, Jin T D, Cai Z Q (2019). System reliability allocation and optimization based on generalized Birnbaum importance measure. IEEE Transactions on Reliability, 68(3): 831–843

[91] Singpurwalla N D (2006). Reliability and Risk: A Bayesian Perspective. Hoboken: John Wiley & Sons

[92] Su H, Zhang J J, Zio E, Yang N, Li X Y, Zhang Z J (2018). An integrated systemic method for supply reliability assessment of natural gas pipeline networks. Applied Energy, 209: 489–501

[93] Tian Z G, Zuo M J, Huang H Z (2008). Reliability-redundancy allocation for multi-state series-parallel systems. IEEE Transactions on Reliability, 57(2): 303–310

[94] Tillman F A, Hwang C L, Kuo W (1977). Optimization techniques for system reliability with redundancy: A review. IEEE Transactions on Reliability, R-26(3): 148–155

[95] Vu H C, Do P, Barros A (2016). A stationary grouping maintenance strategy using mean residual life and the Birnbaum importance measure for complex structures. IEEE Transactions on Reliability, 65(1): 217–234

[96] Wang L H, Ma D H, Han X, Wang W (2019). Optimization for postearthquake resilient power system capacity restoration based on the degree of discreteness method. Mathematical Problems in Engineering, 5489067

[97] Wang N, Zhao J B, Jiang Z Y, Zhang S (2018). Reliability optimization of systems with component improvement cost based on importance measure. Advances in Mechanical Engineering, 10(11): 1–15

[98] Wu S M, Chan L Y (2003). Performance utility-analysis of multi-state systems. IEEE Transactions on Reliability, 52(1): 14–21

[99] Wu S M, Chen Y, Wu Q T, Wang Z L (2016). Linking component importance to optimization of preventive maintenance policy. Reliability Engineering & System Safety, 146: 26–32

[100] Wu S M, Coolen F P A (2013). A cost-based importance measure for system components: An extension of the Birnbaum importance. European Journal of Operational Research, 225(1): 189–195

[101] Wu X Y, Wu X Y (2017). An importance based algorithm for reliability-redundancy allocation of phased-mission systems. In: Proceedings of International Conference on Software Quality, Reliability and Security Companion. Prague: IEEE, 152–159

[102] Wu X Y, Wu X Y, Balakrishnan N (2018). Reliability allocation model and algorithm for phased-mission systems with uncertain component parameters based on importance measure. Reliability Engineering & System Safety, 180: 266–276

[103] Xiahou T F, Liu Y, Jiang T (2018). Extended composite importance measures for multi-state systems with epistemic uncertainty of state assignment. Mechanical Systems and Signal Processing, 109: 305–329

[104] Xiang S H, Yang J (2018). Performance reliability evaluation for mobile ad hoc networks. Reliability Engineering & System Safety, 169: 32–39

[105] Xiao R S, Xiang Y M, Wang L F, Xie K G (2018). Power system reliability evaluation incorporating dynamic thermal rating and network topology optimization. IEEE Transactions on Power Systems, 33(6): 6000–6012

[106] Xie M, Shen K (1989). On ranking of system components with respect to different improvement actions. Microelectronics and Reliability, 29(2): 159–164

[107] Xing L D, Dugan J B (2002). Analysis of generalized phased-mission system reliability, performance, and sensitivity. IEEE Transactions on Reliability, 51(2): 199–211

[108] Xiong G Z, Zhang C, Zhou F (2017). A robust reliability redundancy allocation problem under abnormal external failures guided by a new importance measure. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 231(2): 180–199

[109] Xu Z P, Ramirez-Marquez J E, Liu Y, Xiahou T F (2020). A new resilience-based component importance measure for multi-state networks. Reliability Engineering & System Safety, 193: 106591

[110] Yao Q, Zhu X, Kuo W (2011). Heuristics for component assignment problems based on the Birnbaum importance. IIE Transactions, 43(9): 633–646

[111] Yao Q, Zhu X, Kuo W (2014). A Birnbaum-importance based genetic local search algorithm for component assignment problems. Annals of Operations Research, 212(1): 185–200

[112] Yeh W C (2019). A novel boundary swarm optimization method for reliability redundancy allocation problems. Reliability Engineering & System Safety, 192: 106060

[113] Yeh W C, Chu T C (2018). A novel multi-distribution multi-state flow network and its reliability optimization problem. Reliability Engineering & System Safety, 176: 209–217

[114] Yeh W C, Hsieh T J (2011). Solving reliability redundancy allocation problems using an artificial bee colony algorithm. Computers & Operations Research, 38(11): 1465–1473

[115] Yu H, Yang J, Lin J, Zhao Y (2017). Reliability evaluation of non-repairable phased-mission common bus systems with common cause failures. Computers & Industrial Engineering, 111: 445–457

[116] Yu J W, Zheng S L, Pham H, Chen T (2018). Reliability modeling of multi-state degraded repairable systems and its applications to automotive systems. Quality and Reliability Engineering International, 34(3): 459–474

[117] Zaretalab A, Hajipour V, Tavana M (2020). Redundancy allocation problem with multi-state component systems and reliable supplier selection. Reliability Engineering & System Safety, 193: 106629

[118] Zhang S, Zhao J B, Li H G, Wang N (2017). Reliability optimization and importance analysis of circular-consecutive k-out-of-n system. Mathematical Problems in Engineering, 1831537

[119] Zhang S, Zhao J B, Zhu W J, Du L (2019). Reliability optimization of linear consecutive k-out-of-n: F systems with Birnbaum importance-based quantum genetic algorithm. Advances in Mechanical Engineering, 11(4): 1–16

[120] Zhao J B, Cai Z Q, Si W T, Zhang S (2019a). Mission success evaluation of repairable phased-mission systems with spare parts. Computers & Industrial Engineering, 132: 248–259

[121] Zhao J B, Si S B, Cai Z Q (2019b). A multi-objective reliability optimization for reconfigurable systems considering components degradation. Reliability Engineering & System Safety, 183: 104–115

[122] Zhao J B, Si S B, Cai Z Q, Su M, Wang W (2019c). Multiobjective optimization of reliability-redundancy allocation problems for serial parallel-series systems based on importance measure. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 233(5): 881–897

[123] Zhao X B, Si S B, Dui H Y, Cai Z Q, Sun S D (2013). Integrated importance measure for multi-state coherent systems of k level. Journal of Systems Engineering and Electronics, 24(6): 1029–1037

[124] Zhu X Y, Yao Q Z, Kuo W (2011). Birnbaum importance in solving component assignment problems. In: Proceedings of Annual Reliability and Maintainability Symposium. Lake Buena Vista, FL: IEEE,1–6

[125] Zhu X Y, Fu Y Q, Yuan T, Wu X Y (2017). Birnbaum importance based heuristics for multi-type component assignment problems. Reliability Engineering & System Safety, 165: 209–221

[126] Zio E, Marella M, Podofillini L (2007). Importance measures-based prioritization for improving the performance of multi-state systems: Application to the railway industry. Reliability Engineering & System Safety, 92(10): 1303–1314

[127] Zio E, Podofillini L (2003a). Importance measures of multi-state components in multi-state systems. International Journal of Reliability Quality and Safety Engineering, 10(3): 289–310

[128] Zio E, Podofillini L (2003b). Monte Carlo simulation analysis of the effects of different system performance levels on the importance of multi-state components. Reliability Engineering & System Safety, 82(1): 63–73

[129] Zio E, Podofillini L (2007). Importance measures and genetic algorithms for designing a risk-informed optimally balanced system. Reliability Engineering & System Safety, 92(10): 1435–1447

[130] Zuo M, Kuo W (1990). Design and performance analysis of consecutive-k-out-of-n structure. Naval Research Logistics, 37(2): 203–230

RIGHTS & PERMISSIONS

Higher Education Press