Abstract
Failure interactions and multiple states are two common phenomena in engineering systems. However, most of the redundancy allocation problems assume binary states and ignore failure interactions, which will cause inaccurate and misleading results. Although some research work focuses on the multistate systems, failure interactions have been ignored. This paper, for the first time, solves the redundancy allocation problems considering the systems having both multiple states and failure interactions. The system studied in this paper is a kind of multistate system containing a main subsystem and an auxiliary subsystem with the failure interaction existing from the auxiliary subsystem to the main subsystem. Semi-Markov process is proposed as the model for the system analysis, and a reliability measure, availability, is obtained based on the proposed semi-Markov process models. The system availability is used as the constraint in the redundancy allocation problem. A case study from a navy application is presented to demonstrate the applicability of the proposed method.
Issue Section:
Design Automation
References
1.
Ebeling
, C.
, 1997
, An Introduction to Reliability and Maintainability Engineering
, McGraw-Hill Companies
, Boston
.2.
Shin
, J.
, and Lee
, I.
, 2014
, “Reliability-Based Vehicle Safety Assessment and Design Optimization of Roadway Radius and Speed Limit in Windy Environments
,” ASME J. Mech. Des.
, 136
(8
), p. 081006
.3.
Bichon
, B. J.
, Eldred
, M. S.
, Mahadevan
, S.
, and McFarland
, J. M.
, 2013
, “Efficient Global Surrogate Modeling for Reliability-Based Design Optimization
,” ASME J. Mech. Des.
, 135
(1
), p. 011009
.4.
Beji
, N.
, Jarboui
, B.
, Eddaly
, M.
, and Chabchoub
, H.
, 2010
, “A Hybrid Particle Swarm Optimization Algorithm for the Redundancy Allocation Problem
,” J. Comput. Sci.
, 1
(2
), pp. 159
–167
.5.
Levitin
, G.
, 2005
, Universal Generating Function in Reliability Analysis and Optimization
, Springer-Verlag
, London
.6.
Lai
, M. T.
, and Chen
, Y. C.
, 2006
, “Optimal Periodic Replacement Policy for a Two-Unit System With Failure Rate Interaction
,” Int. J. Adv. Manuf. Technol.
, 29
(3–4
), pp. 367
–371
.7.
Sun
, Y.
, Ma
, L.
, Mathew
, J.
, and Zhang
, S.
, 2006
, “An Analytical Model for Interactive Failures
,” Reliab. Eng. Syst. Saf.
, 91
(5
), pp. 495
–504
.8.
Wang
, J.
, and Li
, M.
, 2014
, “Redundancy Allocation for Reliability Design of Engineering Systems With Failure Interactions
,” ASME
Paper No. DETC2014-34257.9.
Chryssaphinou
, O.
, Limnios
, N.
, and Malefaki
, S.
, 2011
, “Multi-State Reliability Systems Under Discrete Time Semi-Markovian Hypothesis
,” IEEE Trans. Reliab.
, 60
(1
), pp. 80
–87
.10.
Li
, Y. F.
, and Zio
, E.
, 2012
, “A Multi-State Model for the Reliability Assessment of a Distributed Generation System Via Universal Generating Function
,” Reliab. Eng. Syst. Saf.
, 106
, pp. 28
–36
.11.
Lisnianski
, A.
, Elmakias
, D.
, Laredo
, D.
, and Ben Haim
, H.
, 2012
, “A Multi-State Markov Model for a Short-Term Reliability Analysis of a Power Generating Unit
,” Reliab. Eng. Syst. Saf.
, 98
(1
), pp. 1
–6
.12.
Lisnianski
, A.
, and Levitin
, G.
, 2003
, Multi-State System Reliability: Assessment, Optimization and Applications
, World Scientific
, Singapore
.13.
Soro
, I. W.
, Nourelfath
, M.
, and Ait-Kadi
, D.
, 2010
, “Performance Evaluation of Multi-State Degraded Systems With Minimal Repairs and Imperfect Preventive Maintenance
,” Reliab. Eng. Syst. Saf.
, 95
(2
), pp. 65
–69
.14.
Muhammad
, M.
, Majid
, A.
, and Amin
, M.
, 2011
, “Reliability and Availability Evaluation for a Multi-State System Subject to Minimal Repair
,” J. Appl. Sci.
, 11
, pp. 2036
–2041
.15.
Liu
, Y.
, Huang
, H.-Z.
, Wang
, Z.
, Li
, Y.
, and Yang
, Y.
, 2013
, “A Joint Redundancy and Imperfect Maintenance Strategy Optimization for Multi-State Systems
,” IEEE Trans. Reliab.
, 62
(2
), pp. 368
–378
.16.
Liu
, Y.
, and Huang
, H.-Z.
, 2010
, “Optimal Replacement Policy for Multi-State System Under Imperfect Maintenance
,” IEEE Trans. Reliab.
, 59
(3
), pp. 483
–495
.17.
Gen
, M.
, and Cheng
, R.
, 2000
, Genetic Algorithms and Engineering Optimization
, Wiley
, New York
.18.
Ramirez-Marquez
, J. E.
, and Coit
, D. W.
, 2004
, “A Heuristic for Solving the Redundancy Allocation Problem for Multi-State Series–Parallel Systems
,” Reliab. Eng. Syst. Saf.
, 83
(3
), pp. 341
–349
.19.
Agarwal
, M.
, and Gupta
, R.
, 2007
, “Homogeneous Redundancy Optimization in Multi-State Series–Parallel Systems—A Heuristic Approach
,” IIE Trans.
, 39
(3
), pp. 277
–289
.20.
Nourelfath
, M.
, Châtelet
, E.
, and Nahas
, N.
, 2012
, “Joint Redundancy and Imperfect Preventive Maintenance Optimization for Series–Parallel Multi-State Degraded Systems
,” Reliab. Eng. Syst. Saf.
, 103
, pp. 51
–60
.21.
Kumar
, V.
, Tripathi
, M.
, Pandey
, M.
, and Tiwari
, M.
, 2009
, “Physical Programming and Conjoint Analysis-Based Redundancy Allocation in Multistate Systems: A Taguchi Embedded Algorithm Selection and Control (TAS&C) Approach
,” Proc. Inst. Mech. Eng., Part O
, 223
(3
), pp. 215
–232
.22.
Murthy
, D.
, and Nguyen
, D.
, 1985
, “Study of Two-Component System With Failure Interaction
,” Nav. Res. Logist. Q.
, 32
(2
), pp. 239
–247
.23.
Murthy
, D.
, and Nguyen
, D.
, 1985
, “Study of a Multi-Component System With Failure Interaction
,” Eur. J. Oper. Res.
, 21
(3
), pp. 330
–338
.24.
Nakagawa
, T.
, and Murthy
, D. N. P.
, 1993
, “Optimal Replacement Policies for a Two-Unit System With Failure Interactions
,” Oper. Res.
, 27
(4
), pp. 427
–438
.25.
Zequeira
, R.
, and Berenguer
, C.
, 2004
, “Maintenance Cost Analysis of a Two-Component Parallel System With Failure Interaction
,” Reliability and Maintainability Symposium (RAMS)
, pp. 220
–225
.26.
Augustine
, M.
, Yadav
, O.
, Jain
, R.
, and Rathore
, A.
, 2011
, “An Approach to Capture System Interaction Failures of a Complex System
,” Reliability and Maintainability Symposium
(RAMS
), Lake Buena Vista, FL, Jan. 24–27.27.
Dobson
, I.
, Carreras
, B. A.
, and Newman
, D. E.
, 2004
, “Probabilistic Load-Dependent Cascading Failure With Limited Component Interactions Circuits and Systems
,” International Symposium on Circuits and Systems
, Vancouver, Canada.28.
Elsayed
, A.
, 2012
, Reliability Engineering
, Wiley
, Hoboken, NJ
.29.
Levitin
, G.
, 2001
, “Incorporating Common-Cause Failures Into Nonrepairable Multistate Series–Parallel System Analysis
,” IEEE Trans. Reliab.
, 50
(4
), pp. 380
–388
.30.
Maatouk
, I.
, Chatelet
, E.
, and Chebbo
, N.
, 2011
, “Reliability of Multi-States System With Load Sharing and Propagation Failure Dependence
,” 2011 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering
(ICQR2MSE
), Xi'an, China, June 17–19, pp. 42
–46
.31.
Levitin
, G.
, 2004
, “A Universal Generating Function Approach for the Analysis of Multi-State Systems With Dependent Elements
,” Reliab. Eng. Syst. Saf.
, 84
(3
), pp. 285
–292
.32.
Dao
, C. D.
, and Zuo
, M.
, 2015
, “Reliability Analysis of Multi-State Systems With S-Dependent Components
,” 2015 Annual Reliability and Maintainability Symposium
(RAMS
), Palm Harbor, FL, Jan. 26–29, pp. 1
–6
.33.
Levitin
, G.
, and Xing
, L.
, 2010
, “Reliability and Performance of Multi-State Systems With Propagated Failures Having Selective Effect
,” Reliab. Eng. Syst. Saf.
, 95
(6
), pp. 655
–661
.34.
Xing
, L.
, and Levitin
, G.
, 2011
, “Combinatorial Algorithm for Reliability Analysis of Multi-State Systems With Propagated Failures and Failure Isolation Effect
,” IEEE Trans. Syst., Man, Cybernet., Part A: Syst. Humans
, 41
(6
), pp. 1156
–1165
.35.
Levitin
, G.
, Xing
, L.
, Ben-Haim
, H.
, and Dai
, Y.
, 2011
, “Multi-State Systems With Selective Propagated Failures and Imperfect Individual and Group Protections
,” Reliab. Eng. Syst. Saf.
, 96
(12
), pp. 1657
–1666
.36.
D'Amico
, G.
, Janssen
, J.
, and Manca
, R.
, 2009
, “Semi-Markov Reliability Models With Recurrence Times and Credit Rating Applications
,” J. Appl. Math. Decis. Sci.
, 2009
, p. 625712
.37.
Distefano
, S.
, Longob
, F.
, and Trivedi
, K.
, 2012
, “Investigating Dynamic Reliability and Availability Through State–Space Models
,” Comput. Math. Appl.
, 64
(12
), pp. 3701
–3716
.38.
Malefaki
, S.
, Limnios
, N.
, and Dersin
, P.
, 2014
, “Reliability of Maintained Systems Under a Semi-Markov Setting
,” Reliab. Eng. Syst. Saf.
, 131
, pp. 282
–290
.39.
Hildalgo, E. M. P., Silva, D. W. R., and de Souza, G. F. M.
, 2013
, “Application of Markov Chain to Determine the Electric Energy Supply System Reliability for the Cargo Control System of LNG Carriers
,” ASME
Paper No. OMAE2013-11388.40.
Veeramany
, A.
, and Pandey
, M.
, 2011
, “Reliability Analysis of Nuclear Component Cooling Water System Using Semi-Markov Process Model
,” Nucl. Eng. Des.
, 241
(5
), pp. 1799
–1806
.41.
Veeramany
, A.
, and Pandey
, M.
, 2011
, “Reliability Analysis of Nuclear Piping System Using Semi-Markov Process Model
,” Ann. Nucl. Energy
, 38
(5
), pp. 1133
–1139
.42.
Lee
, S.
, Li
, L.
, and Ni
, J.
, 2013
, “Markov-Based Maintenance Planning Considering Repair Time and Periodic Inspection
,” ASME J. Manuf. Sci. Eng.
, 135
(3
), p. 031013
.43.
Zhong
, C.
, and Jin
, H.
, 2014
, “A Novel Optimal Preventive Maintenance Policy for a Cold Standby System Based on Semi-Markov Theory
,” Eur. J. Oper. Res.
, 232
(2
), pp. 405
–411
.44.
Tomasevicz
, C.
, and Asgarpoor
, S.
, 2009
, “Optimum Maintenance Policy Using Semi-Markov Decision Processes
,” Electric Power Syst. Res.
, 79
(9
), pp. 1286
–1291
.45.
Butenko
, V.
, 2014
, “Modeling of a Reactor Trip System Using Markov Chains: case Study
,” ASME
Paper No. ICONE22-31156.46.
Limnios
, N.
, and Oprisan
, G.
, 2001
, Semi-Markov Processes and Reliability
, Springer
, New York.47.
D'Amico
, G.
, 2011
, “Age-Usage Semi-Markov Models
,” Appl. Math. Modell.
, 35
(9
), pp. 4354
–4366
.48.
Ardakan
, M.
, and Hamadani
, A.
, 2014
, “Reliability–Redundancy Allocation Problem With Cold-Standby Redundancy Strategy
,” Simul. Modell. Pract. Theory
, 42
, pp. 107
–118
.49.
Ahmadizar
, F.
, and Soltanpanah
, H.
, 2011
, “Reliability Optimization of a Series System With Multiple-Choice and Budget Constraints Using an Efficient Ant Colony Approach
,” Exp. Syst. Appl.
, 38
(4
), pp. 3640
–3646
.50.
Georgiopoulos
, P.
, Jonsson
, M.
, and Papalambros
, P.
, 2005
, “Linking Optimal Design Decisions to the Theory of the Firm—The case of Resource Allocation
,” ASME J. Mech. Des.
, 127
(3
), pp. 358
–366
.51.
Huang
, C.
, Lo
, J.
, Kuo
, S.
, and Lyu
, M.
, 2004
, “Optimal Allocation of Testing-Resource Considering Cost, Reliability, and Testing-Effort, Dependable Computing
,” 10th IEEE Pacific Rim International Symposium on Dependable Computing
, Mar. 3–5, pp. 103
–112
.52.
Ramirez-Marquez
, J.
, Coit
, D. W.
, and Konak
, A.
, 2004
, “Redundancy Allocation for Series–Parallel Systems Using a Max–Min Approach
,” IIE Trans.
, 36
(9
), pp. 891
–898
.53.
Kartik
, S.
, and Siva Ram Murthy
, C.
, 1995
, “Improved Task-Allocation Algorithms to Maximize Reliability of Redundant Distributed Computing Systems
,” IEEE Trans. Reliab.
, 44
(4
), pp. 575
–586
.54.
Allella
, F.
, Chiodo
, E.
, and Lauria
, D.
, 2005
, “Optimal Reliability Allocation Under Uncertain Conditions, With Application to Hybrid Electric Vehicle Design
,” Int. J. Qual. Reliab. Manage.
, 22
(6
), pp. 626
–641
.55.
Jacobson
, D.
, and Arora
, S.
, 1996
, “Simultaneous Allocation of Reliability and Redundancy Using Simplex Search
,” Reliability and Maintainability Symposium, International Symposium on Product Quality and Integrity
, Las Vegas, NV, June 22–25, pp. 243
–250
.56.
Levitin
, G.
, and Lisnianski
, A.
, 2001
, “Optimal Separation of Elements in Vulnerable Multi-State Systems
,” Reliab. Eng. Syst. Saf.
, 73
(1
), pp. 55
–66
.57.
Garg
, H.
, and Sharma
, S. P.
, 2013
, “Multi-Objective Reliability-Redundancy Allocation Problem Using Particle Swarm Optimization
,” Comput. Ind. Eng.
, 64
(1
), pp. 247
–255
.58.
Cai
, T.
, and Freiheit
, T.
, 2014
, “Resource Allocation for Lean Product Development Using a Value Creation Cell Model
,” ASME J. Mech. Des.
, 136
(10
), p. 101701
.59.
Haider
, S. I.
, Burton
, L.
, and Joshi
, Y.
, 2006
, “A Reduced Order Modeling Framework for Thermal Modeling of Shipboard Power Electronics Cabinets
,” AIAA
Paper No. 2006-3610.60.
Jin
, X.
, and Hong
, Y. J.
, 2007
, System Reliability and Availability Analysis
, National Defense Industry Press
, Beijing, China
.61.
Ericsson
, 2010
, Reliability Aspects on Power Supplies
, Ericsson Power Modules Design Note 002
, Kista, Sweden.62.
Sikos
, L.
, and Klemeš
, J.
, 2010
, “Reliability, Availability and Maintenance Optimization of Heat Exchanger Networks
,” Appl. Therm. Eng.
, 30
(1
), pp. 63
–69
.63.
Wang
, J.
, and Li
, M.
, 2014
, “Improve System Reliability and Robustness Using Axiomatic Design and Fault Tree Analysis
,” ASME
Paper No. DETC2014-34259.64.
Dieter
, G.
, and Schmidt
, L.
, 2008
, Engineering Design
, 4th ed., McGraw-Hill
, Boston, MA.Copyright © 2015 by ASME
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