Dependent competing-risk degradation systems

Springer Series in Reliability Engineering

Volumn 34, Issue , 2011, Pages 197-218

  Wang, Yaping ^a   Pham, Hoang ^a  

^a DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INDUSTRIAL ENGINEERING;

DEPENDENT COMPETING RISKS;

ENGINEERING;

EID: 84951788819     PISSN: 16147839     EISSN: 2196999X     Source Type: Book Series    
DOI: 10.1007/978-0-85729-470-8_7     Document Type: Chapter

References (102)

1. Esary JD, Marshall AW (1973) Shock models and wear process. Annu Prob 1(4):627–649
2. Hameed MSA, Proschan F (1973) Nonstationary shock models. Stoch Process Appl 1(10):383–404
3. Agrafiotis GK, Tsoukalas MZ (1987) On excess-time correlated cumulative process. J Oper Res Soc 46:1269–1280
4. Gut A, Husler J (2005) Realistic variation of shock models. Stat Prob Lett 74(2):187–204
5. Nakagawa T, Kijima M (1989) Replacement policies for a cumulative damage model with minimal repair at failure. IEEE Trans Reliab 28:581–584
6. Qian C, Nakamura S, Nakagawa T (2003) Replacement and minimal repair polices for a cumulative damage model with maintenance. Comput Math Appl 46:1111–1118
7. Wortman MA, Klutke G-A, Ayhan H (1994) A maintenance strategy for systems subjected to deterioration governed by random shocks. IEEE Trans Reliab 43(3):439–445
8. Chelbi A, Ait-Kadi D (2000) Generalized inspection strategy for randomly failing systems subjected to random shocks. Int J Prod Econ 64:379–384
9. Ross SM (1981) Generalized poisson models. Annu Prob 9(5):896–898
10. Shanthikumar JG, Sumita U (1983) General shock models associated with correlated renewal sequences. J Appl Prob 20:600–614
11. Chen J, Li Z (2008) An extended extreme shock maintenance model for a deteriorating system. Reliab Eng Syst Safety 93:1123–1129
12. Li Z (1984) Some probability distribution on Poisson shocks and its application in city traffic. J Lanzhou Univ 20:127–136
13. Li Z, Kong X (2007) Life behavior of d-shock model. Stat Prob Lett 77(6):577–587
14. Li Z, Zhao P (2007) Reliability analysis on the d-shock model of complex systems. IEEE Trans Reliab 56(2):340–348
15. Lam Y, Zhang YL (2004) A shock model for the maintenance problem of repairable system. Comput Oper Res 31:1807–1820
16. Rangan A, Tansu A (2008) A new shock model for system subject to random threshold failure. Proc World Acad Sci Eng Technol 30:1065–1070
17. Fan J, Ghurke SG, Levine RA (2000) Multicomponent lifetime distribution in the presence of ageing. J Appl Prob 37:521–533
18. Igaki N, Sumita U, Kowada M (1995) Analysis of Markov renewal shock models. J Appl prob 32:821–831
19. Gut A (2001) Mixed shock models. Bernoulli 7(3):541–555
20. Mallor F, Omey E (2001) Shocks, runs and random sums. J Appl Prob 38:438–448
21. Mallor F, Santos J (2003) Classification of shock model in system reliability. Monografias del Semin Matem Garcia de Galdeano 27:405–412
22. Mallor F, Santos J (2003) Reliability of systems subject to shocks with a stochastic dependence for the damages. Test 12(2):427–444
23. Mallor F, Omey E, Santos J (2006) Asymptotic results for a run and cumulative mixed shock model. J Math Sci 138(1):5410–5414
24. Finkelstein MS, Zarudnij VI (2001) A shock process with a non-cumulative damage. Reliab Eng Syst Safety 71:103–107
25. Bai J-M, Li Z-H, Kong X-B (2006) Generalized shock models based on a cluster point process. IEEE Trans Reliab 55(3):542–550
26. Lu CJ, Meeker WQ (1993) Using degradation measures to estimate of time-to-failure distribution. Technometrics 35:161–176
27. Yuan X-X, Pandey MD (2009) A nonlinear mixed-effects model for degradation data obtained from in-service inspections. Reliab Eng Syst Safety 94:509–519
28. Robinson ME, Crowder MJ (2000) Bayesian methods for a growth-curve degradation model with repeated measures. Life Data Anal 6:357–374
29. Wu S-J, Shao J (1999) Reliability analysis using the least squares method in nonlinear mixed-effect degradation models. Stat Sinica 9:855–877
30. van Noortwijk JM, Cooke RM, Kok M (1995) A Bayesian failure model based on isotropic deterioration. Eur J Oper Res 82:270–282
31. van Noortwijk JM, Pandey MD (2003) A stochastic deterioration process for timedependent reliability analysis. Proceedings of the eleventh IFIP WG 7.5 working conference on reliability and optimization of structural systems, pp 259–265
32. Nicolai RP, Dekker R, van Noortwijk JM (2007) A comparison of models for measurable deterioration: an application to coatings on steel structures. Reliab Eng Syst Safety 92:1635–1650
33. Hsieh M-H, Jeng S-L, Shen P-S (2009) Assessing device reliability based on scheduled discrete degradation measurements. Prob Eng Mech 24:151–158
34. Xue J, Yang K (1995) Dynamic reliability analysis of coherent multistate systems. IEEE Trans Reliab 44(4):683–688
35. Kharoufeh JP (2003) Explicit results for wear processes in a Markovian environment. Oper Res Lett 31:237–244
36. Saassouh B, Dieulle L, Grall A (2007) Online maintenance policy for a depredating system with random change of mode. Reliab Eng Syst Safety 92:1677–1685
37. Kharoufeh JP, Cox SM (2005) Stochastic models for degradation-based reliability. IIE Trans 37(6):533–542
38. Ebrahimi N (2001) A stochastic covariate failure model for assessing system reliability. J Appl Prob 38:761–767
39. Huang W, Dietrich DL (2005) An alternative degradation reliability modeling approach using maximum likelihood estimation. IEEE Trans Reliab 54(2):310–317
40. Bae SJ, Kuo W, Kvam PH (2007) Degradation models and implied lifetime distributions. Reliab Eng Syst Safety 92:601–608
41. Zuo MJ, Jiang R, Yam RCM (1999) Approaches for reliability modeling of continuous-state devices. IEEE Trans Reliab 48(1):9–18
42. Bae SJ, Kvam PH (2005) A nonlinear random coefficients model for degradation testing. Technometrics 46(4):460–469
43. Grall A, Berenguer C, Dieulle L (2002) A condition-based maintenance policy for stochastically deteriorating systems. Reliab Eng Syst Safety 76:167–180
44. Wang L, Chu J, Mao W (2009) A condition-based replacement and spare provisioning policy for deteriorating systems with uncertain deterioration to failure. Eur J Oper Res 194:184–205
45. Kiessler PC, Klutke G-A, Yang Y (2002) Availability of periodically inspected systems subject to Markovian degradation. J Appl Prob 39:700–711
46. Yang Y, Klutke G-A (2000) Lifetime-characteristics and inspection-schemes for levy degradation process. IEEE Trans Reliab 49(4):377–382
47. Zhao YX (2003) On preventive maintenance policy of a critical reliability level for system subject to degradation. Reliab Eng Syst Safety 79:301–308
48. Pandey MD, Yuan XX, van Noortwijk JM (2005) Gamma process model for reliability analysis and replacement of aging structural components, Safety and Reliability of Engineering Systems and Structures. In: Proceedings of the Ninth International Conference on Structural Safety and Reliability (ICOSSAR), Rome, pp 2439–2444
49. van Noortwijk JM, Frangopol DM (2004) Two probabilistic life-cycle maintenance models for deteriorating civil infrastructures. Prob Eng Mech 19:345–359
50. Delia M-C, Rafael P-O (2006) A deteriorating two-system with two repair modes and sojourn times phase-type distributed. Reliab Eng Syst Safety 91:1–9
51. Delia M-C, Rafael P-O (2008) A maintenance model with failures and inspection following Markovian arrival processes and two repair modes. Eur J Oper Res 186:694–707
52. Sim SH, Endrenyi J (1993) A failure-repair model with minimal & major maintenance. IEEE Trans Reliab 42(1):134–140
53. Ciampoli M (1998) Time dependent reliability of structural systems subject to deterioration. Comput Struct 67:29–35
54. Hosseini MM, Kerr RM, Randall RB (2000) An inspection model with minimal and major maintenance for a system with deterioration and poisson failures. IEEE Trans Reliab 49(1):88–987
55. Zhu Y, Elsayed EA, Liao H, Chan LY (2010) Availability optimization of systems subject to competing risk. Eur J Oper Res 202(3):781–788
56. van der Weide JAM, Pandey MD, van Noortwijk JM (2010) Discounted cost model for condition-based maintenance optimization. Reliab Eng Syst Safety 95:236–246
57. Chiang JH, Yuan J (2001) Optimal maintenance policy for a Markovian system under periodic inspection. Reliab Eng Syst Safety 71:165–172
58. Delia M-C, Rafael P-O (2006) Replacement times and costs in a degrading system with several types of failure: the case of phase-type holding times. Eur J Oper Res 175:1193–1209
59. Kharoufeh JP, Finkelstein DE, Mixon DG (2007) Availability of periodically inspected systems with Markovian wear and shocks. J Appl Prob 43:303–317
60. Tang Y-Y, Lam Y (2006) A d-shock maintenance model for a deteriorating system. Eur J Oper Res 168:541–556
61. Frostig E, Kenzin M (2009) Availability of inspected systems subject to shocks—a matrix algorithmic approach. Eur J Oper Res 193:168–183
62. Mori Y, Ellingwood BR (1994) Maintaining: reliability of concrete structures. I: role of inspection/repair. Struct Eng 120(3):824–845
63. van Noortwijk JM, van der Weide JAM, Kallen MJ, Pandey MD (2007) Gamma processes and peaks-over-threshold distribution for time-dependent reliability. Reliab Eng Syst Safety 92:1651–1658
64. Elio C, Giovanni M (2006) Indirect reliability estimation for electric devices via a dynamic ‘stress-strength’ model, SPEEDAM international symposium on power electronics, electrical drives, automation and motion
65. Lehmann A (2009) Joint modeling of degradation and failure time data. J Stat Plan Infer 139(5):1693–1706
66. Fan J, Ghurye SG, Levine RA (2000) Multi-component lifetime distributions in the presence of ageing. J Appl Prob 37:521–533
67. Cha JH, Finkelstein M (2009) On a terminating shock process with independent wear increments. J Appl Prob 46:353–362
68. Finkelstein M (2009) On damage accumulation and biological aging. J Stat Plan Infer 139(5):1643–1648
69. Satow T, Teramoto K, Nakagawa T (2000) Optimal replacement policy for a cumulative damage model with time deterioration. Math Comput Model 31:313–319
70. Deloux E, Castanier B, Berenguer C (2009) Predictive maintenance policy for a gradually deteriorating system subject to stress. Reliab Eng Syst Safety 94(2):418–431
71. Klutke G-A, Yang Y (2002) The availability of inspected systems subject to shocks and graceful degradation. IEEE Trans Reliab 51(3):371–374
72. Wenjian L, Pham H (2005) Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks. IEEE Trans Reliab 54(2):297–303
73. Wenjian L, Pham H (2005) An inspection-maintenance model for systems with multiple competing processes. IEEE Trans Reliab 54(2):318–327
74. Peng W, Coit DW (2004) Reliability prediction based on degradation modeling for systems with multiple degradation measures, Reliability and maintainability 2004 annual symposium-RAMS, pp 302–307
75. Yifan Z, Lin M, Rodney C, H-E Kim (2009) Asset life prediction using multiple degradation indicators and lifetime data: a gamma-based state space model approach. The 8th international conference on reliability, maintainability and safety
76. Embrechts P, Puccetti G (2010) Bounds for the sum of dependent risks having overlapping marginals. J Multivar Anal 101:177–190
77. Kojadinovic I, Yan J (2010) Comparison of three semiparametric methods for estimating dependence parameters in copula models. Insur Math Econ 47(1):52–63
78. Rodriguez-Lallena JA (2003) Manuel Ubeda-Flores, distribution functions of multivariate copulas. Stat Prob Lett 64:41–50
79. Chen X, Fan Y (2006) Estimation of copula-based semiparametric time series models. J Econ 130:307–335
80. Hurlimann W (2004) Fitting bivariate cumulative returns with copulas. Comput Stat Data Anal 45:355–372
81. Abegaz F, Naik-Nimbalkar UV (2008) Modeling statistical dependence of Markov chains via copula models. J Stat Plan Infer 138:1131–1146
82. Zezula I (2009) On multivariate Gaussian copulas. J Stat Plan Infer 139:3942–3946
83. Van den Goorbergh RWJ, Genest C, Werker BJM (2005) Bivariate option pricing using dynamic copulae models. Insur Math Econ 37:101–114
84. Zhang L, Singh VP (2007) Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol 332:93–109
85. Fernandez V (2008) Copula-based measures of dependence structure in assets returns. Physica A 387:3615–3628
86. Al-Harthy M, Begg S, Bratvold RB (2007) Copulas: a new technique to model dependence in petroleum decision making. J Petrol Sci Eng 57:195–208
87. Valle LD (2009) Bayesian copulae distributions, with application to operational risk management. Methodol Comput Appl Probab 11:95–115
88. Dakovic R, Czado C (2009) Comparing point and interval estimates in the bivariate t-copula model with application to financial data. Statistical Papers, 1613-9798 (online)
89. Ning C (2010) Dependence structure between the equity market and the foreign exchange market—a copula approach. J Int Money Finance 29(5):743–759
90. Roch O, Alegre A (2006) Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market. Comput Stat Data Anal 51:1312–1329
91. Concepcion Ausin M, Lopes HF (2010) Time-varying joint distribution through copulas. Comput Stat Data Anal 54(11):2383–2399
92. Renard B, Lang M (2007) Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology. Adv Water Resour 30:897–912
93. Kaishev VK, Dimitrina DS, Haberman S (2007) Modeling the joint distribution of competing risks survival times using copula functions. Insur Math Econ 41(3):339–361
94. Bedford T (2006) Copulas, degenerate distributions and quantile tests in competing risk problems. J Stat Plan Infer 136(5):1572–1587
95. Lo SMS, Wilke RA (2010) A copula model for dependent competing risks. J Roy Stat Soc Ser C (Appl Stat) 59(2):359–376
96. Cossette H, Marceau E, Marri F (2008) On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern. Insur Math Econ 43:444–455
97. Cossette H, Gaillardetz P, Marceau E, Rioux J (2002) On two dependent individual risk models. Insur Math Econ 30:153–166
98. Embrechts P, Hoing A, Juri A (2003) Using copulae to bound the value-at-risk for functions of dependent risks. Finance Stoch 7:145–167
99. Wang Y, Pham H (2009) The imperfect preventive maintenance policies for two-process cumulative damage model (submitted to Int J Syst Sci)
100. Wang Y, Pham H (2011) Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas. IEEE Trans Reliab, vol 6(4) to appear
101. Wang Y, Pham H (2010) Dependent competing risk model with multiple-degradation and random shock using time-varying copulas. 16th ISSAT international conference on reliability and quality in design, Washington D.C., pp 100–104
102. Wang Y, Pham H (2011) A multi-objective optimization of imperfect preventive maintenance policy for dependent competing risk system with hidden failure. IEEE Trans Reliab, vol 6(3) to appear