RESEARCH ARTICLE
Allocation of a relevation in redundancy problems
Félix Belzunce,
Carolina Martínez-Riquelme,
José M. Ruiz,
Corresponding Author
Félix Belzunce
Departamento Estadística e Investigación Operativa, Universidad de Murcia, Murcia, Spain
Félix Belzunce, Departamento Estadística e Investigación Operativa, Universidad de Murcia, Murcia, Spain.
Email: [email protected]
Search for more papers by this authorCarolina Martínez-Riquelme
Facultad de Matemáticas, Campus de Espinardo, Universidad de Murcia, Murcia, Spain
Search for more papers by this authorJosé M. Ruiz
Facultad de Matemáticas, Campus de Espinardo, Universidad de Murcia, Murcia, Spain
Search for more papers by this authorFélix Belzunce,
Carolina Martínez-Riquelme,
José M. Ruiz,
Corresponding Author
Félix Belzunce
Departamento Estadística e Investigación Operativa, Universidad de Murcia, Murcia, Spain
Félix Belzunce, Departamento Estadística e Investigación Operativa, Universidad de Murcia, Murcia, Spain.
Email: [email protected]
Search for more papers by this authorCarolina Martínez-Riquelme
Facultad de Matemáticas, Campus de Espinardo, Universidad de Murcia, Murcia, Spain
Search for more papers by this authorJosé M. Ruiz
Facultad de Matemáticas, Campus de Espinardo, Universidad de Murcia, Murcia, Spain
Search for more papers by this authorAbstract
The relevation can be considered as a replacement or repair policy in reliability, in which, when a unit fails, the unit is restored to a working condition just previous to the failure, in the sense that the age of the unit is not changed but the failure rate changes. It can be also considered as a generalization of the minimal repair policy and the load-sharing model. In this paper, we consider the problem of where to allocate a relevation in a system to increase the reliability of the system and the particular cases of load-sharing and minimal repair policies.
REFERENCES
- 1Boland PJ, El-Neweihi E, Proschan F. Stochastic order for redundancy allocations in series and parallel systems. Adv Appl Probab. 1992; 24(1): 161-171.
- 2El-Neweihi E, Sethuraman J. Optimal allocation under partial ordering of lifetimes of components. J Appl Probab. 1993; 25(4): 914-925.
- 3Boland PJ, Proschan F. Stochastic order in system reliability theory. Stochastic Orders and Their Applications. Cambridge, MA: Academic Press; 1994: 485-508.
- 4Singh H, Misra N. On redundancy allocations in systems. J Appl Probab. 1994; 31(4): 1004-1014.
- 5Meng FC. More on optimal allocation of component in coherent systems. J Appl Probab. 1996; 33(2): 548-556.
- 6Xie M, Lai CD. On the increase of the expected lifetime by parallel redundancy. Asia-Pacific J Oper Res. 1996; 13(2): 171-179.
- 7Singh H, Singh RS. Note: optimal allocation of resources to nodes of series systems with respect to failure rate ordering. Nav Res Logist. 1997; 44(1): 147-152.
- 8Mi J. Optimal active redundancy allocation in k-out-of-n system. J Appl Probab. 1999; 36(3): 927-933.
- 9Valdés JE, Zequeira RI. On the optimal allocation of an active redundancy in a two-component series system. Stat Probab Lett. 2003; 63(3): 325-332.
- 10Valdés JE, Zequeira RI. On the optimal allocation of two active redundancies in a two-component series system. Oper Res Lett. 2006; 34(1): 49-52.
- 11Romera R, Valdés JE, Zequeira RI. Active-redundancy allocations in systems. IEEE Trans Reliab. 2004; 53(3): 313-318.
- 12Yalaoui A, Chu C, Châtelet E. Reliability allocation problem in a series-parallel system. Reliab Eng Syst Saf. 2005; 90(1): 55-61.
- 13Li X, Hu X. Some new stochastic comparisons for redundancy allocations in series and parallel systems. Stat Probab Lett. 2008; 78(18): 3388-3394.
- 14Cha JH, Mi J, Yun WY. Modelling a general standby system and evaluation of its performance. Appl Stoch Model Bus Ind. 2008; 24(2): 159-169.
- 15Hu T, Wang Y. Optimal allocation of active redundancies in r-out-of-n systems. J Stat Plan Infer. 2009; 139(10): 3733-3737.
- 16Misra N, Dhariyal I, Gupta N. Optimal allocation of active spares in series systems and comparison of component and system redundancies. J Appl Probab. 2009; 46(1): 19-34.
- 17Valdés JE, Arango G, Zequeira RI, Brito G. Some stochastic comparisons in series systems with active redundancy. Stat Probab Lett. 2010; 80(11-12): 945-949.
- 18Li X, Ding W. Optimal allocation of the active redundancies to k-out-of-n systems with heterogeneous components. J Appl Probab. 2010; 47(1): 254-263.
- 19Misra N, Misra AK, Dhariyal ID. Standby redundancy allocation in series and parallel systems. J Appl Probab. 2011; 48(1): 43-55.
- 20Misra N, Misra AK, Dhariyal ID. Active redundancy allocations in series systems. Probab Eng Info Sci. 2011; 25(2): 219-235.
- 21Belzunce F, Martínez-Puertas H, Ruíz JM. On optimal allocation of redundant components for series and parallel systems of two dependent components. J Stat Plan Infer. 2011; 141(9): 3094-3104.
- 22Belzunce F, Martínez-Puertas H, Ruíz JM. On allocation of redundant components for systems with dependent components. Eur J Oper Res. 2013; 230(3): 573-580.
- 23Zhao P, Chan PS, Ng HKT. Optimal allocation of redundancies in series systems. Eur J Oper Res. 2012; 220(3): 673-683.
- 24Ding W, Li X. The optimal allocation of active redundancies to k-out-of-n systems with respect to the hazard rate ordering. J Stat Plan Infer. 2012; 142(7): 1878-1887.
- 25Nanda AK, Hazra NK. Some results on active redundancy at component level versus system level. Oper Res Lett. 2013; 41(3): 241-245.
- 26Li X, Wu Y, Zhang Z. On the allocation of general standby redundancy to series and parallel systems. Commun Stat Theory Methods. 2013; 42(22): 4056-4069.
- 27Zhao P, Chan PS, Li L, Ng HKT. On allocation of redundancies in two-component series systems. Oper Res Lett. 2013; 41(6): 690-693.
- 28Hazra NK, Nanda AK. Components redundancy versus system redundancy in different stochastic orderings. IEEE Trans Reliab. 2014; 63(2): 567-582.
- 29You Y, Li X. On allocating redundancies to k-out-of-n reliability systems. Appl Stoch Model Bus Ind. 2014; 30(3): 361-371.
- 30Zhuang J, Li X. Allocating redundancies to k-out-of-n systems with independent and heterogeneous components. Commun Stat Theory Methods. 2015; 44(24): 5109-5119.
- 31Zhao P, Zhang Y, Li L. Redundancy allocation at component level versus system level. Eur J Oper Res. 2015; 241(2): 402-411.
- 32Fang R, Li X. On allocating one active redundancy to coherent systems with dependent and heterogeneous components' lifetimes. Nav Res Logist. 2016; 63(4): 335-345.
- 33Jeddi H, Doostparast M. Optimal redundancy allocation problems in engineering systems with dependent component lifetimes. Appl Stoch Model Bus Ind. 2016; 32(2): 199-208.
- 34You Y, Fang R, Li X. Allocating active redundancies to k-out-of-n reliability systems with permutation monotone component lifetimes. Appl Stoch Model Bus Ind. 2016; 32(5): 607-620.
- 35Zhao P, Zhang Y, Chen J. Optimal allocation policy of one redundancy in a n-component series. Eur J Oper Res. 2017; 257(2): 656-668.
- 36Schechner Z. A load-sharing model: the linear breakdown rule. Nav Res Logis Quarter. 1984; 31(1): 137-144.
- 37 Home Reliability Edge Quarter 2,3. http://www.reliasoftindia.com/newsletter/4q2002/qalt.htm. Published 2003.
- 38Sutar SS, Naik-Nimbalkar UV. A model for k-out-of-n load-sharing systems. Commun Stat Theory Methods. 2016; 45(20): 5946-5960.
- 39Deshpande JV, Dewand I, Naik-Nimbalkar UV. A family of distributions to model load sharing systems. J Stat Plan Infer. 2010; 140(6): 1441-1451.
- 40Barlow R, Hunter L. Optimum preventive maintenance policies. Oper Res. 1960; 8(1): 90-100.
- 41Ascher H, Feingold H. Repairable Systems Reliability. New York, NY: Marcel Decker; 1984.
- 42Chahkandi M, Ahmadi J, Baratpour S. Some results for repairable systems with minimal repairs. Appl Stoch Model Bus Ind. 2014; 30(2): 218-226.
- 43Beutner E, Cramer E. Nonparametric meta-analysis for minimal-repair systems. Aust N Z J Stat. 2010; 52: 383-401.
- 44Li L, Hanson T, Damien P, Popova E. A Bayesian nonparametric test for minimal repair. Technometrics. 2014; 56(3): 393-406.
- 45Krakowski M. The relevation transform and a generalization of the gamma distribution function. RAIRO. 1973; 7(V2): 107-120.
- 46Baxter LA. Reliability applications of the relevation transform. Nav Res Logis Quater. 1982; 29(2): 323-330.
- 47Shanthikumar JG, Baxter LA. Closure properties of the relevation transform. Nav Res Logis Quater. 1985; 32(1): 185-189.
- 48Pellerey F, Shaked M, Zinn J. Nonhomogeneous Poisson processes and logconcavity. Probab Eng Inf Sci. 2000; 14(3): 353-373.
- 49Belzunce F, Lillo RE, Ruiz JM, Shaked M. Stochastic comparisons of nonhomogeneous processes. Probab Eng Inf Sci. 2001; 15(2): 199-224.
- 50Kapodistria S, Psarrakos G. Some extensions of the residual lifetime and its connection to the cumulative residual entropy. Probab Eng Inf Sci. 2012; 26(1): 129-146.
- 51Sordo MA, Psarrakos G. Stochastic comparisons of inter failure times under a relevation replacement policy. J Appl Probab. 2017; 54(1): 134-145.
- 52Cui L, Kuo W, Loh HT, Xie M. Optimal allocation of minimal & perfect repairs under resource constraints. IEEE Trans Reliab. 2004; 53(2): 193-199.
- 53da Costa Bueno V. Minimal repair redundancy for coherent system in its signatures representation. Am J Oper Res. 2011; 1(01): 8-15.
10.4236/ajor.2011.11002 Google Scholar
- 54Lindqvist BH, Samaniego FJ. On the signature of a system under minimal repair. Appl Stoch Model Bus Ind. 2015; 31(3): 297-306.
- 55Müller A, Stoyan D. Comparison methods for stochastic models and risks. Wiley Series in Probability and Statistics. Chichester, England: John Wiley & Sons, Ltd.; 2002.
- 56Shaked M, Shanthikumar GJ. Stochastic orders. Springer Series in Statistics. New York, NY: Springer; 2007.
10.1007/978-0-387-34675-5 Google Scholar
- 57Belzunce F, Martínez-Riquelme C, Mulero JM. An Introduction to Stochastic Orders. London, UK: Elsevier-Academic Press; 2015.
- 58Barlow RE, Proschan F. Statistical Theory of Reliability and Life Testing Probability Models. Silver Spring, MD: Holt Rinehart and Winston; 1975.
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