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Reliability assessment of a repairable system under online and offline preventive maintenance

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Abstract

This paper deals with the reliability modelling and evaluation of a linear consecutive 2-out-of-4 system under online and offline preventive maintenance. The failure and repair time are assumed exponentially distributed. Through the transition diagrams, a system of first-order linear differential difference equations is obtained. Explicit expressions of system availability, mean time to failure busy period of repairman and profit function using probabilistic approach have been developed. Impacts of online preventive maintenance, offline preventive maintenance, and failure and repair rate on system availability, profit and mean time to failure have been investigated. The results of this paper will enhance the system performance and will be useful for timely execution of proper maintenance improvement, decision, planning and optimisation.

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References

  • Adhikary DD, Bose GK, Bose D, Mitra S (2013) Maintenance class-based cost-effective preventive maintenance scheduling of coal-fired power plants. Int J Reliab Saf 7(4):358–371

    Google Scholar 

  • Aggarwal AK, Kumar S, Singh V (2017) Mathematical modeling and reliability analysis of the serial processes in feeding system of a sugar plant. Int J Syst Assur Eng Manag 8(1):435–450

    Google Scholar 

  • Ahmad R (2018) Reliability analysis comparison on punching tool sets due to different maintenance decisions: a case study from the pulp manufacturing industry. Int J Adv Manuf Technol 94(5–8):1969–1979

    Google Scholar 

  • Ali A, Khaliq S, Ali Z (2018) Reliability estimation of s-out-of-k system for non-identical stress–strength components. Life Cycle Reliab Saf Eng 7(1):33–41

    Google Scholar 

  • Barak MS, Sudesh N, Barak K (2018) Profit analysis of a two-unit cold standby system model operating under different weather conditions. Life Cycle Reliab Saf Eng 7(3):173–183

    MATH  Google Scholar 

  • Barron Y, Frostig E, Levikson B (2006) Analysis of r out of n systems with several repairmen, exponential life times and phase type repair times: an algorithmic approach. Eur J Oper Res Algorithm Approach 169:202–225

    MathSciNet  MATH  Google Scholar 

  • Batun S, Azizoglu M (2009) Single machine scheduling with preventive maintenances. Int J Prod Res 47:1753–1771. https://doi.org/10.1080/00207540701636348

    Article  MATH  Google Scholar 

  • Bhardwaj RK, Malik SC (2010) MTSF and cost effectiveness of 2-out-of-3 cold standby system with probability of repair and inspection. Int J Eng Sci Technol 2(1):5882–5889

    Google Scholar 

  • Bhardwj RK, Chander S (2007) Reliability and cost benefit analysis of 2-out-of-3 redundant system with general distribution of repair and waiting time, DIAS—technology review. Int J Bus IT 4(1):28–35

    Google Scholar 

  • Chander S, Bhardwai RK (2009) Reliability and economic analysis of 2-out-of-3 redundant system with priority to repair. Afr J Maths Comp Sci 2(11):230–236

    Google Scholar 

  • Chang C (2013) Optimum preventive maintenance policies for systems subject to random working times, replacement, and minimal repair. Comput Ind Eng 67:187–194

    Google Scholar 

  • Eryilmaz S (2012) m-consecutive-k-out-of-n: F system with overlapping runs: signature-based reliability analysis. Int J Oper Res 15(1):64–73

    MathSciNet  MATH  Google Scholar 

  • Feng Q, Coit DW (2010) Reliability analysis for multiple dependent failure processes: an MEMS application. Int J Perform Eng 6(1):100–102

    Google Scholar 

  • Goel LR, Sharma GC (1986) Gupta P (1986) Reliability analysis of a system with preventive maintenance, inspection and two types of repair. Microelectron Reliab 26(3):429–433

    Google Scholar 

  • GölbAs O, Demirel N (2017) Risk-based reliability allocation methodology to set a maintenance priority among system components: a case study in Mining. Eksploatacja i niezawodnosc 19(2):191

    Google Scholar 

  • Goyal N, Ram M, Amoli S, Suyal A (2017) Sensitivity analysis of a three-unit series system under k-out-of-n redundancy. Int J Qual Reliab Manag 34(6):770–784

    Google Scholar 

  • Grall A, Berenguer C, Dieulle L (2002) A condition-based maintenance policy for stochastically deteriorating systems. Reliab Eng Syst Saf 76:469–489

    Google Scholar 

  • Haggag MY (2009) Cost analysis of a system involving common cause failures and preventive maintenance. J Math Stat 5(4):305–310

    MATH  Google Scholar 

  • Huang W, Askin RG (2003) Reliability analysis of electronic devices with multiple competing failure modes involving performance aging degradation. Qual Reliab Eng Int 19:241–254

    Google Scholar 

  • Joseph VR, Yu IT (2006) Reliability improvement experiments with degradation data. IEEE Trans Reliab 55:149–157

    Google Scholar 

  • Julanto A, Yun EWY, Yamamoto H (2016) Preventive maintenance policy for linear consecutive k-out-of-n: F system. J Oper Res Soc Jpn 59(4):334–346

    MathSciNet  MATH  Google Scholar 

  • Julien B, Barreau M, Gerville-Rache L, Gurin F, Schimmerling P (2014) Reliability assessment based on degradation measurements: how to compare some models? Reliab Eng Syst Saf 131:236–241

    Google Scholar 

  • Kadyan MS (2013) Reliability and profit analysis of a single-unt system with preventive maintenance subject to maximum operation time. Eksploatacja i Niezawodnosc Maint Reliab 15(2):176–181

    Google Scholar 

  • Kadyan MS, Promila Kumar J (2014) Reliability modeling of a single-unit system with arbitrary distribution subject to different weather condition. Int J Syst Assur Eng Manag 5(3):313–319. https://doi.org/10.1007/s13198-013-0168-3

    Article  Google Scholar 

  • Keedy E, Feng Q (2012) A physics-of-failure based reliability and maintenance modeling framework for stent deployment and operation. Reliab Eng Syst Saf 103:94–101

    Google Scholar 

  • Khatab A, Nahas N, Nourelfath M (2009) Availbilty of k-out-of-n: G systems with non identical components subject to repair priorities. Reliab Eng Syst Saf 94:142–151

    Google Scholar 

  • Kumar R, Kadyan MS (2018) Reliability modelling and study of failure mechanism of distillery plant using supplementary variable technique. Life Cycle Reliab Saf Eng 7(3):137–146

    Google Scholar 

  • Kumar A, Ram M (2017) Effects of k-out-of-n: G/F and parallel redundancy in an industrial system through reliability approach. In: AIP conference proceedings, vol 1860, No. 1. AIP Publishing, p 020046

  • Kumar A, Saini M (2018) Comparison of reliability characteristics of two semi-Markov repairable systems under degradation and abnormal environment. Life Cycle Reliab Saf Eng 7(4):257–268

    Google Scholar 

  • Kumar A, Saini M, Devi K (2018a) Stochastic modeling of non-identical redundant systems with priority, preventive maintenance, and Weibull failure and repair distributions. Life Cycle Reliab Saf Eng 7(2):61–70

    Google Scholar 

  • Kumar R, Rajeevan AK, Shouri PV, Nair U (2018b) Markov modeling and reliability allocation in wind turbine for availability enhancement. Life Cycle Reliab Saf Eng 7(3):147–157

    Google Scholar 

  • Lal AK, Kaur M, Lata S (2013) Behavioral study of piston manufacturing plant through stochastic models. J Ind Eng Int 9:24

    Google Scholar 

  • Li Y, Yun MX (2011) Reliability analysis of a warm standby repairable system with priority in use. Appl Math Model 35:4295–4303. https://doi.org/10.1016/j.apm.2011.03.002

    Article  MathSciNet  MATH  Google Scholar 

  • Lin J, Pulido J, Asplund M (2015) Reliability analysis for preventive maintenance based on classical and Bayesian semi-parametric degradation approaches using locomotive wheel-sets as a case study. Reliab Eng Syst Saf 134:143–156

    Google Scholar 

  • Liu Y, Fan X (2016) Time-independent reliability analysis of bridge system based on mixed copula models. Math Probl Eng. https://doi.org/10.1155/2016/2720614

    Article  MathSciNet  MATH  Google Scholar 

  • Liu Z, Ma X, Yang J, Zhao Y (2014) Reliability modeling for systems with multiple degradation processes using inverse Gaussian process and copulas mathematical problems in engineering. Math Probl Eng. 2014:1–10. https://doi.org/10.1155/2014/829597

    Article  Google Scholar 

  • Lu H, Kolarik WJ, Lu SS (2001) Real-time performance reliability prediction. IEEE Trans Reliab 50:353–357

    Google Scholar 

  • Mahmoud MAW, Moshref ME (2010) On a two-unit cold standby system considering hardware, human error failures and preventive maintenance. Math Comput Model 51(5–6):736–745

    MathSciNet  MATH  Google Scholar 

  • Malik SC, Kumar A (2012) Reliability modelling of a computer system with priority to s/w replacement over h/w replacement subject to MOT and MRT. Int J Pure Appl Math 3(9):7191–7204

    Google Scholar 

  • Mujahid SN, Abdur Rahim M (2010) Optimal preventive maintenance warranty policy for repairable products with periodically increasing failure rate. Int J Oper Res 9(2):227–240

    MathSciNet  MATH  Google Scholar 

  • Niwas R, Kadyan MS (2015) Kumar J (2015) Probabilistic analysis of two reliability models of a single-unit system with preventive maintenance beyond warranty and degradation. Eksploatacja i Niezawodnosc Maint Reliab 17(4):535–543. https://doi.org/10.17531/ein.2015.4.8

    Article  Google Scholar 

  • Nourelfath M, Fitouhi M, Machani M (2010) An integrated model for production and preventive maintenance planning in multi-state systems. IEEE Trans Reliab 59(3):496–506

    Google Scholar 

  • Pan Z, Balakrishnan N (2011) Reliability modelling of degradation of products with multiple performance characteristics based on gamma processes. Reliab Eng Syst Saf 96:949–957

    Google Scholar 

  • Pawan AG, Lal AK, Sharma AK, Singh J (2005) Numerical analysis of reliability and availability of the serial processes in butter oil processing plant. Int J Qual Reliab Manag 22:303–316

    Google Scholar 

  • Peng H, Feng Q, Coit DW (2009) Simultaneous quality and reliability optimization for microengines subject to degradation. IEEE Trans Reliab 58:98–105

    Google Scholar 

  • Ram M (2013) On system reliability approaches: a brief survey. Int J Syst Assur Eng Manag 4(2):101–117

    Google Scholar 

  • Ram M, Kumar A (2014) Performance of a structure consisting a 2-out-of-3: F substructure under human failure. Arab J Sci Eng 39(11):8383–8394

    MATH  Google Scholar 

  • Ram M, Kumar A (2015) Performability analysis of a system under 1-out-of-2: G scheme with perfect reworking. J Braz Soc Mech Sci Eng 37(3):1029–1038. https://doi.org/10.1007/s40430-014-0277-y

    Article  Google Scholar 

  • Shakuntla C, Lal AK, Bhatia SS, Singh J (2011) Reliability analysis of polytube industry using supplementary variable technique. Appl Math Comput 218:3981–3992

    MATH  Google Scholar 

  • Shao J, Lamberson LR (1991) Modelling shared-load k-out-of-n : G systems. IEEE Trans Reliab. https://doi.org/10.1109/24.87129

    Article  MATH  Google Scholar 

  • Singh VV, Rawal DK, Ram M (2011) Study of reliability measures of a local area network via copula linguistics approach. Int J Qual Reliab 32(1):97–111

    Google Scholar 

  • Song S, Coit DW, Feng Q, Peng H (2014) Reliability analysis for multi-component systems subject to multiple dependent competing failure processes. IEEE Trans Reliab 63(1):331–345

    Google Scholar 

  • Taneja G, Goyal A, Singh D (2011) Reliability and cost benefit analysis of a system comprising one big unit and two small identical units with priority for operation/repair to big unit. Math Sci 5:234–248

    MATH  Google Scholar 

  • Tang J, Chen C, Huang L (2018) Reliability assessment models for dependent competing failure processes considering correlations between random shocks and degradations. Qual Reliab Eng Int. https://doi.org/10.1002/qre.2390

    Article  Google Scholar 

  • Tsai YA (2004) A study of availability centred preventive maintenance for multicomponent systems. Reliab Eng Syst Saf 84:261–270

    Google Scholar 

  • Uemura T, Dohi T, Kaio N (2010) Availability analysis of an intrusion tolerant distributed server system with preventive maintenance. IEEE Trans Reliab 59(1):18–29

    Google Scholar 

  • Umarani D, Seyezhai R (2018) Reliability assessment of two-phase interleaved boost converter. Life Cycle Reliab Saf Eng 7(1):43–52

    Google Scholar 

  • Uprety I (2012) Stochastic analysis of a reheating-furnace system subject to preventive maintenance and repair. Int J Oper Res 13(3):256–280

    MathSciNet  MATH  Google Scholar 

  • Waghmode LY, Patil RB (2016) Reliability analysis and life cycle cost optimization: a case study from Indian industry. Int J Qual Reliab Manag 33(3):414–429

    Google Scholar 

  • Wang S (2013) Integrated model of production planning and imperfect preventive maintenance policy for single machine system. Int J Oper Res 18(2):140–156

    MathSciNet  MATH  Google Scholar 

  • Wu S, Zuo MJ (2010) Linear and nonlinear preventive maintenance models. IEEE Trans Reliab 59(1):242–249

    Google Scholar 

  • Yusuf I (2016) Reliability modelling of a parallel system with a supporting device and two types of preventive maintenance. Int J Oper Res 25(3):269–287

    MathSciNet  MATH  Google Scholar 

  • Yusuf I, Hussaini N (2012) Evaluation Of reliability and availability characteristics of 2-out-of-3 standby system under a perfect repair condition. Am J Math Stat 2(5):114–119

    Google Scholar 

  • Zhang Y, Ma Y, Ouyang L, Liu L (2018) A novel reliability model for multi-component systems subject to multiple dependent competing risks with degradation rate acceleration. Eksploatacja i Niezawodnosc Maint Reliab 20(4):579–589. https://doi.org/10.17531/ein.2018.4.9

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to the anonymous reviewers for their constructive comments which have helped to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Bayero University, Kano, Nigeria

    Ibrahim Yusuf

  2. Department of Mathematics, Federal University, Dutse, Nigeria

    Bashir Yusuf

  3. Department of Mathematics and Computer Science, Sule Lamido University, Kafin Hausa, Nigeria

    Kabiru Suleiman

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  1. Ibrahim Yusuf
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  2. Bashir Yusuf
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  3. Kabiru Suleiman
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Correspondence to Ibrahim Yusuf.

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Yusuf, I., Yusuf, B. & Suleiman, K. Reliability assessment of a repairable system under online and offline preventive maintenance. Life Cycle Reliab Saf Eng 8, 391–406 (2019). https://doi.org/10.1007/s41872-019-00094-z

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