Abstract
Availability is a very important measure of system performance. A great deal of research works on it have been done. This article reviews the recent major results in this field. Systems whose failures are either self-announcing or not self-announcing are considered in these works, various repair methods and different inspection policies are explored as well. Some of these studies derive the expressions of the steady-state availability, limiting average availability, and others give the expressions of the instantaneous availability explicitly or recursively.
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Barlow, R. E., & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart & Winston.
Barroeta, C. E. (2005). Risk and economic estimation of inspection policy for periodically tested repairable components, MS thesis.
Berrade, M. D. (2012). A two-phase inspection policy with imperfect testing. Applied Mathematical Modelling, 36, 108–114.
Biswas, J., & Sarkar, J. (2000). Availability of a system maintained through several imperfect repairs before a replacement or a perfect repair. Statistics & Probability Letters, 50, 105–114.
Biswas, A., Sarkar, J., & Sarkar, S. (2003). Availability of a periodically inspected system, maintained under an imperfect-repair policy. IEEE Transactions on Reliability, 52(3).
Block, H. W., Borges, W. S., & Savits, T. H. (1985). Age-dependent minimal repair. Journal of Applied Probability, 22, 370–385.
Brown, M., & Proschan, F. (1983). Imperfect repair. Journal of Applied Probability, 20, 851–859.
Cha, J. H., & Kim, J. J. (2001). On availability of Bayesian imperfect repair model. Statistics & Probability Letters, 53, 181–187.
Cha, J. H., & Kim, J. J. (2002). On the existence of the steady state availability of imperfect repair model. Sankhya Series B, 64, 76–81.
Cha, J. H., Lee, S., & Mi, J. (2004). Bounding the optimal burn-in time for a system with two types of failure. Naval Research Logistics: An International Journal, 51, 1090–1101.
Chelbi, A., & Ait-Kadi, D. (2000). Generalized inspection strategy for randomly failing systems subjected to random shocks. International Journal of Production Economics, 64, 379–384.
Chung, W. K. (1994). Reliability and availability analysis of warm standby systems with repair and multiple critical errors. Microelectronics Reliability, 34(1), 153–155.
Cui, L. R. & Xie, M. (2001). Availability analysis of periodically inspected systems with random walk model 38, 860–871.
Cui, L. R., & Xie, M. (2005). Availability of a periodically inspected system with random repair or replacement times. Journal of Statistical Planning and Inference, 131, 89–100.
De Smidt-Destombes, K. S., van der Heijdenb, M. C., & van Harten, A. (2004). On the availability of a k-out-of-N system given limited spares and repair capacity under a condition based maintenance strategy. Reliability Engineering and System Safety, 83, 287–300.
De Smidt-Destombes, K. S., van der Heijden, M. C., & van Harten, A. (2006). On the interaction between maintenance, spare part inventories and repair capacity for a k-out-of-N system with wear-out. European Journal of Operational Research, 174, 182–200.
De Smidt-Destombes, K. S., van der Heijdenb, M. C., & van Harten, A. (2007). Availability of k-out-of-N systems under block replacement sharing limited spares and repair capacity. International Journal of Production Economics, 107, 404–421 (2007)
De Smidt-Destombes, K. S., vander Heijden, M. C., & van Harten, A. (2009). Joint optimization of spare part inventory, maintenance frequency and repair capacity for k-out-of-N systems. International Journal of Production Economics, 118, 260–268.
Dhillon, B. S., & Yang, N. (1992). Reliability and availability analysis of warm standby systems with common-cause failures and human errors. Microelectron Reliability, 32(4), 561–575.
Dhillon, B. S. (1993). Reliability and availability analysis of a system with warm standby and common cause failures. Microelectron Reliability, 33(9), 1343–1349.
Dieulle, L. (1999). Reliability of a system with Poisson inspection times. Journal of Applied Probability, 36, 1140–1154.
Fawzi, B. B., & Hawkes, A. G. (1991). Availability of an R-out-of-N system with spares and repairs. Journal of Applied Probability, 28, 397–408.
Frostig, E., & Levikson, B. (2002). On the availability of R out of N repairable systems. Naval Research Logistics, 49(5), 483–498.
Gut, A., & Jansons, S. (1983). The limiting behaviour of certain stopped sums and some applications. Scandinavian Journal of Statistics, 10, 281–292.
Høyland, A., & Rausand, M. (1994). System reliability theory. New York: Wiley.
Huang, K., & Mi, J. (2013). Properties and computation of interval availability of system. Statistics and Probability Letter, 83, 1388–1396.
Ito, K., & Nakagawa, T. (2000). Optimal inspection policies for a storage system with degradation at periodic tests. Mathematical and Computer Modelling, 31, 191–195.
Jardine, A. K. S., & Tsang, A. H. C. (2006). Maintenance, replacement, and reliability: Theory and applications. Boca Raton: CRC Press.
Jiang, R. Y., & Jardine, A. K. S. (2006). Optimal failure-finding interval through maximizing availability. International Journal of Plant Engineering and Management, 11, 174–178.
Klutke, G. A., Wortman, M. A., & Ayhan, H. (1996). The availability of inspected systems subject to random deterioration. Probability in the Engineering and Informational Sciences, 10, 109–118.
Klutke, G. A., & Yang, Y. J. (2002). The availability of inspected systems subject to shocks and graceful degradation. IEEE Transactions on Reliability, 51(3), 371–374.
Lau, H. C., Song, H. W., See, C. T., & Cheng, S. Y. (2004). Evaluation of time-varying availability in multi-echelon spare parts systems with passivation. European Journal of Operational Research, 170(1), 91–105.
Li, X., Zuo, M. J., & Yam, R. C. M. (2006). Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down. Reliability Engineering and System Safety, 91, 305–310.
Lim, J. H., Lu, K. L., & Park, D. H. (1998). Bayesian imperfect repair model. Communication in Statistics Theory, 27(4), 965–984.
Mi, J. (1994). Burn-in and maintenance policies. Advanced Applied Probability, 26, 207–221.
Mi, J. (1995). Limiting behavior of some measures of system availability. Journal of Applied Probability, 32, 482–493.
Mi, J. (1999). On measure of system interval availability. Probability in the Engineering and Informational Sciences, 13, 359–375.
Mi, J. (2002). On bounds to some optimal policies in reliability. Journal of Applied Probability, 39, 491–502.
Mi, J. (2006a). Limiting availability of system with non-identical lifetime distributions and non-identical repair time distributions. Statistics & Probability Letter, 76, 729–736.
Mi, J. (2006b). Pseudo availability of repairable system. Methodology and Computing in Applied Probability, 8, 93–103.
Mishra, A., & Jain, M. (2013). Maintainability policy for deteriorating system with inspection and common cause failure. International Journal of Engineering Transactions C: Aspects, 26(6), 631–640.
Pak, A., Pascual, R., & Jarding, A. K. S. (2006). Maintenance and replacement policies for protective devices with imperfect repairs, Technical report.
Pascual, R., Louit, D., & Jardine, A. K. S. (2011). Optimal inspection intervals for safety systems with partial inspections. Journal of the Operational Research Society, 62, 2051–2062.
Pham-Gia, T., & Turkkan, N. (1999) System availability in a gamma alternating renewal process. Naval Research Logistics, 46
Rényi, A. (1957). On the asymptotic distribution of the sum of a random number of independent random variables. Acta Mathematica Academiae Scientiarum Hungaricae, 8, 193–199.
Rise, J. (1979). Compliance test plans for reliability. In Proceedings of the 1979 annual reliability and maintenance symposium.
Sarkar, J., & Biswas, A. (2010). Availability of a one-unit system supported by several spares and repair facilities. Journal of the Korean Statistical Society, 39, 165–176.
Sarkar, J., & Chaudhuri, G. (1999). Availability of a system with gamma life and exponential repair time under a perfect repair policy. Statistics & Probability Letters, 43, 189–196.
Sarkar, J., & Li, F. (2006). Limiting average availability of a system supported by several spares and several repair facilities. Statistics & Probability Letters, 76, 1965–1974.
Sarkar, J., & Sarkar, S. (2000). Availability of a periodically inspected system under perfect repair. Journal of Statistical Planning and Inference, 91, 77–90.
Sarkar, J., & Sarkar, S. (2001). Availability of a periodically inspected system supported by a spare unit, under perfect repair or perfect upgrade. Statistics & Probability Letters, 53, 207–217.
Takács, L. (1957). On certain sojourn time problems in the theory of stochastic processes. Acta Mathematica Academiae Scientiarum Hungaricae, 8, 169–191.
Tang, T. Q., Lin, D. M., Banjevic, D., & Andrew, K. S. J. (2013). Availability of a system subject to hidden failure inspected at constant intervals with non-negligible downtime due to inspection and downtime due to repair/replacement. Journal of Statistical Planning and Inference, 143, 176–185.
Vaurio, J. K. (1997). On time-dependent availability and maintenance optimization of standby units under various maintenance policies. Reliability Engineering and System Safety, 56, 79–89.
Vaurio, J. K. (1999). Availability and cost functions for periodically inspected preventively maintained units. Reliability Engineering and Systems Safety, 63, 133–140.
Wang, K. H., Dong, W. L., & Jyh-Bin Ke, J. B. (2006). Comparison of reliability and the availability between four systems with warm standby components and standby switching failures. Applied Mathematics and Computation, 183, 1310–1322.
Wang, K. H., & Chen, Y. J. (2009). Comparative analysis of availability between three systems with general repair times, reboot delay and switching failures. Applied Mathematics and Computation, 215, 384–394.
Wortman, M. A., & Klutke, G. A. (1994). On maintained systems operating in a random environment. Journal of Applied Probability, 31, 589–594.
Wortman, M. A., Klutke, G. A., & Ayhan, H. (1994). A maintenance strategy for systems subjected to deterioration governed by random shocks. IEEE Transaction on Reliability, 43, 439–445.
Yadavalli, V. S. S., Botha, M., & Bekker, A. (2002). Asymptotic confidence limits for the steady state availability of a two-unit parallel system with preparation time for the repair facility. Asia-Pacific Journal of Operational Research, 19, 249–256.
Yam, R. C. M., Zuo, M. J., & Zhang, Y. L. (2003). A method for evaluation of reliability indices for repairable circular consecutive-k-out-of-n: F systems. Reliability Engineering and System Safety, 79(1), 1–9.
Yang, Y. J., & Klutke, G. A. (2000). Improved inspection schemes for deteriorating equipment. Probability Engineering Information Sciences, 14(4), 445–460.
Yang, Y. J., & Klutke, G. A. (2001). A distribution-free lower bound for availability of quantile-based inspection schemes. IEEE Transactions on Reliability, 50(4), 419–421.
Yeh, L. (1995). An optimal inspection-repair-replacement policy for standby systems. Journal of Applied Probability, 32, 212–223.
Zhang, T. L., & Horigome, M. (2000). Availability of 3-out-of-4: G warm standby system. IEEE Transactions on Fundamentals of Electronics Communications and Computer, E83-A(5), 857–862.
Zhang, T. L., Xie, M., & Horigome, M. (2006). Availability and reliability of k-out-of-(M+N): G warm standby systems. Reliability Engineering and System Safety, 91, 381–387.
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Huang, K., Mi, J. (2016). Availability of Systems with or Without Inspections. In: Pham, H. (eds) Quality and Reliability Management and Its Applications. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-6778-5_9
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DOI: https://doi.org/10.1007/978-1-4471-6778-5_9
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