Summary
An overview of some mathematical models of reliability and maintenance is presented. Emphasis is laid on some more recent developments, which use tool from the theory of stochastic processes. This framework allows to observe reliability systems on different information levels and to optimize maintenance actions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arias, E.: A Stochastic Process Approach to Multivariate Reliability Systems: Notions Based on Conditional Stochastic Order. Mathematics of Operations Research 6, 263–276 (1981a)
Arjas, E.: The Failure and Hazard Processes in Multivariate Reliability Systems. Mathematics of Operations Research 6, 551–562 (1981b)
Arjas, E.: Survival Models and Martingale Dynamics. Scand. J. Statist. 16, 177–225 (1989)
Arias, E.: Information and Reliability: A Bayesian Perspective. In: Barlow, R., Clarotti, C., Spizzichino, F. (eds.): Reliability and Decision Making. London: Chapman and Hall 1993, pp. 115–135
Arjas, E., Norros, I.: Change of Life Distribution via Hazard Transformation: An Inequality with Application to Minimal Repair. Mathematics of Operations Research 14, 355–361 (1989)
Aven, T.: Optimal Replacement Under a Minimal Repair Strategy–A General Failure Model. Adv. Appl. Prob. 15, 198–211 (1983)
Aven, T.: Reliability and Risk Analysis. London: Elsevier 1992
Aven, T.: Availability Analysis of Monotone Systems. In this volume (1996a), pp. 206–223
Aven T.: Optimal Replacement of Monotone Repairable Systems. In this volume (1996b), pp. 224–238
Aven, T., Bergman, B.: Optimal Replacement Times, a General Set-up. J. Appl. Prob. 23, 432–442 (1986)
Barlow, R., Hunter, L.: Optimum Preventive Maintenance Policies. Operations Res. 8, 90–100 (1960)
Barlow, R., Proschan, F.: Statistical Theory of Reliability and Life Testing. New York: Holt, Rinehart and Winston 1975
Basu, A.: Multivariate Exponential Distributions and Their Applications in Reliability. In: Krishnaiah, P. R., Rao, C. R. (eds.): Handbook of Statistics 7. Quality Control and Reliability. Amsterdam: North-Holland 1988, pp. 99–111
Beichelt, F.: A Unifying Treatment of Replacement Policies with Minimal Repair. Nay. Res. Log. Q. 40, 51–67 (1993)
Bergman, B.: On Reliability Theory and Its Applications. Scand. J. Statist. 12, 1–41 (1985)
Block, H., Borges, W., Savits, T.: Age-Dependent Minimal Repair. J. Appl. Prob. 22, 370–385 (1985)
Brémaud, P.: Point Processes and Queues. Martingale Dynamics. New York: Springer 1981
Çinlar, E.: Markov and Semi-Markov Models of Deterioration. In: Abdel-Hameed, M., Çinlar, E., Quinn, J (eds.): Reliability Theory and Models. Orlando: Academic Press 1984, pp. 3–41
Çinlar, E., Ozekici, S.: Reliability of Complex Devices in Random Environments. Probab. Engrg. Inform. Sci. 1, 97–115 (1987)
Çinlar, E., Shaked, M., Shanthikumar, G.: On Lifetimes Influenced by a Common Environment. Stoch. Proc. Appl. 33, 347–359 (1989)
Doksum, K.: Degradation Rate Models for Failure Time and Survival Data. CWI Quarterly 4, 195–203 (1991)
Dominé, M.: First Passage Time Distribution of a Wiener Process with Drift Concerning Two Elastic Barriers. J. Appl. Prob.. To appear (1996)
Freund, J. E.: A Bivariate Extension of the Exponential Distribution. J. Amer. Stat. Ass. 56, 971–977 (1961)
Gertsbakh, I.: Asymptotic Methods in Reliability: A Review. Adv. Appl. Prob. 16, 147–175 (1984)
Heinrich, G., Jensen, U.: Optimal Replacement Rules Based on Different Information Levels. Nay. Res. Log. Q. 39, 937–955 (1992)
Heinrich, G., Jensen, U.: Parameter Estimation for a Bivariate Lifetime Distribution in Reliability with Multivariate Extensions. Metrika 42, 49–65 (1995)
Heinrich, G., Jensen, U.: Bivariate Lifetime Distributions and Optimal Replacement. ZOR-Methods and Models of OR. To appear (1996)
Hutchinson, T. P., Lai, C. D.: Continuous Bivariate Distributions, Emphasizing Applications. Adelaide: Rumbsby Scientific Publishing 1990
Jensen, U.: Monotone Stopping Rules for Stochastic Processes in a Semimartingale Representation with Applications. Optimizatiom 20, 837–852 (1989)
Jensen, U.: A General Replacement Model. ZOR-Methods and Models of Operations Research 34, 423–439 (1990)
Jensen, U.: An Optimal Stopping Problem in Risk Theory. Scand. Act. J.. To appear (1996)
Jensen, U., Hsu, G.: Optimal Stopping by means of Point Process Observations with Applications in Reliability. Mathematics of Operations Research 18, 645–657 (1993)
Koch, G.: A Dynamical Approach to Reliability Theory. Proc. Int. School of Phys. “Enrico Fermi”, XCIV. Amsterdam: North-Holland 1986, pp. 215–240
Marshall, A. W., Olkin, I.: A Multivariate Exponential Distribution. J. Amer. Stat. Ass. 62, 30–44 (1967)
Natvig, B.: Reliability: Importance of Components. In: Kotz, S., Johnson, N. (eds.): Encyclopedia of Statistical Sciences 8. New York: Wiley 1988, pp. 17–20
Natvig, B.: On Information-Based Minimal Repair and the Reduction in Remaining System Lifetime due to the Failure of a Specific Module. J. Appl. Prob. 27, 365–375 (1990)
Ozekici, S.: Complex Systems in Random Environments. In this volume (1996a), pp. 137–157
Ozekici, S.: Optimal Replacement of Complex Systems. In this volume (1996b), pp. 158–169
Phelps, R.: Optimal Policy for Minimal Repair. J. Opl. Res. 34, 425–427 (1983)
Pierskalla, W., Voelker, J.: A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems. Nay. Res. Log. Q. 23, 353–388 (1976)
Rogers, C., Williams, D.: Diffusions, Markov Processes and Martingales. Vol. 1, 2nd ed. Chichester: Wiley 1994
Shaked, M., Shanthikumar, G.: Multivariate Imperfect Repair. Oper. Res. 34, 437–448 (1986)
Shaked, M., Shanthikumar, G.: Reliability and Maintainability. In: Heyman, D., Sobel, M. (eds.): Stochastic Models. Vol. 2. Amsterdam: North-Holland 1990, pp. 653–713
Shaked, M., Shanthikumar, G.: Dynamic Multivariate Aging Notions in Reliability Theory. Stoch. Proc. Appl. 38, 85–97 (1991)
Sherif, Y., Smith, M.: Optimal Maintenance Models for Systems Subject to Failure. A Review. Nay. Res. Log. Q. 28, 47–74 (1981)
Stadje, W., Zuckerman, D.: Optimal Maintenance Strategies for Repairable Systems with General Degree of Repair. J. Appl. Prob. 28, 384–396 (1991)
Valdez-Flores, C., Feldman, R.: A Survey of Preventive Maintenance Models for Stochastically Deteriorating Single-Unit Systems. Nay. Res. Log. Q. 36, 419–446 (1989)
Van der Duyn Schouten, F.: Maintenance Policies for Multicomponent Systems: An Overview. In this volume (1996), pp. 117–136
Yashin, A., Arjas, E.: A Note on Random Intensities and Conditional Survival Functions. J. Appl. Prob. 25, 630–635 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jensen, U. (1996). Stochastic Models of Reliability and Maintenance: An Overview. In: Özekici, S. (eds) Reliability and Maintenance of Complex Systems. NATO ASI Series, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03274-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-03274-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08250-4
Online ISBN: 978-3-662-03274-9
eBook Packages: Springer Book Archive