Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T20:16:35.015Z Has data issue: false hasContentIssue false
  • English
  • Français

A modified block replacement policy with two variables and general random minimal repair cost

Part of: Operations research and management science Special processes Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Shey-Huei Sheu
Shey-Huei Sheu*
Affiliation:
National Taiwan Institute of Technology
*
∗Postal address: Department of Industrial Management, National Taiwan Institute of Technology, Taipei, Taiwan.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a modified block replacement with two variables and general random minimal repair cost. Under such a policy, an operating system is preventively replaced by new ones at times kT (k= 1, 2, ···) independently of its failure history. If the system fails in [(k − 1)T, (k − 1)T+ T0) it is either replaced by a new one or minimally repaired, and if in [(k − 1) T + T0, kT) it is either minimally repaired or remains inactive until the next planned replacement. The choice of these two possible actions is based on some random mechanism which is age-dependent. The cost of the ith minimal repair of the system at age y depends on the random part C(y) and the deterministic part ci (y). The expected cost rate is obtained, using the results of renewal reward theory. The model with two variables is transformed into a model with one variable and the optimum policy is discussed.

Keywords

MAINTENANCERELIABILITYSYSTEMS

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K10: Applications (reliability, demand theory, etc.) 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 557 - 572
Copyright
Copyright © Applied Probability Trust 1996 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ait Kadi, D. and Cléroux, R. (1988) Optimal block replacement policies with multiple choice at failure. Naval Res. Logist. 35, 99–110.3.0.CO;2-3>CrossRefGoogle Scholar
[2] Ait Kadi, D., Beaucaire, C. and Cléroux, R. (1990) A periodic maintenance model with used equipment and random minimal repair. Naval Res. Logist. 37, 855–865.Google Scholar
[3] Ait Kadi, D. and Cléroux, R. (1991) Replacement strategies with mixed corrective actions at failure. Comput. Operat. Res. 18, 141–149.CrossRefGoogle Scholar
[4] Barlow, R. E. and Hunter, L. C. (1960) Optimum preventive maintenance policies. Operat. Res. 8, 90–100.Google Scholar
[5] Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability Wiley, New York.Google Scholar
[6] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
[7] Beichelt, F. (1981) A generalized block-replacement policy. IEEE Trans. Reliab. 30, 171–172.CrossRefGoogle Scholar
[8] Berg, M. and Cléroux, R. (1982) The block replacement problem with minimal repair and random repair costs. J. Statist. Comput. Simul. 15, 1–7.Google Scholar
[9] Berg, M., Bienvenu, M. and Cléroux, R. (1986) Age replacement policy with age-dependent minimal repair. Infor 24, 26–32.Google Scholar
[10] Bhat, B. R. (1969) Used item replacement policy. J. Appl. Prob. 6, 309–318.Google Scholar
[11] Blanning, R. W. (1965) Replacement strategies. Operat. Res. Quart. 16, 253–254.Google Scholar
[12] Block, H. W., Borges, W. S. and Savits, T. H. (1985) Age-dependent minimal repair. J. Appl. Prob. 22, 370–385.Google Scholar
[13] Block, H. W., Borges, W. S. and Savits, T. H. (1988) A general age replacement model with minimal repair. Naval Res. Logist. 35, 365–372.Google Scholar
[14] Boland, P. J. (1982) Periodic replacement when minimal repair costs vary with time. Naval Res. Logist. Quart. 29, 541–546.Google Scholar
[15] Boland, P. J. and Proschan, F. (1982) Periodic replacement with increasing minimal repair costs at failure. Operat. Res. 30, 1183–1189.Google Scholar
[16] Cléroux, R., Dubuc, S. and Tilquin, C. (1979) The age replacement problem with minimal repair and random repair cost. Operat. Res. 27, 1158–1167.Google Scholar
[17] Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
[18] Crookes, P. C. I. (1963) Replacement strategies. Operat. Res. Quart. 14, 167–184.Google Scholar
[19] Murthy, D. N. P. and Nguyen, D. G. (1982) A note on extended block replacement policy with used items. J. Appl. Prob. 19, 885–889.Google Scholar
[20] Nakagawa, T. (1981) A summary of periodic replacement with minimal repair at failure. J. Operat. Res. Soc. Japan 24, 213–227.Google Scholar
[21] Nakagawa, T. (1982) A modified block replacement with two variables. IEEE Trans. Reliab. 31, 398–400.Google Scholar
[22] Nakagawa, T. (1979) A summary of block replacement policies. R.A.I.R.O. Operat. Res. 13, 351–361.Google Scholar
[23] Nguyen, D. G. and Murthy, D. N. P. (1984) A combined block and repair limit replacement policy. J. Operat. Res. Soc. 35, 653–658.Google Scholar
[24] Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
[25] Savits, T. H. (1988) Some multivariate distributions derived from a non-fatal shock model. J. Appl. Prob. 25, 383–390.Google Scholar
[26] Shaked, M. and Shanthikumar, J. G. (1986) Multivariate imperfect repair. Operat. Res. 34, 437–448.Google Scholar
[27] Sheu, S. H. (1991) A generalized block replacement policy with minimal repair and general random repair costs for a multi-unit system. J. Opl. Res. Soc. 42, 331–341.Google Scholar
[28] Sheu, S. H. and Griffith, W. S. (1991) Multivariate age dependent imperfect repair. Naval Res. Logist. 38, 839–850.Google Scholar
[29] Tango, T. (1978) Extended block replacement policy with used item. J. Appl. Prob. 15, 560–572.Google Scholar
[30] Tango, T. (1979) A modified block replacement policy using less reliable items. IEEE Trans. Reliab. 5, 400–401.Google Scholar