Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-07-07T14:05:00.614Z Has data issue: false hasContentIssue false

Optimal block replacement policies with multiple choice at failure

Published online by Cambridge University Press:  14 July 2016

Shey-Huei Sheu*
Affiliation:
National Taiwan Institute of Technology
*
Postal address: Department of Industrial Management, National Taiwan Institute of Technology, 43, Keelung Road, Section 4, Taipei, Taiwan 10772.

Abstract

A generalization of the block replacement policy (BRP) is proposed and analysed. Under such a policy, an operating system is preventively replaced at times kT (k = 1, 2, 3, ···), independently of its failure history. At failure an operating system is either replaced by a new or a used one or minimally repaired or remains inactive until the next planned replacement. The cost of the ith minimal repair of the new subsystem at age y depends on the random part C(y) and the deterministic part ci(y). The mathematical model is defined and general analytical results are obtained.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1992 

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]Barlow, R. E. and Hunter, L. C. (1960) Optimum preventive maintenance policies. Operat. Res. 8, 90100.Google Scholar
[2]Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
[3]Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
[4]Beichelt, F. (1981) A generalized block-replacement policy. IEEE Trans. Reliability 30, 171172.Google Scholar
[5]Berg, M. and Cléroux, R. (1982) The block replacement problem with minimal repair and random repair costs. J. Stat. Comput. Simul. 15, 17.Google Scholar
[6]Berg, M, Bienvenu, M. and Cléroux, R. (1986) Age replacement policy with age-dependent minimal repair. Infor 24, 2632.Google Scholar
[7]Bhat, B. R. (1969) Used item replacement policy. J. Appl. Prob. 6, 309318.Google Scholar
[8]Blanning, R. W. (1965) Replacement strategies. Operat. Res. Quart. 16, 253254.Google Scholar
[9]Block, H. W., Borges, W. S. and Savits, T. H. (1985) Age-dependent minimal repair. J. Appl. Prob. 22, 370385.Google Scholar
[10]Block, H. W., Borges, W. S. and Savits, T. H. (1988) A general age replacement model with minimal repair. Naval Res. Logist. 35, 365372.Google Scholar
[11]Boland, P. J. (1982) Periodic replacement when minimal repair costs vary with time. Naval Res. Logist. Quart. 29, 541546.Google Scholar
[12]Boland, P. J. and Proschan, F. (1982) Periodic replacement with increasing minimal repair costs at failure. Operat. Res. 30, 11831189.Google Scholar
[13]Brown, M. and Proschan, F. (1983) Imperfect repair. J. Appl. Prob. 20, 851859.Google Scholar
[14]Cléroux, R., Dubuc, S. and Tilquin, C. (1979) The age replacement problem with minimal repair and random repair cost. Operat. Res. 27, 11581167.Google Scholar
[15]Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
[16]Crookes, P. C. I. (1963) Replacement strategies. Operat. Res. Quart. 14, 167184.Google Scholar
[17]Ait Kadi, D. and Cléroux, R. (1988) Optimal block replacement policies with multiple choice at failure. Naval Res. Logist. 35, 99110.Google Scholar
[18]Marshall, A. W. and Olkin, I. (1967) A multivariate exponential distribution. J. Amer. Statist. Assoc. 62, 3044.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, 885889.Google Scholar
[20]Nakagawa, T. (1981) A summary of periodic replacement with minimal repair at failure. J. Operat. Res. Soc. Japan24, 213227.Google Scholar
[21]Nakagawa, T. (1982) A modified block replacement with two variables. IEEE Trans. Reliability 31, 398400.Google Scholar
[22]Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
[23]Savits, T. H. (1988) Some multivariate distributions derived from a non-fatal shock model. J. Appl. Prob. 25, 383390.Google Scholar
[24]Shaked, M. and Shanthikumar, J. G. (1986) multivariate imperfect repair. Operat. Res. 34, 437448.Google Scholar
[25]Sheu, S. H. (1987) Imperfect Repair Models In Reliability Theory. D. Sc. Thesis, University of Kentucky.Google Scholar
[26]Sheu, S. H. and Griffith, W. S. (1991) Multivariate age dependent imperfect repair. Naval Res. Logist. To appear.Google Scholar
[27]Tango, T. (1978) Extended block replacement policy with used item. J. Appl. Prob. 15, 560572.Google Scholar
[28]Tango, T. (1979) A modified block replacement policy using less reliable items. IEEE Trans. Reliability 5, 400401.Google Scholar