Optimal age and block replacement policies for a multi-component system with failure interaction

In this paper we consider a generalized age and block replacement policy for a multicomponent system with failure interaction. The i-th component (1 i N) has two types of failures. Type I and type II failures are age dependent. Type I failure (minor failure) is removed by a minimal repair, whereas type II failure (catastrophic failure) induces a total failure of the system (i.e. failure of all other components in the system) and is removed by an unplanned (or unscheduled) replacement of the system. For an age replacement maintenance policy, planned (or scheduled) replacements occur whenever an operating system reaches age T , whereas in the block replacement case, planned replacements occur every T units of time. The aim of this paper is to derive the expected long-run cost per unit time for each policy. The optimal T * which would minimize the cost rate is discussed. Various special cases are detailed. A numerical example is given to illustrate the method.

[1]  R. Cléroux,et al.  The block replacement problem , 1975 .

[2]  N. A. J. Hastings,et al.  An Economic Replacement Model , 1967 .

[3]  Thomas H. Savits.  A COST RELATIONSHIP BETWEEN AGE AND BLOCK REPLACEMENT POLICIES , 1988 .

[4]  C. S. Chen,et al.  Optimal Age and Block Replacement for a General Maintenance Model , 1992 .

[5]  Toshio Nishida,et al.  OPTIMAL REPLACEMENT POLICY FOR MINIMAL REPAIR MODEL , 1975 .

[6]  Masashi Kowada,et al.  Analysis of a system with minimal repair and its application to replacement policy , 1983 .

[7]  R. Dekker,et al.  A simple approximation to the renewal function (reliability theory) , 1990 .

[8]  R. Radner,et al.  Opportunistic Replacement of a Single Part in the Presence of Several Monitored Parts , 1963 .

[9]  T. Nakagawa,et al.  Optimal replacement policies for a two-unit system with failure interactions , 1993 .

[10]  Shunji Osaki,et al.  Optimum Replacement Policies for A System Composed of Components , 1981, IEEE Transactions on Reliability.

[11]  Menachem Berg,et al.  The block replacement problem with minima! repair and random repair costs , 1982 .

[12]  Henry W. Block,et al.  Age-dependent minimal repair , 1985, Journal of Applied Probability.

[13]  D. N. P. Murthy,et al.  A Combined Block and Repair Limit Replacement Policy , 1984 .

[14]  Frank Proschan,et al.  Periodic Replacement with Increasing Minimal Repair Costs at Failure , 1982, Oper. Res..

[15]  Shey-Huei Sheu,et al.  A generalized age and block replacement of a system subject to shocks , 1998, Eur. J. Oper. Res..

[16]  R. Barlow,et al.  Optimum Preventive Maintenance Policies , 1960 .

[17]  Mohamed Abdel-Hameed.  Optimum replacement of a system subject to shocks , 1986 .

[18]  Frank Beichelt.  A general preventive maintenance policy , 1976 .

[19]  M. Berg,et al.  Age Replacement Policy With Age-Dependent Minimal Repair* , 1986 .

[20]  T. H. Savits.  Some multivariate distributions derived from a non-fatal shock model , 1988 .

[21]  D. N. P. Murthy,et al.  Study of two‐component system with failure interaction , 1985 .

[22]  D. S. Bai,et al.  An Age Replacement Policy with Minimal Repair Cost Limit , 1986, IEEE Transactions on Reliability.

[23]  C. S. Chen,et al.  A discounted cost relationship , 1988 .

[24]  T. Nakagawa,et al.  Extended optimal replacement model with random minimal repair costs , 1995 .

[25]  Mohamed Abdel-Hameed,et al.  An imperfect maintenance model with block replacements , 1987 .

[26]  Robert Cléroux,et al.  A periodic maintenance model with used equipment and random minimal repair , 1990 .

[27]  Harshinder Singh,et al.  Optimum Replacement of a System Subject to Shocks: A Mathematical Lemma , 1986, Oper. Res..

[28]  Henry W. Block,et al.  A general age replacement model with minimal repair , 1988, Naval Research Logistics (NRL).

[29]  D. N. P. Murthy,et al.  Study of a multi-component system with failure interaction , 1985 .

[30]  Philip J. Boland.  Periodic replacement when minimal repair costs vary with time , 1982 .

[31]  N. Hastings.  The Repair Limit Replacement Method , 1969 .

[32]  Daoud Ait Kadi,et al.  Optimal block replacement policies with multiple choice at failure , 1988 .

[33]  C. T. Corney.  Reliability and Maintenance , 1966 .

[34]  Toshio Nakagawa.  A Modified Block Replacement with Two Variables , 1982, IEEE Transactions on Reliability.

[35]  Toshio Nakagawa.  A SUMMARY OF PERIODIC REPLACEMENT WITH MINIMAL REPAIR AT FAILURE , 1981 .

[36]  E. Muth.  An Optimal Decision Rule for Repair vs Replacement , 1977, IEEE Transactions on Reliability.