A Periodic Replacement Model Based on Cumulative Repair-Cost Limit for a System Subjected to Shocks

A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As these shocks occur, the system experiences one of two types of failures: a type-I failure (minor), rectified by a minimal repair; or a type-II failure (catastrophic) that calls for a replacement. In this paper, we consider a periodic replacement model with minimal repair based on a cumulative repair-cost limit. Under such a policy, the system is anticipatively replaced at the n -th type-I failure, or at the k-th type-I failure (k <; n) at which the accumulated repair cost exceeds the pre-determined limit, or at any type-II failure, whichever occurs first. The minimum-cost replacement policy is studied by showing its existence, uniqueness, and structural properties. Our model is a generalization of several classical models in maintenance literature. Some numerical analyses are also presented.

[1]  Kun‐Jen Chung,et al.  A simple procedure to compute the optimal repair cost limit under minimal repair , 1996 .

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

[3]  Toshio Nakagawa,et al.  Optimal Number of Failures before Replacement Time , 1983, IEEE Transactions on Reliability.

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

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

[6]  Kyung Soo Park.  Cost limit replacement policy under minimal repair , 1983 .

[7]  Kyung Soo Park,et al.  Optimal number of minor failures before replacement , 1987 .

[8]  Cun Hua Qian,et al.  Optimal preventive maintenance policies for a shock model with given damage level , 2005 .

[9]  T. H. Savits,et al.  Age Dependent Minimal Repair. , 1985 .

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

[11]  Tadashi Dohi,et al.  A new graphical method to estimate the optimal repair-time limit with incomplete repair and discounting , 2003 .

[12]  Shey-Huei Sheu,et al.  An Extended Periodic Imperfect Preventive Maintenance Model With Age-Dependent Failure Type , 2009, IEEE Transactions on Reliability.

[13]  Kyung S. Park.  Pseudodynamic cost limit replacement model under minimal repair , 1985 .

[14]  Tadashi Dohi,et al.  A graphical method to repair-cost limit replacement policies with imperfect repair , 2000 .

[15]  Toshio Nakagawa,et al.  The Optimum Repair Limit Replacement Policies , 1974 .

[16]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[17]  Toshio Nakagawa,et al.  GENERALIZED MODELS FOR DETERMINING OPTIMAL NUMBER OF MINIMAL REPAIRS BEFORE REPLACEMENT , 1981 .

[18]  Hidenori Morimura,et al.  ON SOME PREVENTIVE MAINTENANCE POLICIES , 1963 .

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

[20]  Kyung S. Park.  Optimal Number of Minimal Repairs before Replacement , 1979, IEEE Transactions on Reliability.

[21]  Min-Tsai Lai.  A periodical replacement model based on cumulative repair-cost limit , 2007 .

[22]  Kyung Soo Park,et al.  Optimal number of major failures before replacement , 1985 .

[23]  Hidenori Morimura,et al.  A NEW POLICY FOR PREVENTIVE MAINTENANCE , 1962 .

[24]  D. N. P. Murthy,et al.  A Note on the Repair Limit Replacement Policy , 1980 .

[25]  Frank Proschan,et al.  Optimum Replacement of a System Subject to Shocks , 1983, Oper. Res..

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

[27]  Frank Beichelt,et al.  A Replacement Policy Based on Limits for the Repair Cost Rate , 1982, IEEE Transactions on Reliability.

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

[29]  P. K. Kapur,et al.  Some replacement policies with minimal repairs and repair cost limit , 1989 .

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

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

[32]  Shey-Huei Sheu,et al.  Extended optimal age-replacement policy with minimal repair of a system subject to shocks , 2006, Eur. J. Oper. Res..

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

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

[35]  Toshio Nakagawa,et al.  Replacement and minimal repair policies for a cumulative damage model with maintenance , 2003 .

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

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

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

[39]  Frank Beichelt.  A replacement policy based on limiting the cumulative maintenance cost , 2001 .

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

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

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

[43]  Menachem Berg,et al.  A Marginal Cost Analysis for an Age Replacement Policy With Minimal Repair , 1982 .