An Optimal Inspection and Replacement Policy of a Markovian Deterioration System

An optimal inspection and replacement policy is discussed for a continuous time Markovian deterioration system whose state can be identified only by inspection. The costs incurred are inspection cost, operating cost and replacement cost. The problem is to determine an optimal policy which minimizes the expected total discounted cost in an infinite time span and to examine the structure of an optimal policy. Some properties are obtained, that is, a control limit rule for replacement holds and the inspection time interval becomes shorter as the system deteriorates.

[1]  Naoto Kaio,et al.  Optimum ordering policies with two kinds of lead times and non-linear ordering costs , 1978 .

[2]  Karl Johan Åström,et al.  Optimal control of Markov processes with incomplete state information , 1965 .

[3]  James E. Eckles,et al.  Optimum Maintenance with Incomplete Information , 1968, Oper. Res..

[4]  Shunji Osaki,et al.  Optimum ordering policies with lead time for an operating unit , 1978 .

[5]  Edward J. Sondik,et al.  The Optimal Control of Partially Observable Markov Processes over a Finite Horizon , 1973, Oper. Res..

[6]  Donald B. Rosenfield,et al.  Markovian Deterioration with Uncertain Information , 1976, Oper. Res..

[7]  Hanan Luss,et al.  Maintenance Policies When Deterioration Can be Observed by Inspections , 1976, Oper. Res..

[8]  P. Kolesar.  Minimum Cost Replacement Under Markovian Deterioration , 1966 .

[9]  J. Cooper.  TOTAL POSITIVITY, VOL. I , 1970 .

[10]  Bhaskar Sengupta,et al.  Maintenance policies under imperfect information , 1980 .

[11]  Hajime Kawai,et al.  An Optimal Inspection and Replacement Policy , 1975, IEEE Transactions on Reliability.

[12]  Naoto Kaio,et al.  Discrete-Time Ordering Policies , 1979, IEEE Transactions on Reliability.

[13]  Hajime Kawai.  AN OPTIMAL ORDERING AND REPLACEMENT POLICY OF A MARKOVIAN DETERIORATION SYSTEM UNDER INCOMPLETE OBSERVATION : PART II , 1983 .

[14]  Cyrus Derman,et al.  Finite State Markovian Decision Processes , 1970 .

[15]  Hajime Kawai,et al.  AN OPTIMAL INSPECTION AND MAINTENANCE POLICY OF A DETERIORATING SYSTEM , 1982 .