AGE REPLACEMENT POLICY CONSIDERING WARRANTY WITH ONE CORRECTIVE REPLACEMENT AND MINIMAL REPAIRS

AbstractThe performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

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A weak derivative approach to optimization of threshold parameters in a multicomponent maintenance system

Journal of Applied Probability ◽

10.1017/s0021900200019926 ◽

2001 ◽

Vol 38 (02) ◽

pp. 386-406 ◽

Cited By ~ 1

Author(s):

Bernd Heidergott

Keyword(s):

Optimization Problems ◽

Estimation Algorithm ◽

Replacement Policy ◽

Cost Performance ◽

Weak Derivative ◽

Preventive Replacement ◽

Maintenance System ◽

Threshold Optimization ◽

Age Replacement ◽

The Cost

We consider a multicomponent maintenance system controlled by an age replacement policy: when one of the components fails, it is immediately replaced; all components older than a threshold age θ are preventively replaced. Costs are associated with each maintenance action, such as replacement after failure or preventive replacement. We derive a weak derivative estimator for the derivative of the cost performance with respect to θ. The technique is quite general and can be applied to many other threshold optimization problems in maintenance. The estimator is easy to implement and considerably increases the efficiency of a Robbins-Monro type of stochastic approximation algorithm. The paper is self-contained in the sense that it includes a proof of the correctness of the weak derivative estimation algorithm.

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AN ADAPTIVE AGE REPLACEMENT POLICY

10.21236/ad0621579 ◽

1965 ◽

Cited By ~ 5

Author(s):

Bennett L. Fox

Keyword(s):

Replacement Policy ◽

Age Replacement

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On optimal age replacement policy for a class of coherent systems

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.112888 ◽

2020 ◽

Vol 377 ◽

pp. 112888 ◽

Cited By ~ 1

Author(s):

Serkan Eryilmaz ◽

Mustafa Hilmi Pekalp

Keyword(s):

Replacement Policy ◽

Coherent Systems ◽

Age Replacement

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A hybrid preventive maintenance model for systems with partially observable degradation

IMA Journal of Management Mathematics ◽

10.1093/imaman/dpz018 ◽

2020 ◽

Vol 31 (3) ◽

pp. 345-365 ◽

Cited By ~ 2

Author(s):

Maxim Finkelstein ◽

Ji Hwan Cha ◽

Gregory Levitin

Keyword(s):

Preventive Maintenance ◽

Replacement Policy ◽

Hybrid Strategy ◽

Cost Rate ◽

Shot Noise Process ◽

Shock Process ◽

Long Run ◽

Age Replacement ◽

Partially Observable ◽

Maintenance Model

Abstract A new model of hybrid preventive maintenance of systems with partially observable degradation is developed. This model combines condition-based maintenance with age replacement maintenance in the proposed, specific way. A system, subject to a shock process, is replaced on failure or at some time ${T}_S$ if the number of shocks experienced by this time is greater than or equal to m or at time $T>{T}_S$ otherwise, whichever occurs first. Each shock increases the failure rate of the system at the random time of its occurrence, thus forming a corresponding shot-noise process. The real deterioration of the system is partially observed via observation of the shock process at time ${T}_S$. The corresponding optimization problem is solved and a detailed numerical example demonstrates that the long-run cost rate for the proposed optimal hybrid strategy is smaller than that for the standard optimal age replacement policy.

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