Maintenance of Deteriorating Systems Subject to Shocks

Sarada, G.; Rangan, A.

doi:10.1007/bf03398617

Cited by 1 publication

(1 citation statement)

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“…Park et al (2000) generalize the random shock model of Lee and Lee (1993) to the case where the system is checked according to a renewal process. Sarada and Rangan (2000) consider a maintenance policy for tile system subject to random shocks. Lam (2003) study an inspection‐repair‐replacement model for a deteriorating system where a minimal repair is performed if the system is in down state.…”

Section: Introductionmentioning

confidence: 99%

A random shock model for a continuously deteriorating system

Lim

Baek

Lee

2005

Journal of Quality in Maintenance Engineering

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PurposeA random shock model for a system whose state deteriorates continuously is introduced and stochastically analyzed. It is assumed in the model that the state of the system follows a Brownian motion with negative drift and is also subject to random shocks. A repairman arrives at the system according to a Poisson process and repairs the system if the state has been below a threshold since the last repair.Design/methodology/approachKolmogorov's forward differential equation is adopted together with a renewal argument to analyze the model stochastically. The renewal reward theorem is used to obtain the long‐run average cost per unit time.FindingsAn explicit expression is deduced for the stationary distribution of the state of the system. After assigning several costs to the system, an optimization is also studied as an example.Practical implicationsThe present model can be used to manage a complex system whose state deteriorates both continuously and jumpwise due to the continuous wear and random shocks, such as a machine and a production line in a factory. The model can also be applied to an inventory which supplies the stock both continuously and jumpwise, such as a gas station and the distribution center for a franchise, if the continuous wear and random shocks are considered as demands for the stock.Originality/valueThe present model is quite complicate, however, more realistic than the previous models where the state of the system is subject to either one of continuous wear and random shocks.

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Section: Introductionmentioning

confidence: 99%