استراتژی نگهداری پیشگیرانه پویا برای سیستم های تولید کهنه و رو به زوال

This paper proposes a dynamic preventive maintenance strategy for a multi-state deteriorating production system. A real-time operating state can be derived via the healthy index. A time-dependent state transition probability matrix is used to describe the aging and deteriorating system. The current probability transition matrix and the aging factor are estimated based on historical data. Then one can update the transition probability matrix the next time in terms of the aging factor. Multiple actions at risk are provided to maintain the system with time spent considered. The optimal maintenance action at each operating state and at each specific time is obtained at the minimum expected total cost per unit time during a given finite time interval.

Extensive reviews of various maintenance policies on a deteriorating system can be found in Pierskalla and Voelker, 1976, Sherif and Smith, 1981 and Valderz-Flores and Feldman, 1989. However, such maintenance policies can be classified into two groups. The first group deals with the maintenance action which is taken under failure without inspection. Such a group includes: (1) the age replacement policy (i.e. replacement upon failure or at age) (Barlow & Hunter, 1960) and their extensions by including minimal repair such as Bagai and Jaint, 1994, Chen and Feldman, 1997, Cleroux et al., 1979, Jhan and Sheu, 1999, Mazzuchi and Soyer, 1996 and Sheu et al., 1999; (2) the block replacement policy (i.e. replacement at kT for k = 1, 2 … or upon failure) and the failure replacement policy (i.e. replacement upon failure) ( Berg and Epstein, 1978, Block et al., 1993 and Lam and Yeh, 1994); and (3) the scheduled maintenance policies through predicting failure time statistically (Canfield, 1986 and Chaudrhuri and Sahu, 1977). The second group deals with the maintenance action which is taken under failure with inspection equipment. Such a system can be regarded as a multi-state deteriorating system with states in deteriorating order 1 < 2 < ⋯ < i < ⋯ < j < ⋯ < L, (1: perfect,…, L: complete failure). Lam and Yeh (1994) proposed a control-limit replacement policy under continuous inspection so that replacement is taken optimally upon the threshold state j∗ which is identified by inspection or when the complete failure L is observed. Lam and Yeh (1994) proposed another control-limit replacement policy under inspection at each nd to determine the optimal (d∗, j∗) so that the replacement takes places at nd whenever the system state x at nd satisfies j∗ ⩽ x ⩽ L. Chiang and Yuan, 2001 and Chiang and Yuan, 2000 proposed still another two control-limit preventive maintenance policies under continuous and periodic inspection respectively to determine optimal (i∗, j∗) (two threshold states 1 < i∗ < j∗ < L) so that the repair (resp. replacement, do-nothing) is taken whenever the system state x satisfies i∗ ⩽ x < j∗ (resp. j∗ ⩽ x ⩽ L: otherwise). Wood (1998) proposed a control limit rule that requires the system to be restored whenever its damage exceeds a certain level under continuous inspection. All of the methods stated above have to assume that the system satisfies a continuous-time Markov chain. Also, the threshold states were obtained and the optimal maintenance action taken is state-dependent only (i.e. not time-dependent). Jardine, Banjevic, and Makis (1997) and Makis and Jardine (1992) proposed an optimal dynamic (i.e. both state- and time-dependent) replacement policy for condition-based maintenance. Wildeman, Dekker, and Smith (1997) proposed another dynamic preventive maintenance policy that a long-time tentative plan was taken based on a subsequent adaptation and according to available information on the short term with a rolling-horizon approach. Chen, Chen, and Yuan (2003) proposed a dynamic preventive maintenance policy for a multi-state deteriorating system. The system is equipped with sufficient inspection equipment connected to a computer center. The measurement or inspection is taken in a fixed time period nd for a fixed d. The system healthy index is calculated to identify the system state x and to choose the maintenance action at the minimum expected total cost from the set Ax of alternatives. However, a multi-state Markov chain with time independent transition probabilities is used to model the system without aging. The maintenance policy is state-dependent only. Liao, Elsayed, and Chan (2006) considered a condition-based maintenance model for continuously degrading system under continuous monitoring. The states of the system are randomly distributed with residual damage after maintenance. The optimum maintenance threshold is determined using condition-based availability limit policy. Lu, Tu, and Lu (2007) studied a predictive condition-based maintenance approach based on monitoring and predicting a system’s deterioration. The system’s deterioration is considered to be a stochastic dynamic process with continuous degrading. Yeh, Kao, and Chang (2009) proposed a maintenance scheme for leased equipment using failure rate reduction method and derives an optimal preventive maintenance policy that minimize expected total cost. A contemporary thorough review on these topics has been surveyed by Sheu, Lin, and Liao (2005) and Wang (2002). By considering time-dependent transition probabilities, which are updated in terms of the aging factor in Chen and Wu, 2007 and Guo et al., 1998, this paper is to propose a dynamic multi-action preventive maintenance strategy for a system under aging and deteriorating environment.

This article extends the research of Chen et al. (2003) by further considering time dependent transition probability matrix and using the aging factor in Chen and Wu, 2007 and Guo et al., 1998. A discrete-time multi-state Markov chain with time-dependent state transition probability matrix is used to describe the system whose deterioration has aging property. One can estimate the current probability transition matrix and the ageing factor based on historical data. Then one can update the transition probability matrix the next time in terms of the aging factor. Multiple actions at risk are provided to maintain the system with times spent considered. The optimal maintenance action at each operating state and each specific time is obtained with the minimum expected total cost per unit time during a given finite time interval.