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This paper deals with two different shock models in a Markovian environment. We study a system from a reliability point of view under these two shock models. According to the first model, the system fails if the cumulative shock magnitude exceeds a critical level, while in the second model the failure occurs when the cumulative effect of the shocks in consecutive periods is above a critical level. The shock occurrences over discrete time periods are assumed to be Markovian. We obtain expressions for the failure time distributions of the system under the two model. Illustrative computational results are presented for the survival probabilities and mean time to failure values of the system. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a system consisting of two major units, A and B, each subject to two types of shocks that occur according to a non-homogeneous Poisson process. A type II shock causes a complete system failure which is corrected by a replacement; and a type I shock causes a unit A minor failure, which is rectified by a minimal repair. The shock type probability is age-dependent. Each unit A minor failure results in a random amount of damage to unit B. Such a damage to unit B can be accumulated to a specified level of the complete system failure. Moreover, unit B with a cumulative damage of level z may become minor failed with probability \pi(z) at each unit A minor failure, and fixed by a minimal repair. We consider a more general replacement policy where the system is replaced at age T, or the Nth type I shock, or first type II shock, or when the total damage to unit B exceeds a specified level, whichever occurs first. We determine the optimal policy of T^\ast and N^\ast to minimize the s-expected cost per unit time. We present some numerical examples, and show that our model is the generalization of many previous maintenance models in the literature. [ABSTRACT FROM AUTHOR]

Adverse environmental conditions cause infrastructure systems to deteriorate (e.g., loss capacity) over time. Modeling system deterioration is essential to define optimum design strategies, and inspection and maintenance (intervention) programs. In particular, the main purpose of maintenance is to increase the system availability by extending the life of the system. Most strategies for maintenance optimization focus on defining long term strategies based on the system's condition at the decision time (e.g., t=0). However, due to the large uncertainty in the system's performance through life, an optimal maintenance policy requires both permanent monitoring and a cost-efficient plan of interventions. This paper presents a model to define an optimal maintenance policy of systems that deteriorate as a result of shocks. Deterioration caused by shocks is modeled as a compound Poisson process, and the optimal maintenance strategy is based on an impulse control model. In the model, the optimal time and size of interventions are executed according to the system state, which is obtained from permanent monitoring. [ABSTRACT FROM PUBLISHER]

We consider a system subject to shocks that arrive according to a nonhomogeneous pure birth process (NHPBP). As a shock occurs, the system has two types of failures. Type-I failure (minor failure) is rectified by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The probabilities of these two types of failures depend on the number of shocks since the last replacement. We consider a policy with which the system is replaced at the nth type-I failure, or at any type-II failure. The aim of this paper is to determine the optimal policy n^\ast, the number of minor failures up to replacement that minimizes the expected cost rate of the system subject to NHPBP shocks. The model is a generalization of the existing models, and is more applicable in practice. We present some numerical examples, and show that several classical models are the special cases of our model. [ABSTRACT FROM PUBLISHER]

This note studies the block replacement policy with general repairs for an operating system subject to shocks occurring according to a non-homogeneous pure birth process. A shock causes the system to fail. There are two types of failures: a type-I failure (minor failure) is fixed by a general repair, whereas a type-II failure (catastrophic failure) is removed by an unplanned (or unscheduled) replacement. The failure type probabilities depend on the number of type-I failure shocks that occurred since the last replacement. Under the block replacement policy, the operating system is replaced every T time units to reduce the chances of more expensive unplanned replacements due to type-II failures. The aim of this note is to determine the optimal block interval T^\ast, which minimizes the expected cost rate and the expected total discounted cost rate of the proposed policy. As the shock process is a more general non-homogeneous pure birth process, several previous models become the special cases of our model. [ABSTRACT FROM PUBLISHER]

A geometric process δ-shock maintenance model for a repairable system is introduced. If there exists no shock, the successive operating time of the system after repair will form a geometric process. Assume that the shocks will arrive according to a Poisson process. When the interarrival time of two successive shocks is smaller than a specified threshold, the system fails, and the latter shock is called a deadly shock. The successive threshold values are monotone geometric. The system will fail at the end of its operating time, or the arrival of a deadly shock, whichever occurs first. The consecutive repair time after failure will constitute a geometric process. A replacement policy N is adopted by which the system will be replaced by a new, identical one at the time following the Nth failure. Then, for the deteriorating system, and the improving system, an optimal policy N* for minimizing the long-run average cost per unit time is determined analytically. [ABSTRACT FROM AUTHOR]