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The purpose of this paper is to determine optimal replacement threshold and optimal inspection interval for an item subjected to condition-based maintenance (CBM). The primarily assumption is that the item's failure replacement cost depends on the item's degradation state at which failure occurs and/or the time the item fails. The cost of inspection is also taken into account.

The control limit replacement policy framework, already reported by some research referred to in this paper, is first extended to include the non-decreasing failure replacement cost assumption. Then, for alternative inspection intervals, replacement thresholds together with their associated total cost including the inspection cost are computed. By comparing the total costs, the optimal inspection interval and its corresponding optimal replacement threshold are simultaneously identified.

The mathematical formulation required for the determination of optimal replacement threshold and optimal inspection interval for an item subjected to CBM under the assumption of non-decreasing failure cost is provided.

In some practical situations where CBM is implemented, the failure replacement cost may depend on the time the failure happens and/or may depend on the system's degradation state. In addition, inspections often incur cost. Under such circumstances, findings of this paper can be utilized for the determination of optimal replacement threshold and optimal inspection interval for the underlying system.

Using the approach proposed in this paper, one could obtain the optimal replacement threshold and the optimal inspection interval for a system subjected to CBM.

Considers an economic manufacturing quantity (EMQ) model with an unreliable production facility and a production process subject to random deterioration. Notes that the shift of the process to the “out‐of‐control” state, which may result in producing defective items, is recognized only through inspections; and that the production unit can be replaced preventively or overhauled after finishing a certain number of production runs. Proposes that the objective is to determine the lot size, inspection interval and a preventive replacement time minimizing the expected average cost per unit of time. Obtains the formula for the expected average cost for a generally distributed time to failure. Presents computational results and studies the joint effect of process deterioration and machine breakdowns on the optimal policy.

The authors consider systems that generate damage to environment as they get older and degrade. The purpose of this paper is to develop an optimal condition-based maintenance strategy for such systems in situations where they have a finite operational time requirement. The authors determine simultaneously the optimal number of inspections and the threshold level of environmental damage which minimize the total expected cost over the considered finite time horizon.

The environmental degradation level is monitored through periodic inspections. The authors model the environmental degradation process due to the equipment’s degradation by the Wiener process. A mathematical model and a numerical procedure are developed. Numerical calculations are performed and the influence of the variation of key parameters on the optimal solution is investigated.

Numerical tests indicate that as the cost of the penalty related to the generation of an excess damage to environment increases, inspections should become more frequent and the threshold level should be lowered in order to favor preventive actions reducing the probability to pay the penalty.

Given the complexity of the cost function to be minimized, it is difficult to derive analytically the optimal solution. A numerical procedure is designed to obtain the optimal condition-based maintenance policy. Also, the developed model is based on the assumption that the degradation follows a process with stationary independent increments. This may not be appropriate for all types of degradation processes.

The proposed optimal maintenance policy may be relevant and very useful in the perspective of green operations. In fact, this paper offers to decision-makers a comprehensive approach to implement a green maintenance policy and to rapidly understand the net effect of the maintenance policy with respect to environmental regulation requirements.

The main contribution consists in the modeling and optimization of the condition-based maintenance policy over a finite time horizon. Indeed, existing condition-based maintenance models over an infinite time horizon are not applicable for systems with a finite operational time requirement.

The purpose of this paper is to model a block-based inspection policy for a multi-component system with stochastic dependence. Some components may develop a hidden failure, an occurrence of which neither stops the system nor accelerates the other components’ deterioration. On the other hand, other components may experience three states: healthy, defective and revealed failures. Any revealed failure of each component not only stops the system but also generates a shock to all the other ones, which increases their occurrence rate of hidden, defect and revealed failures.

A block-based inspection policy is considered to take advantage of economic dependence as follows. In addition to the periodic inspections, the system is also inspected at revealed failures’ moments of each component to detect and fix both defects and hidden failures on all the other components. To calculate the expected total cost, the recursive equations for the required expected values is first mathematically derived. Then, due to computational complexity, an efficient Monte Carlo simulation algorithm is designed to calculate the expected values.

The proposed approach is illustrated through a numerical example, and the optimal periodic inspection interval over a finite time horizon is obtained via minimization of the expected total cost. Finally, the correctness of the results is validated by conducting sensitivity analysis.

Planning an appropriate inspection policy over a finite time horizon becomes more complicated when considering a multi-component system because different units may experience different failure modes with stochastic dependence.

Develops a framework which provides a step towards better planning of production, scheming inspection and preventive maintenance. Studies the effects of an imperfect production process on the optimal production cycle time. The system is assumed to deteriorate during the production process and produce some proportion of defective items. Extends to the cases where the proportion of defective items and the cost of process restoration are not constant. Provides a comparative study of two monitoring policies where the preventive maintenance setting is used and not used in the deteriorating production process. These models are directly relevant to the management of the quality and reliability of the production process. When scheming inspection is adopted, it is shown that the optimal inspection intervals are equally spaced in the imperfect production process under the different policies, respectively. Provides a numerical example to illustrate the derivation of the optimal production cycle time in the models.

In this paper, we develop a model for machine maintenance inspection problem. Conditions under which an economical solution exists are derived. An optimal solution procedure yielding the optimal inspection interval length in few iterations is proposed as well as a closed form heuristic solution which provides a very good approximation. An example is used to illustrate both approaches.

Considers a system consisting of several different elementary components. Presents an algorithm to determine the optimal inspection policy for this system. Numerical examples reveal that this algorithm works very well.

Solving an optimal test or inspection interval is a relevant problem for a machine that is subject to random failures when failures can only be revealed by periodic inspection or testing. Frequent testing increases the testing costs, while infrequent testing leads to increasing downtime and loss of production. Develops optimal test intervals and approximate analytical results. The accuracies are studied numerically. The results can also be used for optimizing the availability of standby components without economic considerations.

The present study proposes two types of periodical inspection policies for a scale which weighs products in the final stage of manufacturing some specific products, such as chemical products. The scale is inspected at time iT(i=1,2, … ). Under ModelI, an inspection operation involves detection of a scale malfunction or inaccuracy as well as an adjustment activity. Under ModelII, an inspection is conducted only to detect a scale malfunction. If a scale malfunction is detected, an adjustment activity follows. For each model, the fraction defective and the long‐run average cost are formulated. We then examine the existence of an inspection interval T_α which makes the fraction defective under a prespecified value α (0< α <1). An economical inspection interval T^* minimizing the long‐run average cost is also discussed.

Markov models find optimum inspection intervals for phased deterioration of monitored complex components in a system with severe down time costs. The number of (pseudo)‐phases can be increased, but in most cases, simple models tracking actual states and their perception by the user will suffice, because of paucity of data and near‐constant rates. The matrix is cyclic; it includes renewal and regression to earlier states, simplifying solution and matching observation. An example involves roller bearings in paper mills with three phases, no defect, possible defect, and final deterioration towards failure. In the last phase, continuous monitoring is used.