A maintenance model for two-unit redundant system

In this paper, a maintenance model for two-unit redundant system with one repairman is studied. At the beginning, unit 1 is operating, unit 2 is the standby unit. The costs include the operating reward, repair cost and replacement cost, besides, a penalty cost is incurred if the system breaks down. Two kinds of replacement policy, based on the number of failures for two units and the working age, respectively are used. The long-run average cost per unit time for each kind of replacement policy is derived. Also, a particular model in which the system is deteriorative, two units are identical and the penalty cost rate is high, is thoroughly studied.     

Joint optimization of block-replacement and periodic-review spare-provisioning policy

This paper considers the problem of joint optimization of "preventive maintenance" and "spare-provisioning policy" for system components subject to wear-out failures. A stochastic mathematical model is developed to determine the jointly optimal "block replacement" and "periodic review spare-provisioning policy." The objective function of the model represents the s-expected total cost of system maintenance per unit time, while the preventive replacement interval and the maximal inventory level are chosen as the decision variables. The objective function of the model is in an analytic form with parameters easily obtainable from field data. The model has been tested using field data on electric locomotives in Slovenian Railways. The calculated optimal values of the model decision variables are realistic. "Sensitivity analysis of the model" shows that the model is relatively insensitive to moderate changes of the parameter values. The results of testing and of sensitivity analysis of the model prove that a trade-off exists between the replacement related cost and the inventory related cost. The jointly optimal preventive replacement interval defined by this model differs appreciably from the corresponding interval determined by the conventional model where only replacement related costs are considered. Also, the results of the sensitivity analysis show that even minor modification of the value of each model decision variable (without the appropriate adjustment of the value of the other decision variable) can lead to important increase of the s-expected total cost of system maintenance. This indicates that separate optimization of preventive maintenance policy and spare-provisioning policy does not ensure minimal total cost of system maintenance. This model can be readily applied to optimize maintenance procedures for a variety of industrial systems, and to upgrade maintenance policy in situations where block replacement preventive maintenance is already in use.     

Cost limit replacement policy under minimal repair

This paper presents a policy for either repairing or replacing a system that has failed. When a system requires repair, it is first inspected and the repair cost is estimated. Repair is only then undertaken if the estimated cost is less than the “repair cost limit”. However, the repair cannot return the system to “as new” condition but instead returns it to the average condition for a working system of its age. Examples include complex systems where the repair or replacement of one component does not materially affect the condition of the whole system. A Weibull distribution of time to failure and a negative exponential distribution of estimated repair cost are assumed for analytic amenability. An optimal “repair cost limit” policy is developed that minimizes the average cost per unit time for repairs and replacement. It is shown that the optimal policy is finite and unique.     

Optimal maintenance of a two-unit standby redundant system with a generalized cost structure

To maintain a system there are generally several alternatives available to a decision maker. In this paper a usual 2-unit standby system is considered with exponential distribution for life-time of units and arbitrary distribution for repair time. A generalized cost structure with different earning rates in different states, transition rewards and discounting, has been superimposed upon the semi-Markov process generated by the system model. An optimal maintenance policy for the system is the one that maximizes profit rate of the system. A solution algorithm, based on Howard's policy iteration method, is developed. An illustration is presented at the end.     

An optimal replacement policy for a three-state repairable system with a monotone process model

In this paper, a deteriorating simple repairable system with three states, including two failure states and one working state, is studied. Assume that the system after repair cannot be "as good as new", and the deterioration of the system is stochastic. Under these assumptions, we use a replacement policy N based on the failure number of the system. Then our aim is to determine an optimal replacement policy N/sup */ such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. An explicit expression of the average cost rate is derived. Then, an optimal replacement policy is determined analytically or numerically. Furthermore, we can find that a repair model for the three-state repairable system in this paper forms a general monotone process model. Finally, we put forward a numerical example, and carry through some discussions and sensitivity analysis of the model in this paper.     

A geometric-process maintenance model for a deteriorating system under a random environment

This paper studies a geometric-process maintenance-model for a deteriorating system under a random environment. Assume that the number of random shocks, up to time t, produced by the random environment forms a counting process. Whenever a random shock arrives, the system operating time is reduced. The successive reductions in the system operating time are statistically independent and identically distributed random variables. Assume that the consecutive repair times of the system after failures, form an increasing geometric process; under the condition that the system suffers no random shock, the successive operating times of the system after repairs constitute a decreasing geometric process. A replacement policy N, by which the system is replaced at the time of the failure N, is adopted. An explicit expression for the average cost rate (long-run average cost per unit time) is derived. Then, an optimal replacement policy is determined analytically. As a particular case, a compound Poisson process model is also studied.     

Wireless scheduling with hybrid ARQ

A model for downlink wireless scheduling is studied, which takes into account both user-channel conditions and retransmissions with packet combining hybrid [automatic repeat request (ARQ)]. Quality-of-service (QoS) requirements for each user are represented by a cost function, which is an increasing function of queue length. The objective is to find a scheduling rule that minimizes the average cost over time. We consider two scenarios: 1) the cost functions are linear, and packets arrive to the queues according to a Poisson process and 2) the cost functions are increasing, convex, and there are no new arrivals (draining problem). In each case, we transform the system model into a different model that fits into a framework for stochastic scheduling developed by Klimov. Applying Klimov's results, we show that the optimal schedulers for the transformed models in both scenarios are specified by fixed priority rules. Applying the inverse transformation in each case gives the optimal scheduling policy for the original problem. The priorities can be explicitly computed, and in the first scenario, are given by simple closed-form expressions. For the draining problem, we show that the optimal policy never interrupts the retransmissions of a packet. We also show that a simple myopic scheduling policy, called the U'R rule, performs very close to the optimal scheduling policy in specific cases. We present numerical examples, which compare the performance of the optimal scheduling rule with several heuristic rules.     

The branching nonhomogeneous Poisson process and its application to a replacement model

In studying and analysing the failure patterns of complex system, plausible stochastic models are needed to represent the sequence of events. A simple and frequently used model is derived by the assumption that the times-between-failures of a system are exponentially distributed and independent. Experience has shown, however, that successive times-between-failures are not exponentially distributed and not independent.These deviations are due to imperfect search of failed components. We constitute a plausible stochastic process which describes the sequence of events, and obtain the interval reliability and the expected number of failures.As an application of these results, we deal with the replacement model where a system undergoes minimal repair before time T and is replaced at time T. We discuss an optimum policy minimizing the total expected cost per unit time.     

Deterministic Routing to Buffered Channels

Considernexponential transmission channels which transmit information with different rates. Every channel has a buffer which is capable of storing an unlimited number of messages. A new message first arrives at the controller, which immediately routes it to one of the channels according to an infinite deterministic routing sequence. A cost per unit of staying time is charged in each of the channels (channel dependent cost), and the long-run average staying cost is taken as the cost criterion. For everynand a Poisson arrival process, a lower bound to the cost is found and a new routing policy, the golden ratio policy, is presented and its cost is evaluated. It is shown that for a variety of system parameters, the golden ratio routing policy has a cost close to the lower bound.     

Optimal control of a removable and non-reliable server in a markovian queueing system with finite capacity

This paper studies the economic behavior of a removable and non-reliable server in an Markovian queueing system with finite capacity under steady-state conditions. The removable server applies the N policy which turns the server on when the queue length reaches the value N, and turns the server off when the system is empty. The server may break down only if operating and require repair at a repair facility. Interarrival and service times of the customers, and breakdown and repair times of the server, are assumed to follow a negative exponential distribution. A cost model is developed to determine the optimal operating N policy numerically in order to minimize the total expected cost per unit time.     

Continuous-time predictive-maintenance scheduling for adeteriorating system

A predictive-maintenance structure for a gradually deteriorating single-unit system (continuous time/continuous state) is presented in this paper. The proposed decision model enables optimal inspection and replacement decision in order to balance the cost engaged by failure and unavailability on an infinite horizon. Two maintenance decision variables are considered: the preventive replacement threshold and the inspection schedule based on the system state. In order to assess the performance of the proposed maintenance structure, a mathematical model for the maintained system cost is developed using regenerative and semi-regenerative processes theory. Numerical experiments show that the s-expected maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the replacement threshold and the a periodic inspection times. The proposed maintenance structure performs better than classical preventive maintenance policies which can be treated as particular cases. Using the proposed maintenance structure, a well-adapted strategy can automatically be selected for the maintenance decision-maker depending on the characteristics of the wear process and on the different unit costs. Even limit cases can be reached: for example, in the case of expensive inspection and costly preventive replacement, the optimal policy becomes close to a systematic periodic replacement policy. Most of the classical maintenance strategies (periodic inspection/replacement policy, systematic periodic replacement, corrective policy) can be emulated by adopting some specific inspection scheduling rules and replacement thresholds. In a more general way, the proposed maintenance structure shows its adaptability to different possible characteristics of the maintained single-unit system     

A geometric-process repair-model with good-as-new preventive repair

This paper studies a deteriorating simple repairable system. In order to improve the availability or economize the operating costs of the system, the preventive repair is adopted before the system fails. Assume that the preventive repair of the system is as good as new, while the failure repair of the system is not, so that the successive working times form a stochastic decreasing geometric process while the consecutive failure repair times form a stochastic increasing geometric process. Under this assumption and others, by using geometric process we consider a replacement policy N based on the failure number of the system. Our problem is to determine an optimal replacement policy N such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. And the fixed-length interval time of the preventive repair in the system is also discussed. Finally, an appropriate numerical example is given. It is seen from that both the optimal policies N** and N* are unique. However, the optimal policy N** with preventive repair is better than the optimal policy N* without preventive repair     

An age replacement policy with increasing minimal repair cost

A replacement policy for a system in which minimal repair cost increases in system age is considered. If a system fails before age T, it is minimally repaired. Otherwise, the system is replaced when if fails for the first time after age T. The mean cost rate is used as a criterion for optimization. It is shown that the optimal T minimizing the mean cost rate is finite and unique.     

All opportunity-triggered replacement policy for multiple-unitsystems

A model is presented for a system which consists of n i.i.d units. Hazard rates of these units are increasing in time. A unit is replaced at failure or when the age of a unit exceeds T, whichever occurs first. When a unit is replaced, all the operating units with their age in the interval (T-w,T) are replaced. Both failure replacement and active replacement create the opportunities to replace other units preventively. This policy allows joint replacements and avoids the disadvantages resulting from replacement of new units, down time, and unrealistic assumptions for distributions of unit life. An algorithm is developed to compute the steady-state cost rate. Optimal T&W are obtained to minimize the mean total replacement cost rate. Application and analysis of results are illustrated through a numerical example     

An ordering policy with age-dependent minimal repair and age-dependent random repair costs

In this paper we consider an ordering policy for a one-unit system with age-dependent minimal repair and age-dependent random repair costs. We derive the expected cost per unit time in the steady-state as a criterion of optimality and seek the optimum policy by minimizing that cost. We show that, under certain conditions, there exists a finite and unique optimum policy. Various special cases are discussed.     

Optimal planned maintenance with salvage cost for a two-unit standby redundant system

This paper considers the optimal spare ordering policies for a cold standby redundant system with two dissimilar units. Especially, the planned maintenance schedule with salvage cost is discussed. The failure time distributions for respective units are assumed to be arbitrary. By applying the expected cost per unit time in the steady-state and the stationary availability as criteria of optimality, the optimal ordering policy minimizing or maximizing each criterion is obtained under some economical and/or physical assumptions. Finally, numerical examples are presented, and the effect of the failure time distributions for the optimal ordering policy is examined in detail.     

An inspection-maintenance model for systems with multiple competing processes

In some applications, the failure rate of the system depends not only on the time, but also upon the status of the system, such as vibration level, efficiency, number of random shocks on the system, etc., which causes degradation. In this paper, we develop a generalized condition-based maintenance model subject to multiple competing failure processes including two degradation processes, and random shocks. An average long-run maintenance cost rate function is derived based on the expressions for the degradation paths & cumulative shock damage, which are measurable. A geometric sequence is employed to develop the inter-inspection sequence. Upon inspection, one needs to decide whether to perform a maintenance, such as preventive or corrective, or to do nothing. The preventive maintenance thresholds for degradation processes & inspection sequences are the decision variables of the proposed model. We also present an algorithm based on the Nelder-Mead downhill simplex method to calculate the optimum policy that minimizes the average long-run maintenance cost rate. Numerical examples are given to illustrate the results using the optimization algorithm.     

Age Replacement In Simple Systems With Increasing Loss Functions

Some age replacement policies are investigated and conditions for the unique existence of an optimum policy are derived. The optimum policy is the one which minimizes the expected cost per unit time over an infinite time span or maximizes the proportion of time during which the system is in operation. Losses have been expressed through increasing operating cost, if the objective is to minimize the expected total cost per unit time and through increasing renewal times if the objective is to maximize the availability of the system.     

A failure-repair model with minimal and major maintenance

A Markov model for a continuously operating service device whose condition deteriorates with time in service is proposed. The model incorporates deterioration and Poisson failures, minimal repair, periodic minimal maintenance, and major maintenance after a given number of minimal maintenances. An exact recursive algorithm computes the steady-state probabilities of the device. A cost function is defined using different cost rates for the different types of outages. Based on minimal unavailability or minimal costs, optimal solutions of the model are derived. Major maintenance is seldom beneficial if optimal maintenance intervals are used. If a maintenance policy is based on nonoptical intervals between maintenances, periodic major maintenance can reduce costs