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     

A maintenance policy for repairable systems based on opportunisticfailure-rate tolerance

An opportunistic hazard rate replacement policy for a repairable system with several types of units is presented. A unit is repaired at failure when the hazard rate falls in (0, L-u). A unit is replaced at failure when the hazard rate falls in (L-u , L). An operating unit is replaced when its hazard rate reaches L. When a unit is replaced because its hazard rate reaches L, all operating units with their hazard rates falling in (L-u, L) are replaced. The long-run mean cost rate as a function of L and u is derived. Optimal L and u are obtained to minimize the total maintenance cost rate. Application and analysis of results are demonstrated through a numerical example. The maintenance model is designed for a system with multitype units. Each type has its own increasing hazard rate. Units are repaired or replaced depending on their hazard rate at a failure or active replacement of another unit. The repair interval, replacement limit, and replacement tolerance are determined to yield the optimal total maintenance cost rate     

Hazard-rate tolerance method for an opportunistic-replacementpolicy

A model for a system with several types of units is presented. A unit is replaced at failure or when its hazard (failure) rate exceeds limit L, whichever occurs first. When a unit is replaced because its hazard rates reaches L, all the operating units with their hazard rate falling in the interval (L-u, L) are replaced. This policy allows joint replacements and avoids the disadvantages resulting from the replacement of new units, down time, and unrealistic assumptions for distributions of unit life. The long-run cost rate is derived. Optimal L and u are obtained to minimize the average total replacement cost rate. Application and analysis of results are demonstrated through a numerical example     

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.     

(τ, k) block replacement policy with idle count

The authors propose a new block replacement policy for a group of nominally identical units. Each unit is individually replaced on failure during a specified time interval. Beyond the failure replacement interval, failed units are left idle until a specified number of failures occur, then a block replacement is performed. The average cost rate for this two-phase block replacement policy is derived and analyzed. The policy yields lower cost rate than two block replacement policies published previously. Numerical examples demonstrate the results     

Optimal periodic preventive repair and replacement policy assuming geometric process repair

In this paper, a simple deteriorating system with repair is studied. When failure occurs, the system is replaced at high cost. To extend the operating life, the system can be repaired preventively. However, preventive repair does not return the system to a "good as new" condition. Rather, the successive operating times of the system after preventive repair form a stochastically decreasing geometric process, while the consecutive preventive repair times of the system form a stochastically increasing geometric process. We consider a bivariate preventive repair policy to solve the efficiency for a deteriorating & valuable system. Thus, the objective of this paper is to determine an optimal bivariate replacement policy 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 numerically. An example is given where the operating time of the system is given by a Weibull distribution.     

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.     

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.     

Optimal stocking for replacement with minimal repair

Joint stocking and replacement model with minimal repair at failure is considered. A recursive relationship among the optimal replacement intervals is obtained, which shows that replacement intervals are an increasing sequence due to the inventory carrying cost. Using the relationship, a procedure is given for determining how many units to purchase on each order and when to replace each unit after it has begun operating so as to minimize the total cost per unit time over an infinite time span. The problem can be simplified if equal replacement intervals are assumed, and the solution is very close to that of the unconstrained problem.     

Optimal ordering policies and optimal number of minimal repairs before replacement

Many maintenance policies in the literature have assumed that whenever a unit is to be replaced, a new unit is immediately available. However, if the procurement lead time is not negligible an odering policy should determine when to order a spare and when to replace the operating unit. This paper presents a model for determining the optimal ordering point and the optimal number of minimal repairs before replacement which include the optimal number of minimal repairs before replacement of Park as a special case. 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. Finally, we present the numerical examples for illustration.     

含氢储能的多源联合发电系统调度研究

风电和光伏发电具有间歇性和随机性,为了降低在多源联合发电系统中的弃风弃光率,采用含氢储能系统和火电机组配合来平滑风电和光电机组出力。文中以系统运行成本最小和弃电惩罚成本最小为目标,以系统功率平衡、火电机组出力和爬坡、热备用、风电和光电出力及储能系统储氢罐容量、电解槽和燃料电池功率等为约束条件构建了多源联合发电系统日前调度模型。通过YALMIP工具箱对模型进行编程,并调用CPLEX对编写的程序进行求解。对含有风电、光电、火电机组以及储能系统的多源联合发电系统进行算例分析,通过对比有无储能系统的弃风弃光量和系统总运行成本,证明了含氢储能系统可以有效降低系统的弃风弃光率,并提高系统的经济性。     

Optimum Age Replacement in the Bivariate Exponential Case

An age replacement policy is considered for pairs of units which operate in parallel and which have lifetimes displaying a bivariate exponential distribution. Both units are to be replaced at the same time. The limiting expected cost per unit time is the optimization criterion. The results state that no replacements should be made until at least one of the units in the pair fails. Both units shoould then be replaced either when one fails or when both fail, depending on which procedure involves the smaller limiting expected cost per unit time.     

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.     

An age replacement policy with minimal repair and general random repair cost

An age replacement policy is introduced which incorporates minimal repair, replacement, and general random repair costs. If an operating unit fails at age y<T, it is either replaced by a new unit with probability p(y) at a cost c₀, or it undergoes minimal repair with probability q(y) = 1−p(y). Otherwise, a unit is replaced when it fails for the first time after age T. The cost of the i-th minimal repair of an unit at age y depends on the random part C(y) and the deterministic part c_i(y). The aim of the paper is to find the optimal T which minimizes the long run expected cost per unit time of the policy. Various special cases are considered.     

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     

Extended block replacement policy of a system subject to shocks

A generalization of the block replacement (BR) policy is proposed and analyzed for a system subject to shocks. Under such a policy, an operating system is preventively replaced by new ones at times i·T (i=1,2,3,...) independently of its failure history. If the system fails in: (a) ((i-1)·T, (i-1)·T+T₀), it is either replaced by a new one or minimally repaired; or (b) ((i-1)·T+T₀, i·T), it is either minimally repaired or remains inactive until the next planned replacement. The choice of these two actions is based on some mechanism (modeled as random) which depends on the number of shocks since the latest replacement. The average cost rate is obtained using the results of renewal reward theory. The model with two variables is transformed into a model with one variable and the optimum policy is discussed. Various special cases are considered. The results extend many of the well-known results for BR policies     

A Geometric Process $delta$-Shock Maintenance Model

A geometric process $delta$ -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 $N$th failure. Then, for the deteriorating system, and the improving system, an optimal policy $N^{ast}$ for minimizing the long-run average cost per unit time is determined analytically.      

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 two-unit duplicating standby system with correlated failure-repair/vbreplacement times

This paper considers the stochastic analysis of a two-unit (original and duplicate) cold standby system model with preventive maintenance and replacement of the failed duplicate unit. The failed duplicate unit is non-repairable but its replacement is considered with an identical duplicate unit which is available instantaneously. Joint distributions of failure and repair/replacement times of original/duplicate units are bivariate exponential with different parameters. Various reliability characteristics of the system model under study are obtained by using regenerative point technique. Mean time to system failure and steady state availability have also been studied through graphs.