Pseudodynamic cost limit replacement model under minimal repair

This paper presents a mathematical model to evaluate pseudodynamic cost limit replacement policies for a system that follows a general time-to-failure distribution. When the failed system requires repair, it is first inspected and the repair cost is estimated. Minimal repair is only then undertaken if the estimated cost is less than the exponentially declining repair cost limit. A negative exponential distribution of estimated repair cost is assumed for analytic tractability. An example with a Weibull time-to-failure distribution is given to illustrate the computational results.     

Optimum repair limit policies with a cost constraint

In this paper, we discuss the optimum repair limit policies with a cost constraint for continuous and discrete distributions, respectively. We apply the expected total discounted cost with a discount rate as a criterion, and obtain the optimum policies which minimize it. We show that, under certain conditions, there exist finite and unique optimum policies for continuous and discrete distributions, respectively.     

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.     

Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy an operating system is completely replaced whenever it reaches age T (T > 0) at a cost c₀ while minimal repair is performed at any intervening component failures. The cost of the j-th minimal repair to the component which fails at age y is g(C(y),c_j(y)), where C(y) is the age-dependent random part, c_j(y) is the deterministic part which depends on the age and the number of the minimal repair to the component, and g is an positive nondecreasing continuous function. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

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.     

A scale model of general repair

A general repair model based on a concept of scale transformation is investigated. It us supposed that if the failuretime distribution function of a repairable unit on the cycle before the repair was F(x), then after the repair it would be F(ax), where a > 1 is a scale parameter. The corresponding renewal equations are represented. A simple cost analyses model for stationary case is treated.     

Tradeoffs in multichip module yield and cost with known good die probability and repair

The influences of known good die (KGD) probability, repair, and module testing on multichip module (MCM) yield and cost have been modeled and systematically analyzed. The current work extends our previous efforts on MCMs with single (one KGD probability) and dual (two KGD probabilities) populations to modules containing complex, multiple chip populations. Most of the analysis is performed on modules with multiple populations in the range of three to five (i.e., three to five distinct chip types). In order to develop a total cost picture for an MCM versus the respective KGD probabilities of the underlying chip populations, it was necessary to develop new algorithms or modify previously developed algorithms for the following items: number of modules (necessary to ensure at least one MCM works), KGD chip cost, and chip repair/replacement costs. In order to visualize the results and simplify calculations, averages over the respective subpopulations have been employed. The combination of these models and algorithms produces cost values in multiple (KGD) probability space that contain optimum or minimal points. Associated with the cost minimums are specific KGD probabilities for each chip type in the module population. Thus, one only pays for improved KGD probability up to the values that minimize overall module cost. Repair has a direct and significant impact on overall module yield and cost, with the first repair providing the largest improvement in both yield and cost reduction.     

Expected repair cost under doubly stochastic damage processes

There are a number of instances where the problems of non-stationarity, Poisson compounding and double stochasticity arise. In the theory of space-charge limited shot-noise, the number of beats that occur in a given interval of time obey a doubly stochastic process since the Poisson's parameter λ changes randomly due to individual beats. This paper puts forward a doubly stochastic non-stationary compound Poisson process as a model describing damage sustained by military equipment, solar collectors, … etc., due to hailstones. The expected repair cost due to such damage is formulated.     

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.     

Evaluation of average maintenance cost for imperfect-repair model

The imperfect-repair model considers units which are either perfectly-repaired or minimally-repaired, with known, fixed probabilities. Minimal repair is defined, roughly, as returning the item to the population's average state at the failure time. The average cost of maintaining the unit under this model is studied by assuming fixed amounts of cost for perfect and minimal repairs when failed. The authors' measure of such maintenance cost is an average cost per unit-time over an infinite time span. To obtain this average cost, they use the expressions for average numbers of perfect and minimal repairs under this model. They prove the few theorems necessary to derive the formulae for the average cost per unit-time. The results are applied to some examples     

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 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.     

联合多普勒及MW周跳探测和修复方法

导航定位中针对双频码相组合法(MW)无法探测L1和L2载波同一历元发生相同周跳,以及周跳探测后不能实现频率间周跳分离的情况,提出了一种联合多普勒及MW组合法的周跳探测改进方法。利用多普勒积分可对单频点进行周跳检测和修复的特性,将传统MW组合法与多普勒积分法相结合,建立改进模型,从而计算并分离出L1和L2载波相位产生的周跳。用实测数据进行验证和分析,对比了3种不同情况下改进方法的检测效果,实验表明新算法能精确探测和分离出L1和L2载波相位中的周跳组合,可以准确探测周跳发生位置及周跳数值,并且能够探测和修复1周以上的周跳,有效提高了MW组合算法探测与修复周跳的准确性和可靠性。     

Periodic replacement when minimal repair costs depend on the age and the number of minimal repair for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening component failures. The cost of a minimal repair to the component is assumed to be a function of its age and the number of minimal repair. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

矿用变压器全寿命周期成本分析方法

随着我国煤炭企业的不断发展和先进生产技术的广泛应用,煤矿机械化程度得到了进一步提高。在矿井输配电生产过程中,矿用变压器的使用显得十分重要。因此,如何从矿用变压器全寿命周期成本的角度出发延长其寿命周期,减少矿井资金的浪费,以及最大化企业收益。本文首先介绍了矿用变压器在矿井中应用的重要性从而引出全寿命周期成本研究思路的意义,其次介绍了矿用变压器寿命的主要理论概念,最后是基于全寿命周期成本建立的理论模型,从而为研究内容提供一定的理论参考。     

Availability-based life cycle cost model: A simulation approach

Life Cycle Costing (LCC) has become a popular technique for studying operating facility designs prior to their construction. However, many such designs have operating characteristics that are marked by uncertainty. In particular, component failure rates and repair/replacement rates are uncertain. Thus, downtimes and maintenance costs are similarly uncertain. These various costs and uncertainties must be balanced if intelligent cost-based design decisions are to be made. This paper developes a model of Life Cycle Cost which integrates various availability parameters of reliability and maintainability. A simulation algorithm is presented as the appropriate tool for studying life cycle cost of a plant design.     

Cost-benefit analysis of a one-server two-unit cold standby system with repair and age replacement

This paper deals with the cost-benefit analysis of a one-server two-identical-unit cold standby system with repair and preventive maintenance (PM). The PM is of the age replacement type, where, if a unit has been in operation for a certain period of time, which may be a random variable, and if the other unit is in standby, the operating unit is taken off for PM. The expected net revenue in the interval [0,t) is obtained using two different approaches. The first approach is more general and allows nonlinearities in the revenue and costs. It is assumed that the revenue obtained by operating a unit for an uninterrupted interval of time is some function of the length of that interval. Similarly, the cost of a repair or PM action is function of the length of the repair or PM time, respectively, for that action. The second approach assumes that the revenue, repair cost and PM cost vary linearly with time. The pointwise availability is derived. The busy period of the server is divided into time spent in performing repair and time spent on PM. The expected net revenue in [0,t) is obtained. Both techniques make use of regeneration points. It is finally shown that the results of the first approach under assumptions of linear revenue and cost functions reduce to those of the second approach.     

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     

System characteristic and cost analysis of a two unit standby system with spare units

This paper deals with the stochastic analysis of a standby system having two main units and two spare units.A spare unit is only used for operation when both main units fail and if it fails,it is replaced by the new one until the repair of the failed main unit is completed. The system fails when the last spare unit fails while one main unit is under repair and the other has failed. Using renewal theoretical arguments, certain characteristics of the system are derived and using them the cost of the system is calculated. Particular cases of the model are also considered.     

New analytical models for logistics support cost and life cycle cost vs reliability function

New analytical models have been put forward for logistics support cost (LSC) and life cycle cost (LCC) vs reliability function. Five new models are given for LSC, which are counterpart of the corresponding acquisition cost (AC) curves. LSC and AC have been added together to get the total LCC. For the first time a quantitative footing has been established for the life cycle cost function.