A bivariate optimal replacement policy for a system subject to a generalized failure and repair process

Traditionally, in the studies of the optimal maintenance policies for repairable systems, the nonhomogeneous Poisson process model, which corresponds to the minimal repair process, has been intensively applied. However, in many practical situations, the repair type is not necessarily minimal. In this article, a new repair process based on a new counting process model (so‐called the generalized Polya process) is introduced. Then, the issue of the optimal replacement problem is discussed. A bivariate preventive replacement policy is developed and the properties of the optimal policy are studied. Illustrative examples are also presented. In addition, a comparison with a conventional replacement policy is performed.     

A note on replacement policy for a system subject to non-homogeneous pure birth shocks

A system is subject to shocks that arrive according to a non-homogeneous pure birth process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T. The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.     

索赔次数为复合Poisson-Geometric过程的风险模型及破产概率

本文引入一类复合Poisson-Geometric分布,这类分布包括两个参数,是普通Poisson分布的一种推广,并在保险中有其实际的应用背景;基于此分布产生一个计数过程,称之为复合Poisson-Geometric过程.本文着重研究了索赔次数为复合Poisson-Geometric过程的风险模型,这种模型是经典风险模型的一个推广.针对此模型,本文给出了破产概率公式及更新方程.作为特例,当索赔额服从指数分布时,给出了破产概率的显式表达式.     

A Stagewise Action Elimination Algorithm for the Discounted Semi-Markov Problem

An efficient algorithm for solving discounted semi-Markov (Markov-renewal) problems is proposed. The value iteration method of dynamic programming is used in conjunction with a test for non-optimal actions. A non-optimality test for the discounted semi-Markov processes, which is an extension of Hastings and Van Nunens (1976) test for the undiscounted or discounted returns with infinite or finite planning horizon, is used to identify actions which cannot be optimal at the current stage of a discounted semi-Markov process. The test proposed eliminates actions for one or more stages after which they may enter the set of possibly optimal actions, but such re-entries cease as convergence proceeds.     

基于两种不同延迟过程的退化系统之最优更换策略

将延迟几何过程进行推广并引入延迟α-幂过程,以用于处理退化过程会发生延迟且延迟发生的概率会随故障次数的增多而减小的系统.以系统的故障次数为更换策略,以平均费用率为目标函数,建立了维修更换模型,证明了最优维修更换策略的存在性.最后,通过一个数值例子验证了方法的有效性.     

Adaptive Monte Carlo Variance Reduction for Lévy Processes with Two-Time-Scale Stochastic Approximation

We propose an approach to a twofold optimal parameter search for a combined variance reduction technique of the control variates and the important sampling in a suitable pure-jump Lévy process framework. The parameter search procedure is based on the two-time-scale stochastic approximation algorithm with equilibrated control variates component and with quasi-static importance sampling one. We prove the almost sure convergence of the algorithm to a unique optimum. The parameter search algorithm is further embedded in adaptive Monte Carlo simulations in the case of the gamma distribution and process. Numerical examples of the CDO tranche pricing with the Gamma copula model and the intensity Gamma model are provided to illustrate the effectiveness of our method.      

Productivity Indices and Personnel Comparative Assessment in a Multidivisional Corporation

The objective of this study is to explore the determinants and relative performance of manpower in the distribution divisions of the Electricity Utility in Greece. A cross-sectional factor analysis model is proposed for analyzing differences in operating conditions between the divisions; an initial set of variables, which relate to manpower activities, is reduced to some composite dimensions each representing a distinct characteristic of the environment within which personnel activities take place. Regressing personnel along these dimensions an inter-divisional comparison of manning is carried out and some indices of labour-productivity are derived.     

定期检修可修系统更换模型研究

针对定期检修退化可修系统提出了一种维修更换模型,且假定系统在每个周期中检修时间逐渐递增、检修"修复如旧"和故障维修为"修复非新"时,选择系统的故障次数N为更换策略,利用更新过程和单调的几何过程理论建立数学模型,求出了系统经长期运行单位时间内的期望效益的表达式.最后还对结果进行了讨论,并给出了数值例子验证该方法的有效性.     

Hidden heterogeneity in manpower systems: A Markov-switching model approach

In modeling manpower systems, it is of crucial importance to deal with heterogeneity. Until recently, manpower models are dealing with heterogeneity due to observable sources, neglecting heterogeneity due to latent sources. In this paper a two-step procedure is introduced. In the first step personnel groups homogeneous with respect to the transition probabilities are determined in a classical way by taking into account the observable sources of heterogeneity. In the second step heterogeneity caused by latent sources is handled. A multinomial Markov-switching manpower model is introduced that deals with heterogeneity due to latent sources for the internal flows as well as for the wastage flows. The model incorporates the mover-stayer principle. A re-estimation algorithm is presented to estimate the parameters of the Markov-switching manpower model. The switching approach offers a methodology to build a Markov model with personnel groups as states that are more homogeneous, and therefore can contribute to a better validity of the manpower model.     

A queue with instantaneous tri-route decision process

This paper focuses on the study of several random processes associated with M/G1 queue with instantaneous tri-route decision process. The stationary distribution of the output process is derived. Some particular queues with feedback and without feedback are also analysed. Some operating characteristics are studied for this queue. Optimum service rate is obtained. A numerical study is carried out to test the feasibility of the queueing model.     

Personnel Recruitment Policies and Long-Term Production Planning

Any organization or industry operating in a market where there is unmet demand will be under considerable pressure to meet the demand as quickly as possible. This short-term objective can be met by rapidly expanding productive capacity in terms of both plant or other equipment and also manpower. If the commodity in demand is durable—e.g. housing, cars, computers—then when the initial requirement is met, further output is for replacement purposes. Production during the expansion phase, planned to eliminate the backlog of demand may be much greater than that needed for the next phase, meeting recurrent replacement demand. If capacity is allowed to run down, a later increase in demand will possibly find the organization with too little capacity. There follows a potentially continuing cycle of under- and over-production. Since manpower comprises a significant part of the capacity, this creates a possible cycle of under- and over-employment.Mathematical models of manpower systems can be adapted to investigate the consequences of controlling recruitment policies over fairly long periods of time. If costs can be ascribed to both under- and over-production it is possible to combine the manpower models with mathematical programming techniques to produce optimal longterm recruitment policies.The possible development of the telephone network in the Republic of Ireland is used as an illustrative example. Here it has already been established by government operational research scientists that meeting the original target number of installations for the early 1980's would require impossibly large levels of recruitment immediately. Our model shows that, if the target were achieved, an intolerably large proportion of the workforce would be redundant in a few years time. We use a linear programming model to illustrate viable policies trading off present delays in satisfying demand against future overmanning.     

Opportunity-based age replacement with a one-cycle criterion

In this paper age replacement (AR) and opportunity-based age replacement (OAR) for a unit are considered, based on a one-cycle criterion, both for a known and unknown lifetime distribution. In the literature, AR and OAR strategies are mostly based on a renewal criterion, but in particular when the lifetime distribution is not known and data of the process are used to update the lifetime distribution, the renewal criterion is less appropriate and the one-cycle criterion becomes an attractive alternative. Conditions are determined for the existence of an optimal replacement age T^* in an AR model and optimal threshold age T_opp^* in an OAR model, using a one-cycle criterion and a known lifetime distribution. In the optimal threshold age T_opp^*, the corresponding minimal expected costs per unit time are equal to the expected costs per unit time in an AR model. It is also shown that for a lifetime distribution with increasing hazard rate, the optimal threshold age is smaller than the optimal replacement age. For unknown lifetime distribution, AR and OAR strategies are considered within a nonparametric predictive inferential (NPI) framework. The relationship between the NPI-based expected costs per unit time in an OAR model and those in an AR model is investigated. A small simulation study is presented to illustrate this NPI approach.     

Tactical Manpower Planning via Programming Under Uncertainty

This paper presents models for different types of manpower pooling policies. A multi-grade manpower system with mutually exclusive skills is considered. The work load imposed is a random variable characterized by the known joint distribution of the number of jobs to be performed and of the time to do a job. The basic models are developed as a tool for manpower planning in the jobbing workshops of an oil company. The resulting "two-stage programmes under uncertainty" are shown to reduce to mixed-integer linear programmes. The models are then generalized to permit their use in a larger class of manpower planning problems.     

A difference equation approach for analysing a batch service queue with the batch renewal arrival process

We consider an infinite buffer single server queue wherein customers arrive according to the batch renewal arrival process and are served in batches following the random serving capacity rule. The service-batch times follow exponential distribution. This model has been studied in the past using the embedded Markov chain technique and probability generating function. In this paper we provide an alternative yet simple methodology to carry out the whole analysis which is based on the supplementary variable technique and the theory of difference equations. The procedure used here is simple in the sense that it does not require the complicated task of constructing the transition probability matrix. We obtain explicit expressions of the steady-state system-content distribution at pre-arrival and arbitrary epochs in terms of roots of the associated characteristic equation. We also present few numerical results in order to illustrate the computational procedure.     

企业家人力资源培训问题的整数规划模型

本文强调了企业家人力资源在企业核心能力和可持续成长能力生成中的重要作用和地位。基于时间和费用指标,研究了企业家人力资源培训问题,利用0-1线性整数规划建立了一个带有培训时间约束的最小培训费用模型,给出了求解模型的基于Lagrange松弛的分解算法,计算实例表明给出的算法是有效的。     

Gamma-Dirichlet algebra and applications

The Gamma-Dirichlet algebra corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process through the gamma process and vice versa. In this article, we begin with a brief survey of several existing results concerning this structure. New results are then obtained for the large deviations of the jump sizes of the gamma process and the quasi-invariance of the two-parameter Poisson-Dirichlet distribution. We finish the paper with the derivation of the transition function of the Fleming-Viot process with parent independent mutation from the transition function of the measure-valued branching diffusion with immigration by exploring the Gamma-Dirichlet algebra embedded in these processes. This last result is motivated by an open R. C. Gritfiths. problem proposed by S. N. Ethier and     

Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives

Novel replacement policies that are hybrids of inspection maintenance and block replacement are developed for an n identical component series system in which the component parts used at successive replacements arise from a heterogeneous population. The heterogeneous nature of components implies a mixed distribution for time to failure. In these circumstances, a hybrid policy comprising two phases, an early inspection phase and a later wear-out replacement phase, may be appropriate. The policy has some similarity to burn-in maintenance. The simplest policy described is such a hybrid and comprises a block-type or periodic replacement policy with an embedded block or periodic inspection policy. We use a three state failure model, in which a component may be good, defective or failed, in order to consider inspection maintenance. Hybrid block replacement and age-based inspection, and opportunistic hybrid policies will also arise naturally in these circumstances and these are briefly investigated. For the simplest policy, an approximation is used to determine the long-run cost and the system reliability. The policies have the interesting property that the system reliability may be a maximum when the long-run cost is close to its minimum. The failure model implies that the effect of maintenance is heterogeneous. The policies themselves imply that maintenance is carried out more prudently to newer than to older systems. The maintenance of traction motor bearings on underground trains is used to illustrate the ideas in the paper.     

Stochastic optimal control of internal hierarchical labor markets

This paper develops an optimal control model for a graded manpower system where the demand for manpower is uncertain. The organization's objective is to minimize the discounted costs of operating the manpower system, including excess demand costs. The stock of workers in various grades can be adjusted in two ways. The first method is outside hiring flows, which is the usual control variable used in previous research. The second method is to control the transition rates between grades of the hierarchy, an instrument not previously studied. Incorporating the transition rates into the control variables creates time lags in the control process. The resulting problem is solved numerically using an approximation for the time-lagged control variables. The numerical example is based on the Air Force officer hierarchy. The model is used to examine such issues as the desirability of granting tenure to workers who are not promoted to the highest grade and the effects of length-of-service and demand uncertainty on manpower policy.     

A deteriorating cold standby repairable system with priority in use

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. In this system, it is assumed that the working time distributions and the repair time distributions of the two components are both exponential and component 1 is given priority in use. After repair, component 2 is “as good as new” while component 1 follows a geometric process repair. Under these assumptions, using the geometric process and a supplementary variable technique, some important reliability indices such as the system availability, reliability, mean time to first failure (MTTFF), rate of occurrence of failure (ROCOF) and the idle probability of the repairman are derived. A numerical example for the system reliability R(t) is given. And it is considered that a repair-replacement policy based on the working age T of component 1 under which the system is replaced when the working age of component 1 reaches T. Our problem is to determine an optimal policy T^∗ such that the long-run average cost per unit time of the system is minimized. The explicit expression for the long-run average cost per unit time of the system is evaluated, and the corresponding optimal replacement policy T^∗ can be found analytically or numerically. Another numerical example for replacement model is also given.     

An optimal replacement policy for a multistate degenerative simple system

In this paper, a degenerative simple system (i.e. a degenerative one-component system with one repairman) with k + 1 states, including k failure states and one working state, is studied. Assume that the system after repair is not “as good as new”, and the degeneration of the system is stochastic. Under these assumptions, we consider a new replacement policy T based on the system age. Our problem is to determine an optimal replacement policy T^∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy can be determined, the explicit expression of the minimum of the average cost rate can be found and under some mild conditions the existence and uniqueness of the optimal policy T^∗ can be proved, too. Further, we can show that the repair model for the multistate system in this paper forms a general monotone process repair model which includes the geometric process repair model as a special case. We can also show that the repair model in the paper is equivalent to a geometric process repair model for a two-state degenerative simple system in the sense that they have the same average cost rate and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results of this model.