Optimal replacement period of a two-unit system with failure rate interaction and external shocks

In this article, a periodical replacement model for a two-unit system which is both subjected to failure rate interaction and external shocks will be presented. Without external shocks, each unit 1, whenever it fails, will act as an interior shock to affect the failure rate of unit 2 and increase the failure rate of unit 2 to a certain degree, while each unit 2 failure causes unit 1 into instantaneous failure. Besides failure rate interaction between units, the system is also subjected to external shocks which can be divided into two types. Type A shock causes unit 1 into failure and then converts the damage of such a failure to unit 2, while type B shock makes the system total breakdown. All unit 1 failures are corrected by minimal repairs. The aim of this article is to derive the expected cost rate per unit time by introducing relative costs as a criterion of optimality, and then the optimal replacement period which minimizes that cost will be determined. A numerical example is given to illustrate the method.     

Extended optimal replacement policy for a system subject to non-homogeneous pure birth shocks

This article studies the optimal replacement policy with general repairs for an operating system subject to shocks occurring to a non-homogeneous pure birth process (NHPBP). A shock causes that the system experiences one of two types of failures: type-I failure (minor failure) is rectified by a general repair, or type-II failure (catastrophic failure) is removed by an unplanned replacement. The probabilities of these two types of failures depend on the number of shocks since the last replacement. We consider a bivariate replacement policy (n, T) under which the system is replaced at planned life age T, or at the nth type-I failure, or at any type-II failure, whichever occurs first. The optimal replacement schedule which minimizes the expected cost rate model is derived analytically and discussed numerically.     

Optimal number of minimal repairs with cumulative repair cost limit for a two-unit system with failure rate interactions

A discrete replacement model is presented that includes a cumulative repair cost limit for a two-unit system with failure rate interactions between the units. We assume a failure in unit 1 causes the failure rate in unit 2 to increase, whereas a failure in unit 2 causes a failure in unit 1, resulting in a total system failure. If unit 1 fails and the cumulative repair cost till to this failure is less than a limit L, then unit 1 is repaired. If there is a failure in unit 1 and the cumulative repair cost exceeds L or the number of failures equals n, the entire system is preventively replaced. The system is also replaced at a total failure, and such replacement cost is higher than the preventive replacement cost. The long-term expected cost per unit time is derived using the expected costs as the optimality criterion. The minimum-cost policy is derived, and existence and uniqueness are proved.     

Optimal number of minimal repairs before replacement of a deteriorating system with inspections

In this study, we propose a generalised replacement model for a deteriorating system with failures that could only be detected through inspection work. The system is assumed to have two types of failures and is replaced at the Nth type I failure (minor failure) or first type II failure (catastrophic failure), depending on whichever occurs first. The probability of type I and II failures depends on the number of failures since the last replacement. Such systems can be repaired upon type I failure, but are stochastically deteriorating, that is, the lengths of the operating intervals are stochastically decreasing, whereas the durations of the repairs are stochastically increasing. Then, the expected net cost rate is obtained. Some special cases are considered. Finally, a numerical example is provided.     

Optimal number of minimal repairs before replacement based on a cumulative repair-cost limit policy

In this paper, we consider a replacement model with minimal repair based on a cumulative repair-cost limit policy, where the information of all repair costs is used to decide whether the system is repaired or replaced. As a failure occurs, the system experiences one of the two types of failures: a type-I failure (repairable) with probability q, rectified by a minimal repair; or a type-II failure (non-repairable) with probability p (=1 − q) that calls for a replacement. Under such a policy, the system is replaced anticipatively at the nth type-I failure, or at the kth type-I failure (k < n) at which the accumulated repair cost exceeds the pre-determined threshold, or any type-II failure, whichever occurs first. The object of this paper is to find the optimal number of minimal repairs before replacement that minimizes the long-run expected cost per unit time of this polish. Our model is a generalization of several classical models in maintenance literature, and a numerical example is presented for illustration.     

Preventive replacement policies with time of operations,mission durations,minimal repairs and maintenance triggering approaches

When a mission arrives at a random time and lasts for a duration, it becomes an interesting problem to plan replacement policies according to the health condition and repair history of the operating unit, as the reliability is required at mission time and no replacement can be done preventively during the mission duration. From this viewpoint, this paper proposes that effective replacement policies should be collaborative ones gathering data from time of operations, mission durations, minimal repairs and maintenance triggering approaches. We firstly discuss replacement policies with time of operations and random arrival times of mission durations, model the policies and find optimum replacement times and mission durations to minimize the expected replacement cost rates analytically. Secondly, replacement policies with minimal repairs and mission durations are discussed in a similar analytical way. Furthermore, the maintenance triggering approaches, i.e., replacement first and last, are also considered into respective replacement policies. Numerical examples are illustrated when the arrival time of the mission has a gamma distribution and the failure time of the unit has a Weibull distribution. In addition, simple case illustrations of maintaining the production system in glass factories are given based on the assumed data.     

Optimal number of minimal repairs before replacement based on a cumulative repair-cost limit policy

In this paper, we consider a replacement model with minimal repair based on a cumulative repair-cost limit policy, where the information of all repair costs is used to decide whether the system is repaired or replaced. As a failure occurs, the system experiences one of the two types of failures: a type-I failure (repairable) with probability q, rectified by a minimal repair; or a type-II failure (non-repairable) with probability p (=1 − q) that calls for a replacement. Under such a policy, the system is replaced anticipatively at the nth type-I failure, or at the kth type-I failure (k < n) at which the accumulated repair cost exceeds the pre-determined threshold, or any type-II failure, whichever occurs first. The object of this paper is to find the optimal number of minimal repairs before replacement that minimizes the long-run expected cost per unit time of this polish. Our model is a generalization of several classical models in maintenance literature, and a numerical example is presented for illustration.     

A multi-criteria optimal replacement policy for a system subject to shocks

A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As these shocks occur, the system experiences one of two types of failures: a type-I failure (minor), rectified by a minimal repair; or a type-II failure (catastrophic) that calls for a replacement. In this study, we consider a multi-criteria replacement policy based on system age, nature of failure, and entire repair-cost history. Under such a policy, the system is replaced at planned life time T, or at the nth type-I failure, or at the kth type-I failure (k < n) at which the accumulated repair cost exceeds the pre-determined limit, or at the first type-II failure, whichever occurs first. An optimal policy over the control parameters is studied analytically by showing its existence, uniqueness, and structural properties. This model is a generalization of several existing models in the literature. Some numerical examples are presented to show several useful insights.     

Extended optimal replacement policy for a two-unit system with failure rate interaction and external shocks

This study presents an extended replacement policy for a two-unit system which is subjected to shocks and exhibits failure rate from interaction. The external shocks that affect the system are of two types. A type I shock causes a minor failure of unit-A and the damage that is caused by such a failure affects unit-B, whereas a type II shock causes a total failure of the system (catastrophic failure). All unit-A failures can be recovered by making minimal repairs. The system also exhibits the interaction between the failure rates of units: a failure of any unit-A causes an internal shock that increases the failure rate of unit-B, whereas a failure of a unit-B causes instantaneous failure of unit-A. The goal of this study is to derive the long-run cost per unit time of replacement by introducing relative costs as a factor in determining optimality; then, the optimal replacement period, T*, and the optimal number of unit-A failures, n*, which minimise that cost can be determined. A numerical example illustrates the method.     

Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. When failures occur, the repair of both component 1 and component 2 are not ‘as good as new’. The consecutive operating times of component 1 after repair constitute a decreasing geometric process, while the repair times of component 1 are independent and identically distributed. For component 2, its failure is rectified by minimal repair, and the repair time is negligible. Component 1 has priority in use when both components are good. The replacement policy N is based on the failure number of component 1. Under policy N, we derive the explicit expression of the long-run average cost rate C(N) as well as the average number of repairs of component 2 before the system replaced. The optimal replacement policy N*, which minimises the long-run average cost rate C(N), is obtained theoretically. If the failure rate r(t) of component 2 is increasing, the existence and uniqueness of the optimal policy N* is also proved. Finally, a numerical example is given to validate the developed theoretical model. Some sensitivity analyses are provided to show the influence of some parameters, such as the costs for replacement and repair, and the parameters of the lifetime and repair time distributions of both components, to the optimal replacement policy N* and corresponding average cost rate C(N*).     

A geometric process repair model for a two-component system with shock damage interaction

In this article, the repair-replacement problem for a two-component system with shock damage interaction and one repairman is studied. Assume that component 1 will be replaced as soon as it fails, and each failure of component 1 will induce a random shock to component 2. The shock damages may be accumulative, and whenever the total shock damage equals or exceeds a given threshold Δ, component 2 fails and the system breaks down. Component 2 is repairable, and it follows a geometric process repair. Under these assumptions, we consider a replacement policy N based on the number of failures of component 2. 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 minimised. The explicit expression of the average cost rate is derived by the renewal reward theorem, and the optimal replacement policy can be determined analytically or numerically. The existence and uniqueness of the optimal replacement policy N* is also proved under some mild conditions. Finally, two appropriate numerical examples are provided to show the effectiveness and applicability of the theoretic results in this article.     

Optimal control of a linear system subject to partially specified input noise

One of the most basic problems in control theory is that of controlling a discrete‐time linear system subject to uncertain noise with the objective of minimizing the expectation of a quadratic cost. If one assumes the noise to be white, then solving this problem is relatively straightforward. However, white noise is arguably unrealistic: noise is not necessarily independent, and one does not always precisely know its expectation. We first recall the optimal control policy without assuming independence and show that, in this case, computing the optimal control inputs becomes infeasible. In the next step, we assume only the knowledge of lower and upper bounds on the conditional expectation of the noise and prove that this approach leads to tight lower and upper bounds on the optimal control inputs. The analytical expressions that determine these bounds are strikingly similar to the usual expressions for the case of white noise.     

Optimal cycle production of a manufacturing system subject to deterioration

A single part type, single machine, fluid model manufacturing system is considered. The machine is subject to a deterministic deterioration process, which depends on the operation rate. The objective is to minimize a long term average cost index which penalizes inventory surplus and backlog. The optimal policy determined presents some similarities with the policy conjectured optimal in the past for a similar Markovian formulation. The considered problem can be applied to several real contexts, and not just from the manufacturing domain, as briefly discussed in the paper.     

Maintenance interval decision models for a system with failure interaction

Based on the three types of failure interactions, two periodical maintenance cost models were presented for a two-state series system and a three-state series system respectively, which all subjected to failure interactions between units. Consider any unit fails would cause damages to other units. The failure interaction influences included instantaneous damages and continuous damages between units. The result indicated that failure interactions will shorten system preventive maintenance interval, if the preventive maintenance strategy is based on the cost.     

A fuzzy inference system for pump failure diagnosis to improve maintenance process: The case of a petrochemical industry

Pump operating problems may be either hydraulic or mechanical and there is interdependence between the failure diagnoses of these two categories. Consequently, a correct diagnosis of a pump failure needs to consider many symptoms and hydraulic or mechanical causes. But, due to nonlinear, time-varying behavior and imprecise measurement information of the systems it is difficult to deal with pumps failures with precise mathematical equations, while human operators with the aid of their practical experience can handle these complex situations, with only a set of imprecise linguistic if-then rules and imprecise system state, but this procedure is time consuming and needs the knowledge of human experts and experienced maintenance personnel. The purpose of this study is to provide a correct and timely diagnosis mechanism of pump failures by knowledge acquisition through a fuzzy rule-based inference system which could approximate human reasoning. The proposed fuzzy inference system by: (1) reduction of human error, (2) reduction of repair time (3) creation of expert knowledge which could be used for training (4) reduction of unnecessary expenditures for upgrades and finally, (5) reduction of maintenance costs, will improve the maintenance process. The novelty of this work is the knowledge acquisition (the extraction of linguistic rules) through the interactive impact of the critical failure modes on the both hydraulic and mechanical operating parameters including flow rate, discharge pressure, NPSHR (Net Positive Suction Head Required), BHP (Brake Horse Power), efficiency, vibration and temperature. The proposed approach is tested and applied to a petrochemical industry.     

Stability analysis for a second-order continuous finite-time control system subject to a disturbance

In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.     

一种灌装过程计算机动态仿真系统的开发

简要剖析了液态化学品灌装工艺流程及其灌装原理,应用物料平衡、气体状态方程和过程技术数据,通过微分方程法和动态补偿法等方法建立灌装过程动态仿真数学模型.基于单机智能控制(intelligent process control,IPC)仿真模式,应用自控组态软件Centrey Star,研究了过程的动态仿真实现方法,确定了仿真系统的总体结构组成、总体技术方案与原理,开发了仿真系统的图形用户操作界面,完成了仿真工艺流程图、各类仿真命令按钮及其显示画面、以及流程中各类可操作部件及其参数调整仿真操作画面的设计与命令语言编程,用Visual C++(VC++)开发了模型运算软件,生成了DLL库函数,与图形用户界面集成,研制了一套完备的动态仿真系统,实现了灌装工艺过程的全面动态仿真.最后系统地进行了灌装过程的原理性仿真试验,获得了满意的仿真结果,优化了灌装过程工艺运行条件.     

Using a business process management system to model dynamic teaching methods

Enterprise Information Systems are enjoying an extensive trajectory in the optimization of organizations worldwide, of which predominantly the Business Process Management (BPM) systems stand out for their great flexibility. BPM models describe business workflows and are highly useful in detecting errors and bottlenecks and in identifying possible improvements. On the other hand, educational management software tools offer a large number of functionalities, but have yet to take advantage of these techniques. Our main objective is to perform an empirical analysis in this unexplored area to evaluate the advantages of applying BPM in the implementation of innovative and dynamic teaching activities.Using this methodology, we have designed RubricaSoft, a BPM system focused on providing dynamic educational processes. It automates multiple tasks, including peer evaluation, information integration and the management of deadlines. The results have been very promising from the point of view of the three axes upon which the evaluation has been carried out: satisfaction of students, improvement in academic results and increase in the productivity of teachers. In one of the processes, the time spent by the teacher has been reduced by 80% and student participation increased by 41%.     

缔合体系精馏过程模拟软件开发

建立了缔合体系相平衡模型,并对含缔合组分汽相焓进行了校正,液相用NRTL、Wilson方程修正其非理想性计算出的汽液相平衡数据及焓值,用于缔合体系多股进料精馏模拟取得了满意的效果。本软件采用三对角矩阵法求解精馏过程的MESH方程组,用Visual Basic 6．0开发出缔合体系精馏模拟软件,同时软件也包括了一般体系的多元复杂精馏模拟。