Optimal monitoring strategies for slowly deteriorating repairablesystems

A simple model for determination of an optimal limit on taking corrective action in a slowly deteriorating repairable system is presented. The performance of such a system is assumed to be characterized by a single parameter which is continuously being monitored. The underlying deterioration process is assumed to be governed by a Brownian motion process with a positive drift. When the measured value of the parameter reaches the action limit, the repair/replacement procedure is initiated. The optimal action limit is derived so that the expected long run average total cost is minimized. Some simple numerical examples illustrate the model and the optimization     

Optimal maintenance-policies for deteriorating systems undervarious maintenance strategies

This paper presents algorithms for deriving optimal maintenance policies to minimize the mean long-run cost-rate for continuous-time Markov deteriorating systems. The degree of deterioration (except failure) of the system is known only through inspection. The time durations of inspection and replacement are nonnegligible. The costs are for inspection, replacement, operation, and downtime (idle). In particular, the replacement time, replacement cost, and operating cost-rate increase as the system deteriorates. Five maintenance strategies are considered-failure replacement, age replacement, sequential inspection, periodic inspection, and continuous inspection. Iterative algorithms are developed to derive the optimal maintenance policy and the corresponding cost rate for each strategy. Under sufficient conditions, structural optimal policies are obtained     

Optimal inspection and replacement of a coherent system

In this paper the problem of optimal inspection and replacement of a coherent system with components having exponential life-time distributions is studied. It is assumed that the states of the components are known at system failures and through checking. The problem is formulated in a semi-Markovian decision process framework.     

Optimal continuous-wear limit replacement under periodicinspections

An item breaks down when it wears continuously beyond a certain threshold. The item is preventively replaced as the wear at periodic inspections exceeds a certain wear limit; on failure, it is replaced immediately. The optimal wear limit for preventive replacement that minimizes the long-run total average-cost rate is derived. A numerical example demonstrates its computability     

Optimal wear-limit replacement with wear-dependent failures

The optimal wear-limit for preventive replacement for an item with wear-dependent failure rate is derived by minimizing the long-run total mean cost rate. The generic term wear connotes any type of degradation that accumulates through use and is observed continuously in time. The optimal strategy has the same form as the age replacement policy     

Optimal number of major failures before replacement

When the repair cost of a failed system is random, it is no longer meaningful to expend more than the replacement cost on a catastrophic failure. This paper presents a mathematical model that uses two cost limits to combine and extend the replacement models based on minor-failure number[8] and constant repair cost limit[5] for general time-to-failure distributions. 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 minor repair-cost limit; or if the estimated cost is less than the replacement cost and the predetermined major-failure number is not reached. An example with a Weibull time-to-failure distribution and a negative exponential distribution of estimated repair cost is given to illustrate the computational results.     

一种可提高谐振腔稳定性的结构设计

激光谐振腔稳定性影响其输出激光的光斑分布和光轴稳定度,从而影响测距威力。本文从工程实践的角度对比分析增加副底板结构前后激光谐振腔的形变。通过仿真分析和实验证明,增加副底板结构可以大幅度改善谐振腔的稳定度。这一结论可用于指导激光发射器的结构设计工作。     

Optimal design improving a communication network reliability

Improvement of the reliability of a communication network is an optimal problem that finds some links to add to the network such that the reliability of the network reaches a given level and the total cost of these links is minimized. A decomposition method based on branch and bound is used for solving the problem. In order to speed up the solution procedure, an upper bound on system reliability in terms of node degrees is applied. Specially, when the threshold P_o is large enough, a new algorithm, the cut tree algorithm, can more effectively give the optimal solution.     

Optimal replacement policy for induced draft fans

This paper derives the optimal block replacement policies for four different operating configurations of induced draft fans. Under the usual assumption of higher cost of repair or replacement on failure compared to preventive replacement, the optimal preventive replacement interval is found by minimising the total relevant cost per unit time. Specifically, this paper finds optimal preventive maintenance strategies for the following two situations.

1. (i)|Both the time to failure and time to carry out minimal repair or replacement are exponentially distributed.

2. (ii)|The time to failure follows the Weibull distribution and there is no possibility of on-line repair or replacement.

For both situations closed form expressions are derived whose solutions give optimum preventive maintenance intervals.     

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 replacement policies for systems with multiple standbycomponents

The authors consider two new preventive replacement policies for a multiple-component cold-standby system. The failure rate of the component in operation is constant. The system is inspected at random points over time to determine whether it is to be replaced. The replacement decision is based on the number of failed components at the time of inspection. There are two replacement options if the complete system fails during operation: (i) replace the system if an inspection reveals that it has failed (system failure is not self-announcing), and (ii) replace the system the instant it fails (system failure is self-announcing). There is a threshold value on the number of failed components (at the time of inspection) which minimizes the mean total cost. The authors develop a simple efficient procedure to find the optimal threshold value. They compare the cost of operating a system that is inspected at random points in time, with the cost of operating a system that is monitored continuously through an attached monitoring device, and discuss cost tradeoffs     

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.     

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.     

Optimal design of PML absorbing boundary condition for improving wide-angle reflection performance

A method to optimise the angle reflection performance of Berenger's perfectly matched layer (PML) absorbing boundary condition for finite-difference time-domain (FDTD) method is described. By specifying the conductivity in each of the PML sublayers, the wide-angle reflection performance can be improved. To improve the angle reflection performance as well as to reduce the discretisation error characteristic due to the FDTD approximation, a two-step conductivity profile is used in PML. To obtain the optimal value for each conductivity profile, the micro-genetic algorithm method is employed. Using this method, good wide-angle reflection performance of PML is achieved.     

Optimal replacement time of an equipment via simulation for truncated failure distributions

The optimal replacement time T^* of an equipment for different failure (truncated) distributions is obtained by Monte Carlo simulation and the results verified by analytical methods, whenever possible. The results are illustrated by explicit numerical solutions (wherever feasible) and by simulation runs in all cases.     

Optimal replacement of an item subject to cumulative damage under periodic inspections

An item undergoes cumulative damage through use. The item fails randomly but the failure rate depends on the accumulated damage. The item is preventively replaced if it survives a certain damage limit at periodic inspections; on failure, it is replaced immediately. The optimal damage limit for preventive replacement which minimizes the long-run expected cost rate is derived. It is unique if an item has increasing damage-dependent failure rate. Numerical example for a stationary gamma process with Weibull distributed failure is given.     

Optimal adaptation methods and class of operation: keys to improving feedforward amplifier power efficiency

This paper studies the influences of two new adaptation methods and the class of main amplifier operation on the achievable power efficiency of the feedforward amplifier under typical design constraints. These two influences are weak for a two-tone driving signal, but they interact powerfully for a real-life high-stress signal, leading to optimal designs involving Class AB or even Class B main amplifiers, depending on the required output linearity. Assuming a code-division multiple-access signal, typical MESFETs, and an output linearity commonly used in mobile systems design, the new adaptation methods allowed relative efficiency improvements of 21% and 36% using main amplifiers biased near Class B and at Class B, respectively.     

Optimal replacement policy for a warrantied system with imperfect preventive maintenance operations

This paper determines the optimal replacement time for a system with imperfect preventive maintenance operations under the modified warranty policy. The hazard rate after preventive maintenance lies between the states as good as new and as bad as old. After minimal repair, the hazard rate remains unchanged. Modified warranty policy is a mixed type of free and pro-rata warranty policy. Numerical examples using the Weibull case are presented.     

Reliability analysis of a Markovian deteriorating system

The reliability of a complex system passes through a gradual deterioration until at some critical level, the system fails completely. The study of such a system failure requires the application of Markov processes to obtain reliability measures such as mean time of system failure. The Laplace transform of reliability of the system starting from each operating state is employed for solving such a complex system of differential equations. A four-state deteriorating system is considered and various particular cases of the arbitrary repair times distribution are discussed.     

Stochastic analysis of a deteriorating standby system with three modes and inspection

A two-unit (identical) deteriorating standby system is analysed. Each unit can be in one of the three modes—normal, partial failure and total failure. A unit can fail totally but not partially during its standby state. Standby is inspected at random epochs. Using regenerative point technique in Markovrenewal process theory, several reliability characteristics of interest to system designers and operation managers are obtained.