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 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 reliability of systems subject to imperfect fault-coverage

This paper maximizes the reliability of systems subjected to imperfect fault-coverage. The results include the effect of common-cause failures and `maximum allowable spare limit'. The generalized results are presented and then the policies for some specific systems are given. The systems considered include parallel, parallel-series, series parallel, k-out-of-n, and NMR (k-out-of-(2k-1)) systems. The results are generalized for the non s-identical component case     

SILC dynamics in MOS structures subject to periodic stress

This work investigates stress-induced leakage current (SILC) in thin-oxide MOS capacitors subject to (quasiperiodic) ac voltage stress, under the condition of fixed charge fluence through the oxide. It shows that both trap creation and spontaneous trap annealing play a significant role when the duration of, and the time between, high-voltage pulses are comparable with characteristic times of trap dynamics. A phenomenological model is introduced that is able to accurately represent the main physical phenomena due to pulsed voltage stress under conditions of interest for unconventional programming schemes for fast programming nonvolatile memories (NVMs) with acceptable oxide degradation.     

A general replacement of a system subject to shocks

A system is subject to shocks that arrive according to a nonhomogeneous Poisson process. The system is replaced at age T at a fixed cost c₀. If the k-th shock arrives at time S_k<T, it is either a fatal shock with probability p(S_k) or a nonfatal shock with probability 1−p(S_k). The fatal shock causes the system total breakdown, and the system is replacd at a cost c_∞. The nonfatal shock weakens the system and makes it more expensive to run. 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.     

Optimal maintenance schedules of systems subject to stochastic failure

Almost all operational and standby systems need maintenance, yet this is often overlooked in the stages of design and development. Lately, maintenance has been emphasized by several factors such as rising costs of labor and material, increased complexity of systems and increased quality requirements. The aim of this paper is to develop new algorithms and analysis techniques that can be used in a general way to handle optimization of various types of inspection and maintenance schedules of systems subject to stochastic failure. Physical problems of systems in active operation with increasing failure rate are treated. Examples of such systems are: airborne electronic equipment, radio receivers, aircraft engines, etc. The optimal maintenance schedule incorporates the effects of inspection, maintenance, delayed detection, uptime and downtime costs. The techniques of classical differential calculus and dynamic programming are applied for the development of the optimal maintenance schedule.     

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     

Optimal focusing of scalar fields subject to arbitrary upper bounds

The authors present a new approach for determining the excitations of a given set of sources that will produce a maximum field in a given direction subject to arbitrary sidelobe bounds. The approach guarantees attainment of the globally optimal solution for a large class of pencil beam synthesis problems, including possible near field constraints     

Optimal control output policies of a reservoir subject to Wiener inputs

In this paper we consider two types of optimal control output policies for a finite dam subject to Wiener inputs with positive drift. The long-run average cost per unit time of operating a finite dam controlled by both two types of policies are determined, and therefore the optimal policies can be found numerically.     

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 approximate inverse of linear periodic filters

We propose a method for constructing optimal causal approximate inverse for discrete-time single-input single-output (SISO) causal periodic filters in the presence of measurement noise. The analysis is based on block signals and multi-input multi-output (MIMO) time-invariant models for periodic filters. The objective function to be minimized is the asymptotic block mean square error. The optimization problem is formulated in terms of transfer matrices as an optimal model-matching problem with nonsquare model and plant. Based on an inner-outer factorization on the transpose of the plant rational matrix, it is shown that the problem can be further reduced to one with a lower dimensional square model and plant, which is then solved in the time-domain, and a closed-form solution is obtained. A lower bound on the objective function is given. It is shown that the lower bound can be asymptotically achieved as the order of the optimal transfer matrix increases. The proposed method is extended to MIMO periodic systems. Numerical examples are used to illustrate the performance of the proposed approximate inverse.     

Optimal replacement of improving and deteriorating repairablesystems

System improvement and deterioration are defined in terms of partial orderings between life distributions. The effects of ageing of `the distribution of time to first failure' on improvement and deterioration of a repairable system subject to minimal repairs, are investigated. Under various types of life distributions we derive explicitly the times at which the system should be condemned (replaced by a new one) to minimize the total cost of maintenance and replacement in terms of parameters of the distribution and of the cost function     

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.     

Optimal far-field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions

A new approach providing new theoretical results to the optimal far-field focusing of uniformly spaced arrays, subject to a completely arbitrary mask for sidelobe bounds, is presented and discussed. In both cases of linear or planar arrays (with rectangular boundaries), it is first shown that the problem can be formulated, without any loss to performances on the maximum, as a linear programming one, guaranteeing a globally optimal solution. Second, a sufficient uniqueness criterion for the solution of the overall problem is also developed, which shows how the solution may not be unique (as is actually the case) when planar arrays are considered. In addition, further globally effective optimization procedures are proposed for the latter case in order to optimize directivity, smoothness of excitations, or other performance parameters in the set of equivalent solutions. Last, an extension to planar arrays with a nonrectangular boundary is also given. A thorough numerical analysis confirms the effectiveness of the approach proposed and of the solution codes developed.     

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 Rules to Adopt High Technology under Uncertainty

In recent years, fundamental changes in regulation, global competition, and technology have made it more difficult for firms to maintain their success for a long time. Flexible strategy theories suggest that firms should take advantage of or even create the changes to gain competitive advantages, rather than only adapt to them[1]. During this process, technological innovation is one of the most important strategies. For the constant emergence of high technology, firms with high technology do n…     

Three replacement models with two kinds of damage

This paper proposes three replacement policies for a modified cumulative damage model. An item receives shocks and suffers two kinds of damage: one is produced by shocks and the other increases with time at constant rate a. It fails only when the total damage exceeds a failure level K at some shock and is replaced before failure at time T, at shock N, or at damage k. The expected cost rates of three replacement policies are obtained. When shocks occur in a Poisson process, optimal T^*, N^* and k^* which minimize them are computed numerically. Finally, two extended cases where a is a function of time and K is a random variable are also considered.