Optimal design of k-out-of-n:G subsystems subjected to imperfect fault-coverage

Systems subjected to imperfect fault-coverage may fail even prior to the exhaustion of spares due to uncovered component failures. This paper presents optimal cost-effective design policies for k-out-of-n:G subsystems subjected to imperfect fault-coverage. It is assumed that there exists a k-out-of-n:G subsystem in a nonseries-parallel system and, except for this subsystem, the redundancy configurations of all other subsystems are fixed. This paper also presents optimal design polices which maximize overall system reliability. As a special case, results are presented for k-out-of-n:G systems subjected to imperfect fault-coverage. Examples then demonstrate how to apply the main results of this paper to find the optimal configurations of all subsystems simultaneously. In this paper, we show that the optimal n which maximizes system reliability is always less than or equal to the n which maximizes the reliability of the subsystem itself. Similarly, if the failure cost is the same, then the optimal n which minimizes the average system cost is always less than or equal to the n which minimizes the average cost of the subsystem. It is also shown that if the subsystem being analyzed is in series with the rest of the system, then the optimal n which maximizes subsystem reliability can also maximize the system reliability. The computational procedure of the proposed algorithms is illustrated through the examples.     

Reliability of k-out-of-n:G systems with imperfect fault-coverage

k-out-of-n:G systems are modeled to determine their reliability and availability. Markov models are obtained to examine the fault-tolerant operation of the system. From the Markov chains, reliability and availability measures are found as state probabilities. Recursive expressions for mean time-between-failures and mean time-to-failure are obtained for repairable systems, considering perfect and imperfect fault-coverage     

A separable method for incorporating imperfect fault-coverage intocombinatorial models

This paper presents a new method for incorporating imperfect FC (fault coverage) into a combinatorial model. Imperfect FC, the probability that a single malicious fault can thwart automatic recovery mechanisms, is important to accurate reliability assessment of fault-tolerant computer systems. Until recently, it was thought that the consideration of this probability necessitated a Markov model rather than the simpler (and usually faster) combinatorial model. SEA, the new approach, separates the modeling of FC failures into two terms that are multiplied to compute the system reliability. The first term, a simple product, represents the probability that no uncovered fault occurs. The second term comes from a combinatorial model which includes the covered faults that can lead to system failure. This second term can be computed from any common approach (e.g. fault tree, block diagram, digraph) which ignores the FC concept by slightly altering the component-failure probabilities. The result of this work is that reliability engineers can use their favorite software package (which ignores the FC concept) for computing reliability, and then adjust the input and output of that program slightly to produce a result which includes FC. This method applies to any system for which: the FC probabilities are constant and state-independent; the hazard rates are state-independent; and an FC failure leads to immediate system failure     

Reliability prediction of imperfect switching systems subject to multiple stresses

Reliability prediction plays a very important role in system design, and the two key factors considered in predicting system reliability are: failure distribution of the component/equipment and system configuration. This paper discusses about the imperfect switching system with one component in active and k spares in the standby state. When the operating component breaks down, the switch will be able to detect the failure using the sensor and replace the defective component with a functionable spare, so the system can keep operating. Therefore, the switch and the sensor have direct impact on normal operations of the switching systems.The reliability of two types of imperfect switching system is thoroughly discussed and compared: (1) a non-repairable system with only one standby component, one switch and one sensor and (2) a non-repairable system with two standby components, one switch and one sensor. Since gamma distribution is fairly adequate to describe the failure mechanism of a system under k-times of shock multiple stresses. This paper then assumes in system (1) and (2), the operating components follow gamma failures, sensor and switch failures follow exponential distribution. In addition, three modes are assumed in regards to the switch failure: under energized, under failing-open and under failing-closed condition.This paper uses MAPLE computer language to perform reliability estimation and comparison on the above-mentioned systems with components, switch and sensor under different failure rate and various intended period of use. Its results can provide guidelines on decision making for improving system design in industries.     

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.     

Optimal redundancies for reliability and availability of series systems

Five different series system configurations with standby units are compared based on their overall reliability and availability. The time-to-failure of a component and its repair time are assumed to have the negative exponential distribution. The mean time-to-failure, MTTF, and the steady-state availability, A_T(∞), are obtained for the first three simple configurations and comparisons are performed. For all five configurations, comparisons are made based on assumed numerical values given to the distribution parameters, as well as to the cost of the components. The configurations are ranked based on: MTTF, A_T(∞), cost and cost-benefit where benefit is either MTTF or A_T(∞).     

Cost-benefit analysis of one-server two-unit imperfect switch system subject to multistage repairs

This paper deals with the cost-benefit analysis of 1-server 2-unit system with imperfect switch where repairs take place in stages. The repair times of the unit and of the switch are assumed to be arbitrarily distributed while the failure rates of units and of the switch are constants. Initally, one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. The repair of the switch is given preference after completion of current repair of a unit. The analysis is carried out by regeneration point technique. Explicit expressions for the expected durations the server is busy in (0, t) with particular stages of repair of the unit and of the switch are obtained to carry out the cost-benefit analysis of the system.     

Optimal reliability/availability of uncertain systems via multi-objective genetic algorithms

The determination of optimal Surveillance Test Intervals (STI) is a matter of great importance in risk-informed applications, due both to the implications that maintenance actions have on the safety of the risky plants such as the nuclear ones, and to the important amount of resources invested in maintenance operations by the industrial organizations. The common approach to determining the optimal STI uses a simplified system-availability model relying on a set of parameters at the component level (failure rate, repair rate, frequency of failure on demand, human error rate, inspection duration, etc.), whose values are typically estimated on the basis of few, sparse data, and can suffer from appreciable uncertainties. Thus, the prediction of the system behavior on the basis of the parameters' best estimates is scarcely significant, if not accompanied by some measure of the associated uncertainty, such as the variance. This paper proposes a multi-objective optimization approach, based on genetic algorithms, which transparently and explicitly account for the uncertainties in the parameters. The objectives considered (the inverse of the s-expected system failure probability and the inverse of its variance), are such as to drive the genetic search toward solutions which are guaranteed to give optimal performance with high assurance. For validation purposes, a simple case study regarding the optimization of the layout of a pipeline is firstly presented. The procedure is then applied to a more complex system taken from literature, the Residual Heat Removal safety system of a Boiling Water Reactor, for determining the optimal STI of the system components. The approach provides the decision maker with a useful tool for determining those solutions which, besides being optimal with respect to the s-expected safety behavior, allow a high degree of assurance in the actual system performance.     

Topological optimization of distributed computer networks subject to reliability constraints

A method of topological optimization of the networks with minimum cost subject to reliability constraints is given in this paper. The proposed optimization algorithm is based on branch and bound method. The computational results of this algorithm are discussed.     

Application of expert systems to systems reliability evaluation

An expert system for diagnosing rough ride problems in heavy trucks has been developed and can be used on a personal computer. The system operates on two levels of knowledge data base: shallow — acquired from truck service personnel and causal obtained from a multiprobe vibration analysis system (MVAS) through a preprocessing neural network. The justification for selecting neural networks is presented as are virtues and drawbacks of the developed system.     

Modelling an imperfect debugging phenomenon in software reliability

Several Software Reliability Growth Models (SRGMs) have been developed in the literature assuming the debugging process to be perfect and thus implying that there is one-to-one correspondence between the number of failures observed and errors removed. However, in reality it is possible that the error which is supposed to have been removed may cause a failure again. It may be due to the spawning of a new error because of imperfect debugging. If such a phenomenon exists then the Software Reliability Growth is S-shaped. In this paper, we develop a model which can describe imperfect debugging process and has the inbuilt flexibility of capturing a wide class of growth curves. Earlier attempts of modelling such a process were able to capture only a particular curve. In other words, if a failure observation phenomenon is exponential then the error removal is again modelled by an exponential growth curve. Applicability of the model has been shown on several data sets obtained from different software development projects.     

MOS RF reliability subject to dynamic voltage stress-modeling and analysis

Dynamic stress on MOSFETs with 900-MHz inverter-like waveforms as well as static (or dc) stress were evaluated experimentally. It showed that the degradation due to dynamic stress is less than that of dc stress for our test transistors. A compact model is used to evaluate the degradation in radio frequency performances, such as transconductance, cutoff frequency, linearity, and noise figure. A class-AB power amplifier is presented as an example to demonstrate the effect of dynamic stress on RF circuit performance.     

Optimization of connecting two communication networks subject to a reliability constraint

This paper considers optimization of two networks with a reliability constraint. The objective is to find some links to connect two networks, at a minimal cost, under the constraint that the system reliability of the resultant network is not less than a given level. 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. In particular, when the threshold P_o is large enough, a new algorithm, the cut tree algorithm, can more effectively give an optimal solution.     

The bound of reliability for the system subject to shock breakdowns

For the shock model (t) = E{ _N(t)}, where {N(t), t 0} is a renewal process having the inter-arrival distribution F(t) with a finite mean, we discuss its bounds under the cases as below: (i) F(t) is IFR (DFR). (ii) F(t) is NBUE(NWUE) and obtain more concise results for some specific cases. These results are useful in life testing and quality control management.     

Optimal policies with decreasing probability of imperfect maintenance

This study applies periodic preventive maintenance to three repair models: major repaired, minimal repaired, or fixed until perfect preventive maintenance upon failure. Two types of preventive maintenance are performed, namely imperfect preventive maintenance, and perfect preventive maintenance. The probability that preventive maintenance is perfect depends on the number of imperfect maintenance operations performed since the last renewal cycle. Mathematical formulas for the expected cost per unit time are obtained. For each model, the optimum preventive maintenance time T/sup */, which would minimize the cost rate, is discussed. Various special cases are considered. A numerical example is presented.     

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     

Two-unit standby reliability system subject to effective and non-effective random shocks

This paper considers a system consisting of two units. The system experiences shocks after certain random intervals. These random intervals are independently and identically distributed each with a general probability density function. Further, the shocks are classified into three types according to the effect of the shocks on the system: Type I, the shock that has no effects on the system, Type II, the shock increases the failure rate and Type III, the shock that fails the system. The system can fail either due to a shock of Type III or due to the internal stress and strain of the operation of the unit or due to two successive shocks, the first shock being of Type II. The repair times of the units are assumed to be exponentially distributed. The mean time to system failure (MTSF), steady state availability of the system and expected number of times the repairman is required are investigated. Finally, MTSF-shock rate and steady state availability-shock rate figures are drawn for special cases and certain interesting results are observed therefrom.     

One unit reliability system subject to random shocks and preventive maintenance

In this paper we consider two systems each consisting of one unit. The operating unit is subject to random shocks which occur at random times. Due to the shock the following may happen: (i) The unit is not at all affected by the shock; (ii) the failure rate of the unit increases from λ₀ to λ₁; (iii) the unit fails. The failure time of the unit is exponentially distributed. The repair, shock and preventive maintenance times follow general distributions. In System 2 there is provision of preventive maintenance, whereas in System 1 there is no provision of preventive maintenance. There is one repair man available in each system. In this paper the mean time to system failure, steady state availablities and the impact of shocks on these are studied. In System 2 the effect of the preventive maintenance on MTSF and steady-state availabilities is investigated.     

Control of systems subject to sudden change in character

Dynamic models in which the coefficient processes exhibit sudden changes at random time points can be used to make manifest the influences of subsystem failures or rapid changes in the environment in which a system must operate. Control and regulation of such systems is complicated by the uncertainty which surrounds the effect of future events on system behavior. A satisfactory control policy must quantitatively discount these events of uncertain occurrence to provide good performance for a variety of operating conditions. This paper describes controller synthesis procedures for specific classes of such systems and gives some of the ways in which these controllers differ from those derived under the assumption of perfect knowledge of future plant behavior.     

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.