Reliability of a cascade system with exponential strength and gamma stress

In this paper an expression for the reliability of an n-cascade system is allowed when the strengths of the components follows an exponential distribution and the imminent stress is impinged on the first component with a gamma distribution. Also the stress on the successive components are acted by deterministic but unequal factors. The results are observed for the cases when the parameter p takes higher values, one can infer that the systems with larger parameters value and lesser attenuation factors are more reliable.     

Reliability of a cascade system with normal stress and exponential strength

In this paper we study the reliability of an N-cascade system whose stress and strength follow normal and exponential distributions, respectively. In this system we can observe that reliability increases for lower values of strength parameter (λ) and stress parameter (μ). Marginal reliability rate also increases at higher values of λ. Hence we conclude that the addition of components by a cascade system gives a significant improvement.     

A Monte Carlo Technique for Obtaining System Reliability Confidence Limits from Component Test Data

A digital computer technique is developed, using a Monte Carlo simulation based on common probability models, with which component test data may be translated into approximate system reliability limits at any confidence level. The probability distributions from which the component failures are assumed to come are the exponential, Weibull (shape parameter K known), gamma (shape parameter ? known), normal, and lognormal. The components can be arranged in any system configuration, series, parallel, or both. Since reliability prediction is meaningful only when expressed with an associated confidence leve, this method provides a valuable and economical tool for the reliability analyst.     

A simulation approach for computing systems reliability

The basis of the concept of reliability is that a given component has a certain stress-resisting capacity; if the stress induced by the operating conditions exceeds this capacity, failure results. Most of the published results in this area are based upon analytical modelling of stress and strength, using various probability distributions, and then trying to find an exact expression for system reliability, which can be very difficult to obtain sometimes. The approach used in this paper is very simple and uses simulation techniques to repeatedly generate stress and strength of a system by the computer, using a random number generator and methods such as the inverse transformation technique. The advantage of this approach is that it can be used for any stress-strength distribution functions. Finally, numerical results obtained from using this approach are compared with results obtained using the analytical methods for various strength-stress distribution functions, such as exponential, normal, log normal, gamma and Weibull. Results show the viability of the simulation approach.     

A multi-component standby system subject to inspection and truncated normal failure time distribution

This paper investigates a stochastic model of a single server, two identical unit cold standby system. Each unit consists of n separately maintained independent components arranged in series. After each failure, an inspection is required to detect which component of the unit has failed. The failure time distribution of a unit is truncated normal while all the other time distributions are negative exponential. Using the regenerative point technique, we obtained various measures of system effectiveness to carry out the profit function analysis.     

Estimation of reliability of stress-strength model with non-identical component strengths

An attempt has been made in this paper to estimate the reliability of an s-out-of-k system with non-identical component strengths when component strengths follow an exponential distribution. A further assumption is made that all the components are subjected to a common random stress which also follow an exponential distribution. Bayes and maximum likelihood estimators of such system reliability are considered. A Bayes estimate is obtained by using Lindley's approximation. Comparisons are made on the basis of efficiency and Pitman nearness probability through a Monte-Carlo study.     

Studies in Cascade Reliability?I

An n-Cascade system is defined as a special type of standby system with n components. A component fails if the stress on it is not less than its strength. When a component in cascade fails, the next in standby is activated and will take on the stress. However, the stress on this component will be a multiple k times the stress that acted on its predecessor. The system fails if due to an initial stress, each of the components in succession fails. The stress is random and the component strengths are independent and identically distributed variates, with specified probability functions; k is constant. Expressions for system reliability are obtained when the stress and strength distributions are exponential. Reliability values for a 2-cascade system with Gamma and Normal stress and strength distributions are computed, some of which are presented graphically.     

Reliability comparison of an n cascade system with the addition of an n strength system

In the present paper we are comparing the reliability of two models: (i) the cascade system and (ii) the system having n strengths on a single stress. In both the cases the system has n strengths and a single stress. In the first case n strengths are cascaded and for each attack the stress is decreased. Whereas in the second case n strengths act in combination on the stress component. From the results obtained we can observe that when the attenuation factor is less than 0.5 the cascade model is more reliable, otherwise the second one is more reliable. Hence we infer that, at each attack, if the stress decreases the cascade model is more reliable.     

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.     

Stochastic analysis of a multi-unit cold standby system working in orbit form

This paper considers the analysis of a single server n-similar unit system. Initially k(<n) units form an orbit which functions if one unit functions at a time and the remaining n − k units work as cold standbys. When a unit fails in the orbit it is instantaneously replaced by one of the standbys with the help of a perfect transfer switch. The system is said to fail when n − k + 1 units have failed. The distribution of time to failure and time to repair of a unit are negative exponential. Using the regenerative point technique several reliability characteristics are obtained to carry out the cost-benefit analysis.     

Survival function of a component under random strength attenuation

In this paper the survival of a component, prone to attacks by a succession of random stresses, is examined under the assumption that the strength of the component is attenuated and these attenuated factors are random variables. Expressions have been obtained for these attenuation factors: (i) when the stress strength follows exponential distribution and the random attenuation factors follow rectangular distribution; (ii) when the stress strength follows exponential distribution with the attenuation factors following beta distribution; (iii) when the stress following exponential distribution, strength following gamma distribution and the random attenuation factors following beta distribution.     

Cost-benefit analysis of a multi-unit parallel trichotomous system with random shocks

This paper deals with the analysis of profit function of an n-unit parallel trichotomous system subject to random shocks. Failure times are assumed to follow negative exponential distributions with different parameters whereas the repair time distributions are taken to be general. Several reliability characteristics of interest to system engineers/designers as well as operation managers have been evaluated using the supplimentary variable technique.     

Stochastic analysis of standby system with duplex units

This paper investigates a mathematical model of a system composed of two units, one operative and the other cold standby. Each unit of the system is made of two non-identical parallel components and each component is made of n-elements. Henceforth we call each unit of the system a duplex unit. Failure and repair time distributions of each element of a component are negative exponential and vary from element to element, whereas the repair time distribution of a unit is arbitrary. Upon the failure of the operative unit the standby unit does not operate instantaneously. This type of situation may be found in many electronic networks. Several reliability characteristics of interest have been obtained.     

A reliability model for stress vs strength problem

In this paper a general reliability model for the stress vs strength problem has been discussed. The model has been illustrated by considering the stress to follow normal distribution and the strength to follow the gamma distribution. A numerical estimate of the reliability under different values of the distribution parameters (for both the strength and stress distributions) has been presented.Exponential distribution, to which the gamma distribution reduces when its shape parameter α equals unity, has been discussed as a particular case.     

Bayesian analysis of the mixture of exponential failure distributions

In this paper, a Bayesian reliability analysis is carried out for the mixture of two exponential failure distributions on the basis of failure time data x₁ < x₂ <…< x_r, for a preassigned r, and (n − r) survivors from this mixed failure model. Under the assumptions of the squared error loss function (SELF) and suitable prior densities on the underlying parameter space, exact results for the Bayes estimators of the mean life and the reliability function are obtained.     

An optimal inspection policy for a storage system with high reliability

A system such as missiles and spare parts of aircrafts has to perform a normal operation at any time when it is used. However, a system is in storage for a long time from the transportation to the usage and its reliability goes down with time. Such a system should be inspected and maintained at periodic times to hold a higher reliability than a prespecified value q. This paper suggests a periodic inspection of a storage system with two kinds of units where unit 1 is inspected and maintained at each inspection, however, unit 2 is not done. The system is replaced at detection of failure or at time when the reliability is below q. The total expected cost until replacement is derived and an optimal inspection time which minimizes it is discussed. Numerical examples are given when failure time distributions are exponential and Weibull ones.     

Analysis of reliability bounds for series, parallel and k-out-of-n system configuration

This paper deals with the least upper bounds (LUB) and greatest lower bounds (GLB) for the reliability of the series, parallel and k-out-of-n system configurations. It is assumed that the life-time distribution of each component is negative exponential. In each case the behaviour of LUB and GLB is studied as the number of components in the system varies.     

Optimal allocation of s-identical, multi-functional spares in aseries system

This paper considers the problem of allocating statistically-identical, multi-functional spares to subsystems of a series system. The objective is to maximize the system reliability for mission time T which can be deterministic or stochastic. Several problems which are conceptually similar to this one have been discussed in the literature in different contexts. An algorithm is provided for obtaining standby redundancy allocation, and sufficient conditions are derived for optimality of the resulting allocation for general T. The algorithm is equivalent to a simple allocation rule under the sufficient conditions. The allocation rule gives an optimal allocation for the special cases: the PDF's of component lifetimes are log concave (which implies increasing failure rate), and T is deterministic; the components have exponential failure times, and T follows a gamma distribution; and component lifetime distributions are general, and T follows an exponential or a mixture of exponential distributions. No simpler method is available for latter two cases     

Cost analysis of a two unit priority standby system with imperfect switch and arbitrary distributions

This paper deals with cost analysis of a single server two-unit (one priority and the other ordinary) cold standby system with two modes—normal and total failure. A switch is used to operate the standby unit (ordinary) and it works successfully with known probability p( = 1 ? q). Priority unit gets preference both for operation and repair. Failure and repair time distributions are arbitrary. System fails when switch or both the units fail totally. The system is observed at suitable regenerative epochs in order to obtain reliability characteristics of interest to system designers and operations managers. Explicit results for the exponential time distributions have been obtained in particular cases.     

Reliability analysis of time-dependent cascade system with deterministic cycle times

Reliability analysis of time-dependent 2-cascade and 3-cascade systems is carried out using stress/strength models by considering each of the stress and strength variables as deterministic or random fixed or random independent. The number of cycles in any period of time t is assumed to be deterministic. The components are identical in the sense that the components have exactly the same strength if the strength variable is deterministic and have independent and identical distributions if the strength variable is random. Attenuation factors, K_i's, are constants. Expressions for system reliability are obtained and reliability values are computed for specific values of N, the number of cycles, when stress and strength distributions are exponential.