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

Reliability analysis of time-dependent 2-cascade and 3-cascade systems is carried out using stress/strength models. Each of the stress and strength variables is assumed to be deterministic or random fixed or random independent. The number of cycles in any period of time t is assumed to be random. The particular case when the number of cycles in any period of time t follows a Poisson distribution is also considered. The components are assumed to be identical and the attenuation factors k_i's are assumed to be constants. Also, expressions for the system reliability are obtained, and a few numerical results are computed when the stress and the strength distributions are exponential.     

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 single strength under n-stresses

In this paper we have considered the reliability of a system when n-stresses acted on a single strength component with probability distributions that were exponential, normal and gamma. We infer that when n-stresses act on a single strength component with an exponential distribution, the component has the same reliability as single stress and strength components which are connected in series, whereas normal and gamma distributions do not follow this rule.     

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.     

A reliability physics model for parallel system

Reliability analysis of a nonrepairable 2-unit parallel system is carried out using the stress-strength model of failure physics. The analysis is carried out for correlated strengths and altered stress distribution depending upon the number of components surviving. The analysis includes both the cases of deterministic and random cycle times. In the case of random cycle times, Poisson distributed stress cycle occurrences have been considered. Various system characteristics, such as failure time distribution, reliability and moments of time to failure of the system, have been evaluated for both deterministic and random cycle times. Two particular cases, namely (i) bivariate exponential distribution for strength variables and univariate exponential distributions for stress variables and (ii) bivariate normal distribution for strength variables and univariate normal distributions for stress variables, have also been considered.     

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.     

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.     

Distribution of order statistics with varying number of components in reliability systems

In this paper the authors consider the general problem of determining the reliability of complex systems such as series, parallel etc., when the number of components constituting these complex systems is a random variable following distributions belonging to power series and exponential families. The importance of the study of the distribution of order statistics when the sample size is a random variable is shown in the reliability theory.     

Reliability Physics Models

The generalized stress-strength model which is prevalent in current literature is perhaps the closest that analysts have come to a general physical model. To obtain a failure density function and associated hazard function one must assume a certain probability distribution for the part strength and a particular amplitude distribution and frequency of occurrence distribution for the part stress. If one assumes a normal strength distribution and Poisson distributed stress occurrence times with normally distributed amplitudes, then this leads to an exponential failure density function and a constant hazard. Such a model is probably best suited for situations in which the part generally lasts a long time and only seems to fail when on occasion a large stress occurs. In many situations the failure of parts seems to fit a different pattern. The part is operated at nearly a constant stress level; however, the part strength gradually deteriorates with time. As time goes on the rate of deterioration should increase sharply as wear-out is reached and cause an increase in hazard. A probabilistic model which fits this hypothesis is a constantly applied stress and a Rayleigh distributed part strength. The parameter of the Rayleigh distribution is allowed to increase in an exponential fashion with time which produces the strength deterioration effect. Basically the failure rate turns out to depend on the square of the applied stress; however, if the strength deterioration rate is allowed to be a function of the input stress, other behaviors are predicted.     

Optimization Considerations in Design Reliability by Stress-Strength Interference Theory

Reliability of a component can be computed if the probability distributions for the stress and strength are known. The factors which determine the parameters of the distributions for stress and strength random variables can be controlled in design problems. This leads to the problem of finding the optimal values of these parameters subject to resource and design constraints. Some optimization models are discussed. The special structure of these models is exploited to develop the optimization techniques which are illustrated by simple design examples.     

Bayes estimation of reliability in stress-strength model of Weibull distribution with equal scale parameters

The paper provides a Bayesian approach to inference about the reliability in a multicomponent stress-strength system. We consider Bayes' estimator of the system reliability from data consisting of a random sample from the stress distribution and one from the strength distribution when the two distributions are Weibull with equal and known scale parameters. The estimator of λ, ratio of two shape parameters, is also considered. The proposed estimators can be compared with the maximum likelihood estimators (mles). However, the comparison is carried out for single component stress-strength system and the Monte Carlo efficiencies are obtained. It is found that the proposed estimators are better than the corresponding mles.     

Worst case reliability bounds

This paper gives a method for estimating reliability bounds for the reliability of a component, given the confidence intervals for the parameters in the stress and strength distributions. The method considers the smallest and the largest interference area between the distribution functions for the stress and strength random variables and hence the name. The method is explained via an illustrative example.     

Electronic Noise Modeling in Statistical Iterative Reconstruction

We consider electronic noise modeling in tomographic image reconstruction when the measured signal is the sum of a Gaussian distributed electronic noise component and another random variable whose log-likelihood function satisfies a certain linearity condition. Examples of such likelihood functions include the Poisson distribution and an exponential dispersion (ED) model that can approximate the signal statistics in integration mode X-ray detectors. We formulate the image reconstruction problem as a maximum-likelihood estimation problem. Using an expectation-maximization approach, we demonstrate that a reconstruction algorithm can be obtained following a simple substitution rule from the one previously derived without electronic noise considerations. To illustrate the applicability of the substitution rule, we present examples of a fully iterative reconstruction algorithm and a sinogram smoothing algorithm both in transmission CT reconstruction when the measured signal contains additive electronic noise. Our simulation studies show the potential usefulness of accurate electronic noise modeling in low-dose CT applications.      

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.     

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     

Affaiblissements différentiels a 13 GHz sur 53 km comparaison a des mesures simultanées a 20,5 GHz

Since May 1975, a 53 km link installed in the vicinity of Dijon (France), has been used to measure attenuation due to precipitation at 13 GHz in both vertical and horizontal polarization. A presentation is made of the results covering 1975 and 1976. Differential attenuations are measured on average, 25 % of the horizontal attenuation. This ratio does not vary much with attenuation, yet is higher than those values reported by other research engineers, or predicted by theory on the basis of Laws and Parsons distribution laws. This rather considerable attenuation may be explained by a mean distribution of raindrop diameters differing widely from those of Laws and Parsons. During the summer of 1975, therefore a second 20 GHz link was installed over the same route as the 13 GHz link. Indeed, a given ratio between the differential attenuation and the horizontal attenuation at 13 GHz, assigns the exponent to the distribution of the diameters of drops, assuming this distribution to be exponential (this being verified in the main). This constraint on raindrop diameter distribution, in turn assigns a value to the ratio of horizontal attenuations at 20.5 GHz and 13 GHz, respectively. This has been verified for 9 showers during the summer 1975. The average ratio of attenuation at 20.5 GHz and 13 GHz was 2, and simultaneously, for the same showers, the differential attenuation at 23 GHz equalled 24 % of the horizontal attenuation. Furthermore, it is shown that whatever the chosen exponential distribution is, those two ratios (2 and .24) correspond to the same exponent of the exponential, to which exponent a rainfall intensity can be associated. By way of example for the Laws and Parson distribution, these ratios are accounted for by a rainfall of about 300 mm/h against a rainfall (thunderstorms) of 50 mm/h for Joss.     

Insufficiency of Instantaneous Strength Determinations for Failure Rate Prediction

The failure of an element subjected to a steady applied stress is associated with the time-wise deterioration of the element's strength. At the instant of failure, the element can no longer perform to specifications. The strength of the element can be obtained at a specified point in time by abruptly modifying the applied stress to a level which causes the element to fail. The instantaneous strengths determined by this procedure are investigated for the possibility of reducing the test time necessary in obtaining the failure rate associated with exponentially distributed failure times. A simple, physically plausible class of strength deterioration functions is considered and the distributional character of the instantaneous strengths at any time instant is determined. It is found that when the underlying distribution of time to failure is exponential, the instantaneous strengths have distributions which are invariant with time. This result indicates that no clue to the form of strength deterioration can be obtained by testing for the instantaneous strengths. Thus the conclusion is reached, in the case of the exponential failure distribution, that instantaneous destruction tests for strength determination are ineffective for assessing the underlying failure rate.     

Modelling human performance reliability in a two stage combined manual and decision task

Based on an experimental study in a two stage combined manual and decision task, a stochastic model for the controllability function of human performance is presented. This measure of human performance is formulated from the random variables which led to the formulation of the reliability and correctability functions. Experimental studies show that the time to committing error follows exponential distribution and the time to error correction follows log normal distribution. Accordingly variation in human performance measures in terms of reliability, correctability and controllability are explained at various levels (3 levels of information load (H) and 3 levels of time lag (TL))of experimental conditions.