Confidence Limits for the Reliability of Series Systems

The reliability analysis of a parallel-series system with an order of (3,3,1,1) involving five units (A, B, C, D, and E) organised into three parallel subsystems is investigated. The first subsystem comprises three units (A, B, and C) arranged in series, while the second and third subsystems consist of single units ‘D’ and ‘E’. The failure rates of the units are assumed to follow a negative exponential distribution. The study employs three mathematical methods: decomposition, cut-set, and event space to derive expressions for reliability and mean time to system failure (MTSF). Specific values for these reliability measures are obtained by assuming identical units and assigning particular values to unit failure rate parameters. The sensitivity analysis has been carried out to investigate the overall system reliability by changing the parameter values of the different components and identify the critical components. The practical application of this work is envisioned in power distribution systems.

Components within a system may be related to one another in two primary ways: in either a serial or a parallel configuration. The other way associated system components is developed on the basis of series and parallel systems. Although some complex systems cannot generate from series and parallel system, the result of this paper is helpful to study more complex gradual system reliability problems. In this paper, a hypothesis is formed that the reliability of the components of the system is variable with time. Then, the reliability of the system is gradual, on condition that the components are combined by some related way. If the system reliability analysis is based on the static analysis, it may be different from the actual value of the reliability because the components of the system would afford stochastic load or generate degradation of performance. The method considering the random resistant degradation may make the result of reliability accurate. In this paper, gamma process is used to simulate the use of the components of the system, as deterioration is generally uncertain and non-decreasing, it can best be regarded as a gamma process. Combining the Edgeworth series method and forth moment technique, the method that calculate the reliability of series and parallel system is deduced. Then, the reliability of different systems and the failure rate of the systems are illustrated with time. The results show that the reliability of the systems will decline in different ways with time.

Examines the trade‐off between system redundancy and acceptance sampling as alternative means to improve system reliability. We assume that components of the system follow an exponential failure law and investigate expected times to failure of systems of various levels of component redundancy which have been exposed to acceptance sampling plans of various levels of stringency. We also show the probability distributions of system reliability for outgoing lots at various levels of component redundancy and sampling stringency. The paper shows a straightforward method for calculating these trade‐offs and provides the decision maker with a previously unavailable tool of system design and testing.

We present a method for computing Bayes confidence limits for the reliability of an arbitrary series-parallel system consisting of failure independent modules. Each module has an internal structure of one or more failure independent devices in series, and each device consists of one operating component with identical nonoperating standby components. Each component is assumed to have exponential distribution of life with unknown failure rates that must be estimated from test data. We outline a systematic procedure to compute the posterior distribution of system reliability, from which exact confidence limits can be obtained. The posterior distribution function is developed in terms of an expansion in shifted Chebyshev polynomials of the second kind whose convergence properties and numerical evaluation are well suited for practical applications.

This research paper deals with analysis on reliability of some complex systems using various distributions. The structural designs and configuration of different complex systems with various failure laws are analyzed. In this article, it is observed that reliability of a system can be improved by providing better configuration to components thereof. There are different types of configurations such as series, parallel, series- parallel, parallel- series, k-out-of-n and mixed configurations for a complex system, however, in this paper only two types of systems namely series system and parallel system are discussed with various failure distributions i.e. Weibull, Rayleigh and Exponential distribution. The results of the reliability for arbitrary values of parameters such as number of components, failure rates in three distributions have been obtained which may be very helpful in using various complex systems.

Lehmann and Scheffe have shown how to construct uniformly most powerful unbiased tests of certain hypotheses when the assumed distributions belong to an “exponential family.” The present paper is concerned with particular cases which arise from independent gamma variates with scale parameters θ1 and θ2. Conditional distributions are given which are appropriate for testing γ = γ0, where γ = c 1/θ1+c 2/θ2. As an application, suppose that a series system has two dissimilar components with expected lives θ1 and θ2. When component failures are exponentially distributed, so are system failures, the mean being 1/(1/θ1+1/θ2). From independent estimates of θ1 and θ2 confidence limits can be found for this mean, or for the probability of successful system operation up to any fixed “mission time.” With appropriate restrictions, more general distributions including the Weibull can also be treated.

Mehta, Patel, and Gray proposed a network algorithm for the exact confidence limits of the common odds ratio in several 2 × 2 tables. Their algorithm was implemented in the StatXact and Egret statistical packages and further discussed by Vollset, Hirji, and Elashoff. The need to evaluate polynomials of potentially very high degrees, however, poses some numerical difficulties. This article presents a method that cuts the degree of polynomials by at least one half. Two other modifications to further stabilize and speed the computation are also proposed.

If a known transformation of a random variable X is normally distributed with mean {mu} and variance {sigma}{sup 2}, then the mean, variance, and any other distributional property of X can be expressed in terms of {mu} and {sigma}{sup 2}. For example, if X is lognormally distributed, i.e., X {approx} {Lambda}({mu}, {sigma}{sup 2}) or (equivalently) Y = log(X) {approx} N({mu}, {sigma}{sup 2}), then the expected value, variance, median, and mode of X are, respectively, E(X) = exp({mu} + {sigma}{sup 2}/2), var (X) = exp(2{mu} + {sigma}{sup 2})(exp({sigma}{sup 2}) - 1), med(X) = exp({mu}), and mode(X) = exp({mu} - {sigma}{sup 2}). Exact and optimal (uniformly most accurate unbiased) confidence limit procedures have been developed for linear functions of {mu} and {sigma}{sup 2} (Land, 1971, 1973) and, therefore, because confidence limits for a parameter are invariant under smooth, monotone transformations of that parameter, for the mean and mode of a lognormal distribution. In fact, the lognormal distribution is the only one whose mean can be expressed as a function of a non-trivial linear combination of {mu} and {sigma}{sup 2} (Land, 1971), but other functions, including those arising in connection with other normalizing transformations, can be approximated locally by linear functions for which exact limits can be constructed that define approximate limits for the original parametric functions of interest (Land, 1974, 1988). Tables have been published to facilitate the calculation of confidence limits for arbitrary linear functions of {mu} and {sigma}{sup 2} (Land, 1975), but their use is often tedious, requiring repeated interpolation and calculation. An unpublished Fortran program to compute confidence limits directly from sample estimates of p and u2 has been available from the second author, and has been used by a number of investigators to analyze lognormal data sets. The present paper introduces a more efficient computational algorithm, and documents the program for prospective users. An option has been added which makes it easy for the user to generate tables of confidence limits. Finally, the accuracy of the program has been thoroughly evaluated in terms of coverage probabilities for a wide range of parameter values.

An efficient procedure for computing exact confidence limits for a standardized mortality ratio

Starting from the agreed definition of reliability the use of probability theory enables the design engineer to predict the reliability of a complex system as a function of the reliability of its component parts. The characteristics of series and parallel grouping are given, together with some applications of hammock networks. The exponential survival law is derived, and the conditions under which it may be applied are discussed.The use of redundancy to improve reliability is introduced, and examples are given of the effect of various schemes upon the reliability of a small electronic system, with and without maintenance. Some possible forms of passive redundancy are described, including block redundancy with majority voting, and quadded logic.

Simple SAS macros for the calculation of exact binomial and Poisson confidence limits

Redundant systems, which usually consist of a number of same/similar components (or modules), have been used in various critical infrastructures to ensure the system's normal function. Usually, system reliability can be improved with the adoption of additional components or redundancies. Typically, two types are mainly included, i.e., majority voters and standby redundancies (referred to as SPARE gates for simplicity). Nevertheless, with the increment of redundancies, the consumed cost or space requirement also grows. This study considers a tradeoff between cost and reliability in order to pursue the cost-effective optimal design. The relationships between the total cost and corresponding parameters are discussed thoroughly. Besides, in order to determine the cost-effective design at the expense of a unit of cost, a revised evaluation standard is proposed (referred to as ${\rm{R}\_\rm{per}\_\rm{Cost}}$ ). In this paper, we perform a cost-effective analysis of majority voters with different implementations; and we also perform the analyses of SPARE gates (here, a warm spare gate and a cold spare gate are mainly focused). For deriving corresponding total cost, algorithms are presented to predict the necessary failure time of components. In this line, cost-effective analyses of several case studies are performed.

This study deals with the reliability analysis of a multi-component load sharing system where failure of any component within the system induces higher failure rate on the remaining surviving components. It is assumed that each component failure time follows Chen distribution. In classical set up, the maximum likelihood estimates of the load sharing parameters, system reliability and hazard rate along with their standard errors are computed. Since maximum likelihood estimates are not in closed form, so asymptotic confidence intervals and two bootstrap confidence intervals for the unknown parameters have also been constructed. Further, by assuming both informative and non-informative prior for the unknown parameters, Bayes estimates along with their posterior standard errors and HPD intervals of the parameters are obtained. Thereafter, a simulation study elicitates the theoretical developments. A real data analysis, at the end, eshtablishes the applicability of the proposed theory.

Using a measure of agreement that does not distinguish the "positive" outcome from the "negative" outcome can be sometimes misleading in assessing resemblance. To alleviate this concern, some new indices, including the "positive" and "negative" conditional synchrony measures (CSM) (or the conditional discordant measures [CDM]), as well as their related measures, have been recently proposed elsewhere. We show that one can easily derive exact confidence limits for these new indices. Using Monte Carlo simulation, we find that the asymptotic interval estimator derived from the score test and these exact interval estimators can all perform well in a variety of situations, while the asymptotic interval estimator based on Wald's statistic can lose accuracy. We use the data taken from a cross-sectional validation study assessing the diagnostic performance of the Whooley questions for major depression disorder (MDD) among older adults to illustrate the use of these interval estimators developed here.

The associations between variants of human papillomavirus (HPV) 16 and risk of cervical neoplasia have been reported, but nucleotide variations of HPV 16 in Asian populations and their association with cervical neoplasia have not been evaluated extensively. During 1991-1992, 11,923 women from seven townships in Taiwan were enrolled. The HPV DNA in cervical cells was detected and genotyped using EasyChip HPV blot. Nucleotide variations in the long control region (LCR), E6, and E7 genes were determined using DNA sequencing for 170 HPV 16-positive cervical samples. The Asian variant was the most prevalent variant (81.8%) of HPV 16 in Taiwan, and was also associated with increased prevalence of histologically confirmed cervical intraepithelial neoplasia grade 3 or worse, showing an age-adjusted odds ratio (exact confidence limits) of 10.70 (1.62-451.05; P = 0.0049) compared to the HPV 16 European variant. Similar significant associations with cervical intraepithelial neoplasia grade 3 or worse were also observed for distinct nucleotide substitutions, including T178A/G, A647G, A7730C/G, T7781C, G7842A, and C24T/G. These results demonstrate that non-European variants (non-E) of HPV 16, predominantly Asian variants, are associated with increased risk for severe cervical neoplasia, compared with European variants. Molecular mechanisms accounting for varied cervical neoplasia risk among different HPV 16 variants warrant further investigation.