Bi-directional system analysis under copula-coverage approach

Reliability assessment is a major step, toward the development of fault-tolerant computing system. In different fields of engineering and physical/ailed sciences, researchers or engineers have several reliability approaches for the better performance of the system. By assuming different types of time trends, failure modes and repair effects, the legion stochastic model has been developed for repairable system. This study shows a novel concept for three state fault tolerant repairable systems with two types of repair. This research predicts the effect of the coverage factor using Gumbel-Hougaard family of copula approach on reliability characteristics of the designed system.     

On the Use of the Importance Measure for Multi-State Repairable k-out-of-n: G Systems

Importance measures in reliability systems are used to identify weak components in contributing to proper functioning of the system. Traditional importance measures mainly concern the change of the system reliability as the change of the reliability of one component and seldom consider the expected number of repairs of the objective component in unit time. This paper proposes an improvement potential rate importance (IPR) to verify the effectiveness of the improvement in system reliability for multi-state repairable k-out-of-n: G systems. Then the comparisons between IPR and Birnbaum importance are discussed. Finally, a case study is given to demonstrate the proposed IPR.     

An alternative approach to reliability analysis of cold standby systems

ABSTRACT

An alternative approach is applied for reliability analysis of standby systems on the basis of matrix renewal function. In this regard, a single-server, two identical unit cold standby systems with an imperfect switch is considered as a three-state semi-Markov process. Several important reliability measures such as availability, mean time to failure, expected number of failures, etc., are obtained for general lifetime distributions. Also, the main results have been treated to the case of exponential lifetimes and explicit formulas obtained for this case in addition of some numerical illustrations. This approach can easily be extended to more general standby systems with different configurations.     

A note on replacement policy comparisons from NBUC lifetime of the unit

Age and block replacement policies are commonly used in order to reduce the number of in-service failures when the systems are functioning indefinitely. In reliability theory, the lifetime of a system can be modeled by means of the NBUC aging class that is characterized throughout comparisons of the residual lives in the sense of the icx order. The purpose of this paper is to establish stochastic comparisons between the age (block) replacement policy and a renewal process with no planned replacements when the lifetime of the unit is NBUC. Supported by Ministerio de Ciencia y Tecnología under grant BFM2000-0362     

A Study on Reliability for A Two-Item Cold Standby Markov Repairable System with Neglected Failures

This article studies reliability for a Markov repairable two-item cold standby system with neglected failures. In the system, if a failed time of the system is too short (less than a given critical value) to cause the system to fail, then the failed time may be omitted from the downtime record, i.e., the failure effect could be neglected. In ion-channel modeling, this situation is called the time interval omission problem. The availability indices and the mean downtime are presented as two measures of reliability for this repairable system. Some numerical examples are shown to illustrate the results obtained in this article.     

A combinatorial estimation approach for storage reliability with initial failures based on periodic testing data

Storage reliability that measures the ability of products in a dormant state to keep their required functions is studied in this paper. Unlike the operational reliability, storage reliability for certain types of products may not be always 100% at the beginning of storage since there are existing possible initial failures that are normally neglected in the models of storage reliability. In this paper, a new combinatorial approach, the nonparametric measure for the estimates of the number of failed products and the current reliability at each testing time in storage, and the parametric measure for the estimates of the initial reliability and the failure rate based on the exponential reliability function, is proposed for estimating and predicting the storage reliability with possible initial failures. The proposed method has taken into consideration that the initial failure and the reliability testing data, before and during the storage process, are available for providing more accurate estimates of both initial failure probability and the probability of storage failures. When storage reliability prediction that is the main concern in this field should be made, the nonparametric estimates of failure numbers can be used into the parametric models for the failure process in storage. In the case of exponential models, the assessment and prediction method for storage reliability is provided in this paper. Finally, numerical examples are given to illustrate the method. Furthermore, a detailed comparison between the proposed method and the traditional method, for examining the rationality of assessment and prediction on the storage reliability, is presented. The results should be useful for planning a storage environment, decision-making concerning the maximum length of storage, and identifying the production quality.     

Bayesian analysis for a stress-strength system under noninformative priors

Noninformative priors are used for estimating the reliability of a stress-strength system. Several reference priors (cf. Berger and Bernardo 1989, 1992) are derived. A class of priors is found by matching the coverage probabilities of one-sided Bayesian credible intervals with the corresponding frequentist coverage probabilities. It turns out that none of the reference priors is a matching prior. Sufficient conditions for propriety of posteriors under reference priors and matching priors are provided. A simple matching prior is compared with three reference priors when sample sizes are small. The study shows that the matching prior performs better than Jeffreys's prior and reference priors in meeting the target coverage probabilities.     

The Bayesian approach for highly reliable electro-explosive devices using one-shot device testing

Due to the high reliability and high testing cost of electro-explosive devices, even though an accelerated test is performed, one may observe very few failures or even no failures at all due to censoring. In this paper, we consider modelling the reliability of such devices by an exponential lifetime distribution in which the failure rate is assumed to be a function of some covariates and that the observed data are binary. The Bayesian approach, with three different prior settings, is used to develop inference on the failure rate, lifetime and the reliability under some settings. A Monte Carlo simulation study is carried out to show that this approach is quite useful and suitable for analysing data of the considered form, especially when the failure rates are very small. Finally, illustrative data are analysed using this approach.     

Confidence intervals on intraclass correlation coefficients in a balanced two-factor random design

A modified large-sample (MLS) approach and a generalized confidence interval (GCI) approach are proposed for constructing confidence intervals for intraclass correlation coefficients. Two particular intraclass correlation coefficients are considered in a reliability study. Both subjects and raters are assumed to be random effects in a balanced two-factor design, which includes subject-by-rater interaction. Computer simulation is used to compare the coverage probabilities of the proposed MLS approach (GiTTCH) and GCI approaches with the Leiva and Graybill [1986. Confidence intervals for variance components in the balanced two-way model with interaction. Comm. Statist. Simulation Comput. 15, 301–322] method. The competing approaches are illustrated with data from a gauge repeatability and reproducibility study. The GiTTCH method maintains at least the stated confidence level for interrater reliability. For intrarater reliability, the coverage is accurate in several circumstances but can be liberal in some circumstances. The GCI approach provides reasonable coverage for lower confidence bounds on interrater reliability, but its corresponding upper bounds are too liberal. Regarding intrarater reliability, the GCI approach is not recommended because the lower bound coverage is liberal. Comparing the overall performance of the three methods across a wide array of scenarios, the proposed modified large-sample approach (GiTTCH) provides the most accurate coverage for both interrater and intrarater reliability.     

A multiple warm standby δ-shock system with a repairman having multiple vacations

In this article, a warm standby n-unit system is studied. The system is operational as long as there is one unit normal. The unit online, which has a lifetime distribution governed by a phase-type distribution, is also attacked by a shock from some external causes. Assume that shocks arrive according to a Poisson process. Whenever an interarrival time of shock is less than a threshold, the unit online fails. The lifetimes of the units in warm standby is exponentially distributed. A repairman who can take multiple vacations repairs the failed units based on the “first-in-first-out” rule. The repair times and the vacation times of repairman are governed by different phase-type distributions. For this system, the Markov process governing the system is constructed. The system is studied in a transient and stationary regime; the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated. A numerical application is performed to illustrate the calculations.     

Stochastic analysis of a complex system with an auxiliary unit

This paper considers the stochastic analysis of a complex system having three units. The first two units are designated as unit-1 and unit-2 while the third unit is called an auxiliary unit (unit-3) which enhances the range of transmission and efficiency of unit-1. Joint distributions of failure and repair times are bivariate exponential (B.V.E.) with different parameters. Regenerative point technique is used to obtain various reliability characteristics of the system under study. Behaviour of some characteristics has also been studied through graphs.     

Inference from Accelerated Degradation and Failure Data Based on Gaussian Process Models

An important problem in reliability and survival analysis is that of modeling degradation together with any observed failures in a life test. Here, based on a continuous cumulative damage approach with a Gaussian process describing degradation, a general accelerated test model is presented in which failure times and degradation measures can be combined for inference about system lifetime. Some specific models when the drift of the Gaussian process depends on the acceleration variable are discussed in detail. Illustrative examples using simulated data as well as degradation data observed in carbon-film resistors are presented.     

Numerical solution to stochastic partial differential equation with variable repair rate

ABSTRACT

In this paper, a numerical solution technique to stochastic partial differential equations in reliability engineering is presented. The method is based upon finite difference discretization of the governing equations for the Markovian reliability model. In realistic situations, the repair rates and failure rates of engineering system are variable. Such variable repair and failure rates are difficult to account in reliability modeling. The novelty in this work is to present a numerical method to easily take into consideration such variables and give an accurate prediction of reliability measures of engineering systems.     

An Accelerated Model for Recurrence Data

Recurrence data usually come from sampling a system in different ages. It is common in areas of manufacturing, reliability, medicine, and risk analysis. In this article, an accelerated model for recurrence data is proposed. The model is based on the time between failures (TBFs) for an accelerated time regression method using the number of failures as a dummy covariate. Using this model, the repair (or cure) effect can also be studied. A graphical display of recurrence data created by plotting the log-TBFs versus the number of failures is proposed to detect any linear or nonlinear trend for log-TBFs. The model is then extended to incorporate covariates and/or time factors. Two data sets are used to demonstrate the usefulness of the proposed model.     

Sequential Series Systems and Their Risk Assessments

System reliability models are critical in both theory and engineering. Although there are many system reliability models, they still cannot cover some practical situations. In this article, three sequential series systems are introduced in terms of some real backgrounds. An order profile for the system working is also introduced, because it can be used to describe the working component contribution for the system clearly. As the systems become more and more complicated and important, the safety issue is a hot topic. Risk analysis is one of the important ways for safety studies and implements. The formulae for some risk measures for the sequential systems are presented from a safety point of view. A numerical example is given to illustrate the details of the procedure and formulae.     

Some observations in testing for nonstandard mixtures

We consider optimal testing procedures for specific models of early and instantaneous failures in reliability studies. These models are typically used to accommodate lifetime data that have a higher concentration of failures near time zero. We show that it is possible to derive uniformly most powerful tests, for testing the mixing parameter in the instantaneous failure model, for general lifetime distributions. A novel procedure to test for early failures, which uses an invariance property of the maximum likelihood estimate of the nuisance parameter, is also presented.     

Confidence interval procedures for system reliability and applications to competing risks models

System reliability depends on the reliability of the system’s components and the structure of the system. For example, in a competing risks model, the system fails when the weakest component fails. The reliability function and the quantile function of a complicated system are two important metrics for characterizing the system’s reliability. When there are data available at the component level, the system reliability can be estimated by using the component level information. Confidence intervals (CIs) are needed to quantify the statistical uncertainty in the estimation. Obtaining system reliability CI procedures with good properties is not straightforward, especially when the system structure is complicated. In this paper, we develop a general procedure for constructing a CI for the system failure-time quantile function by using the implicit delta method. We also develop general procedures for constructing a CI for the cumulative distribution function (cdf) of the system. We show that the recommended procedures are asymptotically valid and have good statistical properties. We conduct simulations to study the finite-sample coverage properties of the proposed procedures and compare them with existing procedures. We apply the proposed procedures to three applications; two applications in competing risks models and an application with a $k\text{-out-of-}s$ system. The paper concludes with some discussion and an outline of areas for future research.     

An extension of the Freund's bivariate distribution to model cascading failures

The notion of cascading failures is a common phenomenon we observe around us. Here the initial failure alters the structure function of the system, which leads to subsequent failures within a short period of time referred to as threshold time. The concept of cascading failures within the framework of reliability theory and the Freund bivariate exponential distribution to model cascading failures has been studied by few authors. The Freund bivariate exponential distribution allows modelling a parallel redundant system with two components. In this system, the lifetimes of the two components behave as if they are independent, until one of the components fail, after which the remaining component suffers an increased/decreased stress. In this article, we further generalize this model to accommodate cascading failures. Various properties of the model are investigated and statistical inference procedures are developed using L-moments and method of moments. A practical application of this model is illustrated using data from www.espncricinfo.com. Also well analysed Diabetic Retinopathy Study (DRS) data is further analysed using this model and our findings are presented.     

General analysis of systems in which a 2-unit system is a sub-system

In this paper we consider a system which has three subsystems A, B and C. A and B are one unit systems and two unit systems respectively, and C is exposed to a damage process. The units of B have exponential life times. In model 1, A has a general life time and the damage process of C is Poisson and in model 2, A has an exponential life time and C is exposed to a renewal damage process. Introducing a repair facility which repairs all the failures one by one, this paper presents the joint Laplace-Stieltjes transforms of the ur> and down times. Marginal down time distributions an- calculated whon there exists a repair facility vor every damage.     

Confidence Intervals for Univariate Impulse Responses With a Near Unit Root

This article proposes a method for constructing confidence intervals for the impulse response function of a univariate time series with a near unit root. These confidence intervals control coverage, whereas the existing techniques can all have coverage far below the nominal level. I apply the proposed method to several measures of U.S. aggregate output.