Evaluation of the Accident Rate of a Plant Equipped with an Aging Single Protective Channel by the Method of Supplementary Variables

This work calculates the reliability of protective systems of industrial facilities, such as nuclear, to analyze the case of equipment subject to aging, important in the extension of the qualified life of the facilities. By means of the method of supplementary variables, a system of partial and ordinary integral-differential equations was developed for the probabilities of a protective system of an aging channel. The system of equations was solved by finite differences. The method was validated by comparison with channel results with exponential failure times. The method of supplementary variables exhibits reasonable results for values of reliability attributes typical of industrial facilities.

The four-parameter exponentiated Weibull model with Copula, properties and real data modeling.

A new four-parameter lifetime model is introduced and studied. The new model derives its flexibility and wide applicability from the well-known exponentiated Weibull model. Many bivariate and the multivariate type versions are derived using the Morgenstern family and Clayton copula. The new density can exhibit many important shapes with different skewness and kurtosis which can be unimodal and bimodal. The new hazard rate can be decreasing, J-shape, U-shape, constant, increasing, upside down and increasing-constant hazard rates. Various of its structural mathematical properties are derived. Graphical simulations are used in assessing the performance of the estimation method. We proved empirically the importance and flexibility of the new model in modeling various types of data such as failure times, remission times, survival times and strengths data.

Performance Deterioration of Pitot Tubes Caused by In-Flight Ice Accretion: A Numerical Investigation

In-flight ice accretion on typical pitot-static systems is numerically investigated to reveal their performance deterioration under both rime and glaze icing. Coupled with the open source computational fluid dynamics (CFD) platform, OpenFOAM, the numerical strategy integrates the airflow determination by the Reynolds-averaged Navier-Stokes equations, droplet collection evaluation by Eulerian representation, and ice accumulation by mass and energy conservation. Under varying inflow conditions and wall temperatures, the calculated ice accretion performance indicates that the ambient temperature has the most significant effect on the icing-induced failure time, leading to an almost exponential growth. Meanwhile, the blocking time is found to be linearly proportional to the increase in wall temperature. With the increase in inflow velocity, the failure time follows a parabolic variation with glaze ice accretion while shows a monotonic reduction under rime icing conditions. In addition, when the angle of attack increases, failure accelerates under both the glaze and rime icing scenarios. These findings provide guidance for the protection design of pitot tubes. A nonlinear regression analysis is further conducted to estimate the failure performance. The predicated failure times show reliable consistency with numerical results, demonstrating the capability of the obtained empirical functions for convenient predictions of failure times within the applicable range.

Correction to: Vitality models found useful in modeling tag-failure times in acoustic-tag survival studies

An amendment to this paper has been published and can be accessed via the original article.

A Study on Modelling of Bivariate Competing Risks with Archimedean Copulas

In this study we consider Archimedean copula functions to obtain estimates of cause-specific distribution functions in bivariate competing risks set up. We assume that two failure times of the same group are dependent and this dependency can be modeled by an Archimedean copula. Based on the Archimedean copula which gives best fit to the competing risk data with independent censoring we obtain the estimates of cause specific sub distributions.

On a New Modification of the Weibull Model with Classical and Bayesian Analysis

Modelling data in applied areas particularly in reliability engineering is a prominent research topic. Statistical models play a vital role in modelling reliability data and are useful for further decision-making policies. In this paper, we study a new class of distributions with one additional shape parameter, called a new generalized exponential-X family. Some of its properties are taken into account. The maximum likelihood approach is adopted to obtain the estimates of the model parameters. For assessing the performance of these estimators, a comprehensive Monte Carlo simulation study is carried out. The usefulness of the proposed family is demonstrated by means of a real-life application representing the failure times of electronic components. The fitted results show that the new generalized exponential-X family provides a close fit to data. Finally, considering the failure times data, the Bayesian analysis and performance of Gibbs sampling are discussed. The diagnostics measures such as the Raftery–Lewis, Geweke, and Gelman–Rubin are applied to check the convergence of the algorithm.

A New Lifetime Model: Copulas, Properties and Real Lifetime Data Applications

A new four parameter lifetime model called the Weibullgeneralized Lomax is proposed and studied. The new density function can be "right skewed", "symmetric" and "left skewed" and its corresponding failure rate function can be "monotonically decreasing", " monotonically increasing" and "constant". The skewness of the new distribution can negative and positive. The maximum likelihood method is employed and used for estimating the model parameters. Using the "biases" and "mean squared errors", we performed simulation experiments for assessing the finite sample behavior of the maximum likelihood estimators. The new model deserved to be chosen as the best model among many well-known Lomax extension such as exponentiated Lomax, gamma Lomax, Kumaraswamy Lomax, odd log-logistic Lomax, Macdonald Lomax, beta Lomax, reduced odd log-logistic Lomax, reduced Burr-Hatke Lomax, reduced WG-Lx, special generalized mixture Lomax and the standard Lomax distributions in modeling the "failure times" and the "service times" data sets.

Load-Sharing Reliability Models with Different Component Sensitivities to Other Components’ Working States

We study the distributions of component and system lifetimes under the time-homogeneous load-sharing model, where the multivariate conditional hazard rates of working components depend only on the set of failed components, and not on their failure moments or the time elapsed from the start of system operation. Then we analyze its time-heterogeneous extension, in which the distributions of consecutive failure times, single component lifetimes, and system lifetimes coincide with mixtures of distributions of generalized order statistics. Finally we focus on some specific forms of the time-nonhomogeneous load-sharing model.

PENALIZED LOG-LIKELIHOOD ESTIMATION FOR COX-FRAILTY MODEL WITH NONINFORMATIVE BIVARIATE CURRENT STATUS DATA

A Penalized Maximum Likelihood Estimation (PMLE) procedure is proposed for Cox proportional hazards frailty model with noninformative bivariate current status data. An integrated splines (I-splines) was used to approximate the two unknown baseline cumulative hazard functions of the failure times. The one-parameter gamma frailty distribution was used to model the correlation between the two failure times. An easy to implement computational algorithm is proposed to estimate the regression and splines parameters. Bayesian technique as proposed by Wahba (1983) was employed for the variance estimation. The statistical properties of the estimated parameters were studied through extensive simulation and it was observed that the PMLEs were consistent, asymptotically normal and efcient. In addition, the estimators were robust to the choice of knots, censoring rates and type of frailty distribution used. The proposed methodology is further demonstrated through the analysis of the tumorigenicity experiment data by Lindsey and Ryan (1994).