Transmuted distributions are flexible skewed families constructed by the induction of one or more additional parameters to a parent distribution. This paper investigates the potential usefulness of a two-component mixture of Transmuted Pareto Distribution (TPaD) under a Bayesian framework assuming type-I right censored sampling. For Bayesian analysis, noninformative as well as informative priors are assumed while three loss functions, namely the squared error loss function (SELF), precautionary loss function (PLF), and quadratic loss function (QLF) are considered to estimate the unknown parameters. Furthermore, Bayesian credible intervals (BCIs) are also discussed in this study. Since the posterior distributions do not have explicit forms, posterior summaries are computed using a Markov Chain Monte Carlo (MCMC) technique. The performance of the Bayes estimators is assessed by their posterior risks assuming different sample sizes and censoring rates. To highlight the practical significance of a two-component mixture of transmuted Pareto distribution (TPaD), a medical data set collected for rental calculi problem is analyzed in this study. Furthermore, annual flood rate data collected at the Floyd River are also discussed in this study.

Mixture of transmuted Pareto distribution: Properties, applications and estimation under Bayesian framework

A new lifetime reliability model with four parameters is proposed. We call it the extra modified Weibull model (EMWM), which is an extension of the modified Weibull model (MWM), capable of modeling a different shapes of hazard function. The new model is developed by introducing fourth parameter in MWM called indicator parameter. The main advantage of an indicator (fourth) parameter is that it gives the new model mixture and non-mixture options, besides different shapes of hazard function including bathtub. The model parameters can be estimated based on a Bayesian generalized posterior method that serves as a tool for model identification, and it gives an efficient computational updating approach with new ways of predicting and measuring behavior. To have insight of the new indicator parameter and to see its importance, we have considered three data sets [Murthy et al [1], Badar and Priest [2], and  Aarset [3]) which have been studied in the past. A prediction updating of the earlier studies of the data sets through the generalized posterior summaries using Markov Chain Monte Carlo (MCMC) Gibbs sampling approach are presented for the proposed model for the different parameters. The behavior of the parameters would help the users to have more clarity about the role of the indicator parameter, and hence may be useful for certain sets of data. The proposed model is fully adaptive to the available failure data and gives reliability engineers and scientists another option for modeling the life time data. We provide description of the mathematical properties of the new model along with failure rate function.

http://asrjetsjournal.org/index.php/American_Scientific_Journal/article/download/3443/1327

Reliability Prediction Updating Through Computational Bayesian for Mixed and Non-mixed Lifetime Data Using More Flexible New Extra Modified Weibull Model

In electric vehicles (EVs), owing to the necessity of large amounts of energy and power, lithium-ion batteries need to be used in series and parallel configurations. However, the performance of the battery pack is lower than that of any single cell within the pack because of the inconsistency among the packed cells. Herein, the inconsistent voltages of unpacked cells due to varying capacities during discharge are analyzed to provide mechanical reason for inconsistency of battery pack. In terms of dispersion and symmetry, the statistical characteristics of voltage distribution are described using Weibull parameters and is investigated using a numerical analysis of the characteristic voltage curve. The numerical analysis results agree well with the experimental and statistical ones, which confirms that voltage inconsistency originating from manufacturing processes is primarily related with capacity inconsistency and the features of the voltage curves. Furthermore, this numerical approach can provide not only significant theoretical insight into the formation and evaluation of voltage inconsistency; but also practical guidance for controlling the quality of cell production and state estimation for the battery pack due to its low computational cost.

/pdf/understanding-discharge-voltage-inconsistency-in-lithium-ion-9kpuuh9c1y.pdf

Understanding Discharge Voltage Inconsistency in Lithium-Ion Cells via Statistical Characteristics and Numerical Analysis

http://scientiairanica.sharif.edu/article_4441_09c331f2b7a12c453da49a08c9085d1e.pdf

Reliability analysis of 3-component mixture of distributions

In reliability analysis, electrical systems can have more than one failure mode .For example, systems may have been used in different operating environments or there could be differences in design and /or material. In these cases, failure time data of systems would not fall on a straight line on a Weibull probability paper. Consequently, the finite mixed Weibull can be used to analyze this data .In this paper, we propose a maximum likelihood algorithm for mixture of two Weibull distributions. The mixture distribution and the traditional Weibull distribution are applied to historical failure time data of power transformers of National Society for Electricity and Gas (SONELGAZ) in Western Algeria. A comparison of the reliability analysis through respective probability distributions is presented in this study. Finally, Akaike information criterion (AIC) is used to select a best distribution for modeling this data.

Weibull Mixture Model for Reliability Analysis

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Weibull Mixture Model for Reliability Analysis