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This paper first introduces the Kerridge inaccuracy measure as an extension of the Shannon entropy and then the measure of past inaccuracy has been rewritten based on the concept of quantile function. Then, some characterizations results for lifetimes with proportional reversed hazard model property based on quantile past inaccuracy measure are obtained. Also, the class of lifetimes with increasing (decreasing) quantile past inaccuracy property and some of its properties are studied. In addition, via an example of real data, the application of quantile inaccuracy measure is illustrated.

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In this article, we consider the estimation of R{r,k}= P(X{r:n1} < Y{k:n2}), when the stress X and strength Y are two independent random variables from inverse Exponential distributions with unknown different scale parameters. R{r,k} is estimated using the maximum likelihood estimation method, and also, the asymptotic confidence interval is obtained. Simulation studies and the performance of this model for two real data sets are presented.


 

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This article considers the stress-strength reliability of a coherent system in the state of stress at the component level. The coherent series, parallel and radar systems are investigated. For 2-component series or parallel systems and radar systems, this reliability based on Exponential distribution is estimated by maximum likelihood, uniformly minimum variance unbiased and Bayes methods. Also, simulation studies have been done to check estimators' performance, and real data are analyzed.
 

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This article introduces a new extension of the log-logistic distribution, and its properties and parameter estimation are studied and analyzed. It is shown that adding a parameter to this distribution makes its shape more symmetric and less skewed as the parameter increases. Unlike the original distribution, the moments of the new distribution and its quantile function always exist. Furthermore, it is demonstrated that the reliability measures, such as the hazard rate function, the mean residual life function, and stochastic orderings, are more flexible in the new distribution. Additionally, the parameters of the distribution are estimated using the LLP and ML methods, and the efficiency and consistency of the estimators are evaluated through simulation studies. Finally, the practical applicability of the model is demonstrated by applying the new model to real-world data from airborne equipment and lung cancer patients.