In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated. Furthermore, simulation study is performed to observe the performance of the estimates. Finally, the model with two real data sets is examined.

This article deals with the estimation of R = P(Y < X) when X and Y are distributed as two independent generalized inverted exponential with common scale parameter and different shape parameters. The maximum likelihood and Bayesian estimators of R are obtained on the basis of upper record values and upper record ranked set samples. The Bayesian estimator cannot be obtained in explicit form, and therefore it has been achieved using Lindley approximation. Simulation study is performed to compare the reliability estimators in each record sampling scheme with respect to biases and mean square errors.

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Stress-strength models are of special importance in reliability literature and engineering applications. This paper deals with the estimation problem of a stress-strength model incorporating multi-component system. The system is regarded as alive only if at least S out of k (S < k) strength components exceed the stress. The reliability of such system is obtained when strength and stress variables have Weibull distributions. Maximum likelihood estimator of R S,k and asymptotic confidence intervals are obtained based on upper record values. Bayesian estimator under squared error and linear exponential loss functions using gamma prior distributions and the corresponding credible intervals are obtained. Due to the lack of explicit forms for the Bayes estimates, the Markov Chain Monte Carlo (MCMC) method is employed. A simulation study is implemented to assess the performance of estimates. A real-life example is presented to show how the proposed model may be utilized in breaking strength of jute fibre data.

The ranked set sampling (RSS) methodology is an effective technique of acquiring data when measuring the units in a population is costly, while ranking them is easy according to the variable of interest. In this article, we deal with an RSS-based estimation of the inverted Kumaraswamy distribution parameters, which is extensively applied in life testing and reliability studies. Some estimation techniques are regarded, including the maximum likelihood, the maximum product of spacing’s, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling. We demonstrate a simulation investigation to assess the performance of the suggested RSS-based estimators via accuracy measures relative to simple random sampling. On the basis of actual data regarding the waiting times between 65 consecutive eruptions of Kiama Blowhole, additional conclusions have been drawn. The outcomes of simulation and real data application demonstrated that RSS-based estimators outperformed their simple random sampling counterparts significantly based on the same number of measured units.