Power Generalized DUS Transformation of Inverse Kumaraswamy Distribution and Stress-Strength Analysis

Abstract

Reliability analysis, including stress-strength analysis, for given data is more widely used in the reliability literature. A large number of new distributions are available, but many of them are not showing a good fit for the data under consideration. This inspires a researcher to introduce new lifetime distributions that demonstrate superior fitness in comparison to the existing distributions. So that more accurate reliability estimates can be obtained for the given data. The DUS transformation technique is widely used in reliability literature to create better models. Power generalized DUS(PGDUS) transformation to lifetime distributions, which is found to be useful to introduce more appropriate flexible distributions for the given data. Vinyl chloride data obtained from clean upgrading and monitoring wells in mg/L have been analyzed using DUS inverse Kumaraswamy (DUS IK), inverse Kumaraswamy (IK), and Weibull distributions. As a substitute for these distributions, this paper presents a new lifetime distribution employing PGDUS transformation, utilizing the inverse Kumaraswamy distribution as the baseline. The statistical properties of the proposed distribution are derived. The parameters of the proposed distribution are estimated using the maximum likelihood (ML) method, maximum product spacing (MPS), method of moment, and method of least squares. Additionally, Bayesian parameter estimates are acquired utilizing Lindley’s approximation and the Metropolis-Hastings algorithm. The consistency of the model is verified using mean squared error (MSE) and biases, which are obtained based on simulated values. Then, the proposed distribution is compared with the DUS-IK, IK, and Weibull distributions. In this paper, single-component and multi-component stress-strength reliability analyses are also conducted.