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.
