Multicomponent stress-strength reliability based on a right long-tailed distribution

Abstract

This article deals with the problem of reliability in a multicomponent stress-strength (MSS) model when both stress and strength variables are from inverse Kumaraswamy distribution. The reliability of the system is estimated using classical and Bayesian approaches when the common second shape parameter is known or unknown. The maximum likelihood estimation and its asymptotic confidence interval for the reliability of the system are obtained. Furthermore, two other asymptotic confidence intervals are computed based on Logit and Arcsin transformations. The uniformly minimum variance unbiased estimator for the reliability of the MSS model is obtained when the common second shape parameter is known. The Bayes estimate is obtained exactly when the second shape parameter is known and it is approximated by using the Monte Carlo Markov Chain method when the second shape parameter is unknown. The highest probability density credible interval is established using the Gibbs sampling technique. Monte Carlo simulations are implemented to compare the different proposed methods. Finally, two real data sets are presented in support of the suggested procedures.

Inference for dependent complementary competing risks model from an inverted Kumaraswamy distribution under ranked set sampling

“…The IK distribution has been discussed by many authors, see, for example, some recent works of Abu-Moussa and El-Din, 41 Pasha-Zanoosi and Pourdarvish, 42 Aly and Abuelamayem, 43 Iqbal et al, 44 and Muhammed 45 among others. For illustration, Figure 1 displays the density and HRF plots of the IK distribution to demonstrate its flexibility.…”

“…Consequently, the survival function (SF) and hazard rate function (HRF) of the IK distribution at mission time $$t$$ can be expressed as $$$$\begin{align} S_{IK}(t;\alpha,\beta)=1-[1-(1+t)^{-\alpha}]^{\beta}\nobreakspace \nobreakspace \text{and}\nobreakspace \nobreakspace h_{IK}(t;\alpha,\beta)=\frac{\alpha \beta (1+t)^{-\alpha -1}[1-(1+t)^{-\alpha}]^{\beta -1}}{1-[1-(1+t)^{-\alpha}]^{\beta}}. \end{align}$$$$The IK distribution has been discussed by many authors, see, for example, some recent works of Abu‐Moussa and El‐Din, 41 Pasha‐Zanoosi and Pourdarvish, 42 Aly and Abuelamayem, 43 Iqbal et al., 44 and Muhammed 45 among others. For illustration, Figure 1 displays the density and HRF plots of the IK distribution to demonstrate its flexibility.…”