Stress‐Strength Reliability for Exponentiated Inverted Weibull Distribution with Application on Breaking of Jute Fiber and Carbon Fibers

For the first time and by using an entire sample, we discussed the estimation of the unknown parameters <i>θ</i> ₁, <i>θ</i> ₂, and <i>β</i> and the system of stress-strength reliability <i>R</i>=<i>P</i>(<i>Y</i> < <i>X</i>) for exponentiated inverted Weibull (EIW) distributions with an equivalent scale parameter supported eight methods. We will use maximum likelihood method, maximum product of spacing estimation (MPSE), minimum spacing absolute-log distance estimation (MSALDE), least square estimation (LSE), weighted least square estimation (WLSE), method of Cramér-von Mises estimation (CME), and Anderson-Darling estimation (ADE) when <i>X</i> and <i>Y</i> are two independent a scaled exponentiated inverted Weibull (EIW) distribution. Percentile bootstrap and bias-corrected percentile bootstrap confidence intervals are introduced. To pick the better method of estimation, we used the Monte Carlo simulation study for comparing the efficiency of the various estimators suggested using mean square error and interval length criterion. From cases of samples, we discovered that the results of the maximum product of spacing method are more competitive than those of the other methods. A two real-life data sets are represented demonstrating how the applicability of the methodologies proposed in real phenomena.