Estimation of stress-strength reliability for multicomponent system with a generalized inverted exponential distribution

Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) with common scale parameters, maximum likelihood estimate of MSS reliability is established along with associated existence and uniqueness, and approximate confidence interval is also obtained in consequence. Additionally, alternative generalized estimates are proposed for MSS reliability based on constructed pivotal quantities, and associated Monte-Carlo sampling is provided for computation. Further, classical and generalized estimates are also established under unequal strength and stress parameter case. For comparison, bootstrap confidence intervals are also provided under different cases. To compare the equivalence of the strength and stress parameters, likelihood ratio testing is presented as a complement. Finally, extensive simulation studies are carried out to assess the performance of the proposed methods, and a real data example is presented for application. The numerical results indicate that the proposed generalized methods perform better than conventional likelihood results.