Reliability Inference For Multicomponent Stress–strength Model Under Pareto Distribution

This study considers the reliability of a multi componentstress-strength model involving one stress and multiple strengths from a series system.Both the maximum likelihood and Bayesian methods are presented to obtain the estimates of the reliability when the stress and strength variables follow the General Pareto distribution with the common shape parameter and different scale parameters.Also,the model with unequal shape parameters is considered.Forthemaximum likelihoodmethod,theexistenceanduniqueness of maximum likelihood estimators are shown,while for the Bayesian method,the necessary and sufficient conditions of the propriety of the posterior distribution based on the Jeffreys prior are obtained.For both methods we need to calculate the Jacobian matrix with derivatives of the distribution functions and the determinant of this matrix.After proving all these things,weproceedtomakeanumericalanalysiswithprogrammingtools.Theperformanceoftheproposed methodsisevaluatedby Monte Carlo simulation by running thousands of samples runs with set parameters to estimate these values.After running the simulation,the results show that the Bayesian method outperforms the maximum likelihood method,especially for bigger sample sizes.After all these simulations are ran then we use a real dataset proposed by other authors and is analyzed for illustration.