Reliability Estimation for the Exponential-Pareto Hybrid System


  • Wafaa S. Hasanain Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
  • Waleed Mohammed Elaibi Department of Statistics, College of Administration and Economics, Mustansiriyah University, Baghdad, Iraq



Exponential distribution, Pareto distribution, hybrid (parallel-series) system, Reliability function, Maximum Likelihood Method, Standard Bayes, Quadratic Loss function, Simulation, Mean Squared Error


     The reliability of hybrid systems is important in modern technology, specifically in engineering and industrial fields; it is an indicator of the machine's efficiency and ability to operate without interruption for an extended period of time. It also allows for the evaluation of machines and equipment for planning and future development. This study looked at reliability of hybrid (parallel series) systems with asymmetric components using exponential and Pareto distributions. Several simulation experiments were performed to estimate the reliability function of these systems using the Maximum Likelihood method  and the Standard Bayes method  with a quadratic loss (QL) function and two priors: non-informative (Jeffery) and informative (Conjugate). Different sample sizes and parameter values are used in these simulation experiments, and the Mean Squared Error (MSE) was used to compare those experiments. The simulation results showed that the standard Bayes method with Conjugate loss function is better than the results from the maximum likelihood method.







How to Cite

Reliability Estimation for the Exponential-Pareto Hybrid System. (2023). Iraqi Journal of Science, 64(9), 4622-4633.

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