A comparison and an application of reliability, reliability system, hybrid reliability system functions for Rayleigh, Pareto, and Rayleigh Pareto distributions

Abstract

This study dealt with the analysis of the reliability function for hybrid systems with asymmetric components, where the operating times of these components follow Rayleigh, Pareto, and Rayleigh Pareto distributions, furthermore, we introduced a method of operation based on hybrid systems in order to increase the reliability of the machines operating times. Different simulation experiments were done to estimate the reliability function of these systems using the ML method, then a comparison was made between those estimators, the simulation results proved that the Rayleigh-Pareto distribution gives the best estimate for the reliability functions, also the estimated values for the reliability function for the hybrid parallel-series system greater than the estimated values of the reliability function for the hybrid series-parallel system, finally, the estimated reliability function values of the proposed system are better than the estimated values of the two other systems. In the application part, it was chosen the operating times for the machines of the University House for printing, publishing ,and translation in Baghdad, where the factory management depends on the system hybrid serial-parallel system to operate the factory machines, this system leads to a decrease in the reliability of the operating times of the factory machines to 50% at the first operating hour, but if the blistering hybrid system is followed, i.e. the similar machines are run in parallel, and the different machines are run in series, then the probability that the machinery system will continue to operate for four hours will be 50%.