System reliability can be improved through redundancy by allocating additional components in parallel so the system is creditable even if one or more components fail. Often, the parallel parts are repeated components of the same type. These components usually share the same reliability estimation. Thus, the components reliability estimates are statistically dependent. Various non-parametric models for the system reliability estimation have been discussed a lot. Current reliability estimation models, such as the extended lognormal model and modified maximum likelihood model can partially accommodate the component repetition at the system level, yet in a very limited manner. Therefore, a new reliability estimation model has been proposed to overcome the difficulties of traditional non-parametric estimation models. Based on an approximation approach, the new model provides accurate estimation for the mean and the variance of system reliability estimate when repeated components are used anywhere in the system.
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