Abstract
This paper introduces a model for repairable standby parallel system with two non-identical parts with common cause fault and human error based on a semigroup approach. The development of the model presented in this paper is provided into three folds: (1) the use of pure analysis to prove the uniqueness of some classical solution to this model; (2) verifying this uniqueness by providing non-negative solution to this model; and (3) providing formulate for reliability indices of the studied model, along with numerical examples to explain our expected results. The novelty of the presented approach lies in studying the existence of a unique system solution and its exponential stability based on C0-semigroup, the confinal related theory and the functional analysis method.
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