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Deriving the Likelihood Function of a Combined Structure by Using Crude Lifetime Data

  Competing risks theory concerns the system of logical series structure consisted of several causes of failure. Based on competing risks theory, we derive the likelihood function of a combined of series and parallel structure using obtainable data such as times to failure, causes of failure, functioning or failed states of the system and its parts. A predictive model for the failure rate of each part is also built up by using the derived likelihood function. When additional data are available, it is shown that the failure rate can be updated by using the Bayesian approach.