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In the context of the Poisson censored  δ -shock model, this paper derives the system reliability by directly calculating probabilities, which is different from the existing literature. When the time is equal to  δ , an explicit result that the reliability has a jump is verified. Based on the system reliability, we obtain the expectation of the lifetime of the system. Finally, one application of the model is shown in relationship marketing. The conclusions imply that managers should make a tradeoff between the expected return and variance of return before making decisions.

Reliability of Poisson censored δ -shock model *