A stochastic mathematical model was built and analyzed by using the reliability theory for a manufacturing system in which two machines are arranged in parallel. Under the condition that the system is required to be operated at a constant rate of production, the variation of reliability and failure rate of cutting tools with the lapse of time were investigated, using the stress-strength model in failure physics. A time interval of tool replacement in the continuous operation and a time to failure for a manufacturing system which is composed of two lathes were also investigated.

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