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The failure rate of equipment during long-term operation in severe environment is time-varying. Most studies regard the failure rate as a constant, ignoring the reliability evaluation error caused by the constant. While studying failure data that are few and easily missing, it is common to focus only on the uncertainty of reliability index rather than parameter of failure rate. In this study, a new time-varying failure rate model containing time-varying scale factor is established, and a statistical-fuzzy model of failure rate cumulated parameter is established by using statistical and fuzzy knowledge, which is used to modify the time-varying failure rate model. Subsequently, the theorem of the upper boundary existence for the failure rate region is proposed and proved to provide the failure rate cumulated parameter when the failure rate changes the fastest. The proposed model and theorem are applied to analyze the reliability of subsea emergency shutdown system in the marine environment for a long time. The comparison of system reliability under time-varying failure rate and constant failure rate shows that the time-varying failure rate model can eliminate the evaluation error and is consistent with engineering. The reliability intervals based on the failure rate model before and after modification are compared to analyze differences in uncertainty, which confirm that the modified model is more accurate and more practical for engineering.

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Reliability Study of Parameter Uncertainty Based on Time-Varying Failure Rates with an Application to Subsea Oil and Gas Production Emergency Shutdown Systems