Uncertainty in Multi-Scale Creep Rupture Life Modeling and a New Approach to Estimating Frequency of In-Service Inspection of Components at Elevated Temperatures

Uncertainty in modeling the creep rupture life of a full-scale component using experimental data at microscopic (Level 1), specimen (Level 2), and full-size (Level 3) scales, is addressed by applying statistical theory of prediction intervals, and that of tolerance intervals based on the concept of coverage, p. Using a nonlinear least squares fit algorithm and the physical assumption that the one-sided Lower Tolerance Limit ( LTL ), at 95 % confidence level, of the creep rupture life, i.e., the minimum time-to-failure, minTf, of a full-scale component, cannot be negative as the lack or “Failure” of coverage ( Fp ), defined as 1 - p, approaches zero, we develop a new creep rupture life model, where the minimum time-to-failure, minTf, at extremely low “Failure” of coverage, Fp, can be estimated. Since the concept of coverage is closely related to that of an inspection strategy, and if one assumes that the predominent cause of failure of a full-size component is due to the “Failure” of inspection or coverage, it is reasonable to equate the quantity, Fp, to a Failure Probability, FP, thereby leading to a new approach of estimating the frequency of in-service inspection of a full-size component. To illustrate this approach, we include a numerical example using the published creep rupture time data of an API 579-1/ASME FFS-1 Grade 91 steel at 571.1 C (1060 F) (API-STD-530, 2007), and a linear least squares fit to generate the necessary uncertainties for ultimately performing a dynamic risk analysis, where a graphical plot of an estimate of risk with uncertainty vs. a predicted most likely date of a high consequence failure event due to creep rupture becomes available for a risk-informed inspection strategy associated with an energy-generation or chemical processing plant equipment.