A Statistical Approach to Estimating a 95% Confidence Lower Limit for the Design Creep Rupture Time vs. Stress Curve When the Stress Estimate Has an Error Up to 2%

Recent experimental results on creep-fracture damage with minimum time to failure (minTTF) varying as the 9^th power of stress, and a theoretical consequence that the coefficient of variation (CV) of minTTF is necessarily 9 times that of the CV of the stress, created a new engineering requirement that the finite element analysis of pressure vessel and piping systems in power generation and chemical plants be more accurate with an allowable error of no more than 2% when dealing with a leak-before-break scenario. This new requirement becomes more critical, for example, when one finds a small leakage in the vicinity of a hot steam piping weldment next to an elbow. To illustrate the critical nature of this creep and creep-fatigue interaction problem in engineering design and operation decision-making, we present the analysis of a typical steam piping maintenance problem, where 10 experimental data on the creep rupture time vs. stress (83 to 131 MPa) for an API Grade 91 steel at 571.1 C (1060 F) are fitted with a straight line using the linear least squares (LLSQ) method. The LLSQ fit yields not only a two-parameter model, but also an estimate of the 95% confidence upper and lower limits of the rupture time as basis for a statistical design of creep and creep-fatigue. In addition, we will show that when an error in stress estimate is 2% or more, the 95% confidence lower limit for the rupture time will be reduced from the minimum by as much as 40%.