A Standardized Form of the Random Fatigue-Limit Model

Abstract

This article discusses a standardization of the random fatigue-limit model (RFLM) presented by Pascual and Meeker (Pascual, F. G., Meeker, W. Q. (1999). Estimating fatigue curves with the random fatigue-limit model (with discussion). Technometrics 41:277–290). The basic RFLM has five model parameters and describes the relationship between fatigue life and applied stress, for example, in high-cycle fatigue behavior of materials used in jet engines. Possible extensions of the RFLM are also presented to generalize the model. The discussions here show that the model can be reparameterized so that the probability distribution function (pdf) and the cumulative distribution function (cdf) are indexed by a standardized stress, standardized slope, and a scale parameter. This “standardization” simplifies the computation of the pdf and cdf necessary for maximum likelihood estimation. This also allows for more efficient tabular and graphical presentation of quantiles. A practical example is presented to illustrate how tables and graphs of standardized quantiles can be used to obtain actual quantiles.

Keywords:

• Lifetime distribution
• Reliability
• Standardized quantiles

Acknowledgment

This investigation was supported in part by funds provided by the Washington State University Office of Research.