Reliability Equivalent "Strength" and Its Percentile when Fleet Usage and Usage-to-Failure are Random

SUMMARY & CONCLUSIONSIn engineering applications, both usage and usage to failure (strength) are often random and statistically distributed. One example is the field actual mechanical loading cycles experienced by a vehicle shaft and its cycles to failure at any given stress level. The later is often described by a probabilistic stress-life (P-S-N) curve. Historically, the design engineers often use the mean or median (50thpercentile) value of the usage-to-failure to represent the product strength for product design and risk assessment. However, this practice doesn’t seem to have solid physical and statistical justification.This paper provides a practical engineering insight, from stress-strength interference perspective, regarding the choice of strength percentile in product reliability design when both the field usage and usage to failure (strength) are random variables. Analytic models are developed for quantifying a reliability-equivalent reference percentile for usage-to-failure when both follow Weibull, Normal, and Lognormal distributions. Contrary to the reliability-equivalent usage that is typically taking the value greater than 50thpercentile, the reliability-equivalent strength is typically taking the value less than 50thpercentile. This finding has more physical justification and reveals a mirror image effect between reliability-equivalent usage and reliability-equivalent usage to failure (strength). Compared with traditional approach where mean or median values are selected, this approach assures that the product design will meet population reliability requirement while the traditional method will not. For easier use of the models in engineering, a look up table is developed for various combinations of distribution parameters. We further extended the analysis to cover the case when field usage doesn’t follow any known distribution, but is given in the discrete histogram format.