Makam, S., Lee, Y., and Attibele, P., "Estimation of One-Sided Lower Tolerance Limits for a Weibull Distribution Using the Monte Carlo Pivotal Simulation Technique," SAE Int. J. Mater. Manf. 6(3):369-374, 2013, doi:10.4271/2013-01-0329.
This paper introduces a methodology to calculate confidence bounds for a normal and Weibull distribution using Monte Carlo pivotal statistics. As an example, a ready-to-use lookup table to calculate one-sided lower confidence bounds is established and demonstrated for normal and Weibull distributions.The concept of one-sided lower tolerance limits for a normal distribution was first introduced by G. J. Lieberman in 1958 (later modified by Link in 1985 and Wei in 2012), and has been widely used in the automotive industry because of the easy-to-use lookup tables. Monte Carlo simulation methods presented here are more accurate as they eliminate assumptions and approximations inherent in existing approaches by using random experiments. This developed methodology can be used to generate confidence bounds for any parametric distribution.The ready-to-use table for the one-sided lower tolerance limits for a Weibull distribution is presented. The Weibull distribution is widely adopted in the automotive industry because of its wide range of engineering applications. The Weibull model covers many other parametric distributions (either exactly or approximately) like lognormal and exponential. Typically, the fatigue life of a product follows a Weibull distribution. Estimation of the confidence bounds for a Weibull distribution with limited experimental data is critical in making design and material selection decisions for any product to ensure it complies with durability targets.