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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.

Once a vehicle powertrain is designed and the first prototype is built, extensive on-board instrumentation and testing needs to be carried out at the proving grounds (PG) to generate load histograms for various components. The load histograms can then be used to carry out durability tests in the laboratory. When a component in the vehicle powertrain is changed, the load histograms need to be generated again at the proving grounds. This adds much time and money to the vehicle's development. The objective is to develop a virtual powertrain model that can be simulated through a powertrain endurance driving cycle in order to predict torque histograms and total damage. The predictions are then correlated against measured data acquired on a test vehicle that was driven through the same driving cycle at the proving grounds.