Estimating Sensitivity of Process Capability Modeled by a Transfer Function

Abstract

We assume that the output variable Y of a process with a number of inputs (X1, X2, …, Xn) is subject to specification limits, and that the inputs can be represented as random variables. The probability that Y falls within its specification limits is a measure of process capability. In this paper, we demonstrate a one-pass Monte Carlo simulation method that allows the estimation of the sensitivity of process capability to each parameter of the input variables. The proposed method may have gains in efficiency, in terms of reduction in root mean squared error, of several hundred times over competing methods. The results can be used to improve system performance by directing attention to those parameters for which small changes result in the largest change in capability. In this paper we outline the algorithm, demonstrate it on three problems, and provide some discussion of why it works.