A Bayesian conformity and risk assessment adapted to a form error model

Abstract

Form error is the departure of a manufactured part from its design or ideal shape, and is a key characteristic to be assessed in quality engineering in manufacturing. In practice, form errors are usually estimated from coordinate measurements involving only a finite number of measured points and the form error for the complete workpiece surface has to be inferred on the basis of these measurements. This paper is about determining whether a product meets its specifications based on its form error using a probabilistic model. Based on form error data and a product specification, the relationship between conformance testing and making decisions is established. In this paper, we define a form error model using a uniform distribution with unknown bounds, and then utilize a Bayesian approach to assign a distribution to the form error parameter and use this distribution in a conformity and risk assessment methodology to quantify the risk of incorrect decisions. The risk assessment is carried out using derived expressions of specific risks associated with product conformity. A slightly more extensive posterior model, taking into consideration the probable random effects of form errors, is discussed for the reader's interest. Numerical experiments illustrate the effectiveness of this approach by providing a decision framework to control the risks associated with making a wrong decision.