A Bayesian Procedure for Assessing Process Performance Based on Expected Relative Loss with Asymmetric Tolerances

Taguchi has introduced the loss function approach to quality improvement by focusing on the reduction of variation around the target value. This concept pays attention to the product designer's original intent; that is, values of a critical characteristic at a target lead to maximum product performance. To address this concept, Johnson (1992) proposed the concept of expected relative squared error loss Le for symmetric cases, by approaching capability in terms of loss functions. Unfortunately, the index Le inconsistently measures process capability for processes with asymmetric tolerances, and thus reflects process potential and performance inaccurately. To remedy this, Pearn et al. (2006) proposed a modification of expected loss index, which is referred to as [image omitted] , to handle processes with both symmetric and asymmetric tolerances. The majority of the researches for assessing process performance based on the process loss indices are investigated using the traditional frequentist approach. However, the sampling distribution of the estimated [image omitted]  is intractable, this makes establishing the exact confidence interval and testing process performance difficult. In the paper, we consider an alternative Bayesian approach to assess process performance based on the loss index for processes with asymmetric tolerances. Based on the derived posterior probability, a simple but practical procedure is proposed for practitioners to assess process performance on their shop floor, whether the manufacturing tolerance is symmetric or asymmetric.