10.1 Introduction

The concert of symmetric tolerance was used tacitly in this beak on numerous occasions. A process is said to have a symmetric tolerance if the target value T is set to be the mid-point of the specification interval [LSL, USL], i.e. T = M = (USL + LSL) / 2. Most research in quality assurance literature has been focused so far on cases in which the manufacturing tolerance is symmetric. Examples include the earlier paper by Kane (1986), Chan et al. (1988), Choi and Owen (1990), Boyles (1991), Pearn et al. (1992), V nnman (1995), V nnman and Kotz (1995), Spiring (1997), Pearn et al. (1998), Pearn et al. (2003a, 2003b) among many others. Granted that cases with symmetric tolerances are quite common in practical situations, cases with asymmetric tolerances (T ? M) (see Figure 10.1) also often occur in the manufacturing industry. From the customer's point of view, asymmetric tolerances reflect that deviations from the target that are less tolerable in one direction than the other (see Boyles (1994), Vannman (1997), and Wu and Tang (1998)). Usually they are not directly related to the shape of the supplier's process distribution. Nevertheless, asymmetric tolerances can also arise in those situations where the tolerances are symmetric to start with, but the process distribution is skewed or follows a non-normal distribution. To deal with this the data are usually transformed to achieve approximate normality. A prominent example of this approach is Chou et al.