Identification and Extensions of Quasiconvex Quality Loss Functions

Abstract

This paper presents a set of related quasiconvex quality loss functions. Characteristics of quasiconvex functions that are desirable for modeling quality loss are noted. Three frequently used univariate quasiconvex quality loss functions are discussed. Bivariate and multivariate quasiconvex quality loss functions are developed. A set of necessary and sufficient conditions is established for the quasiconvexity of multivariate quality loss functions. An industrial product example is used to illustrate the development of a bivariate quadratic quality loss function.

Integrating the LambertW Function to a Tolerance Optimization Problem

“…Separate optimization of quality characteristic values in terms of mean and variance using this quadratic QLF has become the cornerstone of Taguchi methods [23][24][25] . Examples for the use of the quadratic QLF are numerous 10,16,[26][27][28][29][30] . Compared with other QLFs, such as step-loss and piecewise linear loss functions, the quadratic QLF may be a good approximation of measuring the quality of a product, particularly over the range of characteristic values in the neighborhood of the target value.…”

Determining the Optimum Process Mean under a Log-normal Distribution

“…EðXÞ ¼ e l à þ 1 2 r 2 : Cho and Leonard (1997) presented the piecewise linear quality loss function for the nominal-is-best quality characteristic is as follows:…”

“…They selected the optimum process mean based on minimizing the costs of falling below the lower specification limit (T L ) and exceeding the upper specification limit (T U ). Cho and Leonard (1997) presented that the piecewise linear quality loss function for product is roughly proportional to the deviation of the quality characteristic from its specification limits. The linear loss function is usually applied in the filling/canning problem for determining the optimum manufacturing target, (e.g., Carlsson, 1984;Golhar and Pollock, 1998;Misiorek and Barnett, 2000;and Lee et al, 2001 etc.…”

Determining optimal process mean of two-market products

“…Mathematical details of the loss function can be found in Cho and Leonard [20], Phillips and Cho [21,22], Kim and Cho [23], and Teeravaraprug and Cho [24]. In this research, two market products are considered.…”