Determining the Optimum Process Mean under a Log-normal Distribution

Abstract

step loss function, piecewise linear loss function, log-normal distribution.,

Determining the optimal process means under mixture normal distributions

“…McLachlan and Peel 2001). Therefore our results are more flexible than those of Chen and Chou (2005).…”

“…For most decision analyses (cf. Cho and Leonard 1997;Wen and Mergen 1999;Chen and Chou 2005), the uses of step loss function and piecewise linear loss function make the calculations relatively straightforward and simple. Therefore, we use these two loss functions to measure the cost of being out-of-specification.…”

“…If the loss differs for values of y that are equidistant from m, for example, a value that exceeds m might be more detrimental than a value that is below m, then an asymmetric loss functions would be appropriate. In this paper we consider two asymmetric loss functions, one is the step loss function (e.g., Wen and Mergen 1999;Chen and Chou 2005) and the other is the piecewise linear loss function (e.g., Carlsson 1984;Golhar and Pollock 1998;Misiorek and Barnett 2000;Lee et al 2001;Chen and Chou 2005).…”