By approaching capability from the point of view of process loss similar to Cpm , Johnson (1992) provided the expected relative loss Le to consider the proximity of the target value. Putting the loss in relative terms, a user needs only to specify the target and the distance from the target at...

The process capability index Cpk has been widely used in manufacturing industry to provide numerical measures of process potential and performance. As noted by many quality control researchers and practitioners, Cpk is yield-based and is independent of the target T. This fails to account for...

Johnson (1992) developed the process loss index Le, which is defined as the ratio of the expected quadratic loss to the square of half specification width. Tsui (1997) expressed the index LeasLe=Lpe+Lot, which provides an uncontaminated separation between information concerning the potential...

Process capability indices have been widely used in the manufacturing industry providing numerical measures on process performance. The index Cp provides measures on process precision (or product consistency). The index Cpm, sometimes called the Taguchi index, meditates on process centring...

Process capability indices have been widely used in the manufacturing industry for measuring process reproduction capability according to manufacturing specifications. Properties of the univariate processes have been investigated extensively, but are comparatively neglected for multivariate...

Over 50 years ago, in a 1955 issue of JASA, a paper on a bounded continuous distribution by Topp and Leone [C.W. Topp and F.C. Leone, A family of J-shaped frequency functions, J. Am. Stat. Assoc. 50(269) (1955), pp. 209-219] appeared (the subject was dormant for over 40 years but recently the...

The distribution of linear combinations of random variables arises explicitly in many areas of engineering. This has increased the need to have available the widest possible range of statistical results on linear combinations of random variables. In this note, the exact distribution of the...

This paper concerns a family of univariate distributions suggested by Topp & Leone in 1955. Topp & Leone provided no motivation for this new family and by way of properties they derived only the first four integer-order moments, i.e. E(Xn) for n=1, r 2, r 3, r 4 . In this paper we provide a...

The Farlie-Gumbel-Morgenstern (FGM) family has been investigated in detail for various continuous marginals such as Cauchy, normal, exponential, gamma, Weibull, lognormal and others. It has been a popular model for the bivariate distribution with mild dependence. However, bivariate FGMs with...

Kotz & Nadarajah (2002) introduced a measure of local dependence which is a localized version of the Pearson's correlation coefficient. In this paper we provide detailed analyses (both algebraic and numerical) of the form of the measure for the class of bivariate extreme value distributions. We...