Most of the inventory control models assume that quality defect never happens, which means production process is perfect. However, in real manufacturing processes, the production process starts its operation in the in-control state; but after a period of time, shifts to the out-of-control state because of occurrence of some disturbances. In this paper, in order to approach the model to real man...

Let R be a non-singular m-factorial correlation matrix, i.e. R = D + AA0 with a diagonal matrixD > 0 and a not necessarily de nite matrix AA0 of the minimal possible rank m. From an expression for the general non-central multivariate distribution function with the accompanying correlation matrix R some simpler cases are derived: The p-variate central -distribution with q degrees of freedom is g...

A 1 ( ) p -variate integral representation is given for the cumulative distribution function of the general p variate non-central gamma distribution with a non-centrality matrix of any admissible rank. The real part of products of well known analytical functions is integrated over arguments from ( , ).    To facilitate the computation, these formulas are given more detailed for 3. p  Furthe...

Multivariate statistical process control charts are often used for process monitoring to detect out-of-control anomalies. However, multivariate control charts based on conventional statistical distance measures, such as the one used in the Hotelling’s T 2 control chart, cannot scale up to large amounts of complex process data, e.g. data with a large number of variables and a high rate of data s...