IJPAM: Volume 64, No. 3 (2010)


Gabriele Stoppa
Department of Computer and Management Sciences
University of Trento
Cia Inama, 5, Trento, 38100, ITALY
e-mail: gabriele.stoppa@economia.unitn.it

Abstract.The on-line quality control must be made on all individual items, namely it is reasonable to consider all produced units. In fact, in case of automated inspection, every manufactured item is accurately monitored and calibrated so that a great part of traditional quality control techniques does not work or is inappropriate. This paper concerns a method for monitoring the multidimensional production process for variables based on the measurement of all items manufactured in real time. We use all the disposable data for determining whether in the first phase (retrospective data) there is an in-control-state with the advantage of maximizing the amount of information collected. Mainly the following questions arise: 1) the technical rank between the variables, that puts the measures in a-symmetric position, is often disregard; 2) individual control charts for the variability and the co-relations do not exist. The xoc-method here suggested accounts for the a-symmetry and can handle the dispersion and the co-relations in the same way as the calibrations. We define the item calibrations, the tool calibrations and the calibration sequence and evaluate them measuring the loss-in-quality derived from the $T^2$-distance. Several topics will be discussed, including: calibrations, oscillations, co-relations and detection of the responsible variable(s). Every chart is associated with the chart of the variable contributions, which is a natural extension of the multivariate chart here suggested to visualize involved tools. The use of the xoc-method is illustrated with an example of industrial data and also some of the issues related to practical interpretations is discussed.

Received: March 14, 2010

AMS Subject Classification: 46N30, 47N30

Key Words and Phrases: individual control chart, variable contribution, $N_p$-distribution, $\chi^2$-distribution, $T^2$-distance, hypothesis testing

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 3