Adimax chart for monitoring multivariate processes
by
Karuthan Chinna
University Technology MARA

First developed by Shewhart (1925), the use of x and R (or x and S) charts has become a standard practice in industrial applications. Recent developments deviate from early ones most notably on the emphasis they place on target values and on simultaneously monitoring both the process mean and process variability in a single chart. The Adimax Chart, proposed by Chinna and Abdullah (2001), is an innovative simultaneous statistical process control chart for univariate processes. This chart is easy to construct and interpret even by the SPC illiterate. This chart uses probability transformation and standardization to transform the mean and variability into two independent and identical standard normal distributions, Zu and Zv. The statistic, D, taken as the maximum absolute value of Zu and Zv follows a chi-square distribution with two degrees of freedom. A large value of D indicates an out-of-control point. The statistic U=P{ F(1,1) £ (Zu2 / Zv2)} ~ U(0,1). Sign(Zu)*U gives the magnitude and direction of shift, R, (-1 £ R £1). The point (R, D) is then plot on a two dimensional chart. When a point is out-of-control, D being very large, R will indicate whether the mean, variability or both mean and variability are out-of-control. A value of R close to |1| indicate a departure from target mean, R close to zero indicate departure in variability and R close to |0.5| indicate departure in both mean and variability.

In this paper, we explore the use of Adimax chart to simultaneously monitor the process mean and process variability for a multivariate situation.

Key words: Probability transformation, simultaneous control charts, multivariate process

Date received: March 26, 2002