Economic Design of Statistical Process Control Using Principal Components Analysis and the Simplicial Depth Rank Control Chart

The principal components analysis (PCA) and the simplicial depth rank control chart (r chart) have been introduced as a nonparametric multivariate statistical process control by transforming the highest principal components (PCs) with cumulative eigenvalues more than 60% to the simplicial depth rank uniform distribution. The correlated trivariate standard normal distribution with the combinations of shift in 0,1,2 and 3 times of standard deviation are simulated. The results show that the Chi-square goodness of fit test rejected the null hypothesis which the simplicial depth rank distribution is a uniform distribution. The transition matrix for variable parameters PCA r chart is simulated from the predetermined action limit (k) and warning limit (w). The dual control schemes using the reference data set (RDS) of n observations for the regular control scheme (1) and the tight control scheme (2) are RDS1 n=150 and 300, RDS2 n=150 and 300, number of observations (n1,n2)=(1,1), sampling intervals (h1,h2)=(1, 19 values ranging from 0.05 to 1.0 with increment in each step 0.05), the warning region for regular scheme (k1-w1)=(0.05-0.10, 0.075-0.15), and for the tight scheme (k2-w2)=(0.05-0.10, 0.075-0.15, 0.10-0.15), within 22 mean shift combinations from total of 64 (4×4×4). The minimum economic cost per time unit (ECTU) using the Lorenzen and Vance’s cost parameters is approximately 937.39.