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

Vadhana Jayathavaj and Adisak Pongpullponsak
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Vadhana Jayathavaj: Rangsit University, Thailan
Adisak Pongpullponsak: King Mongkut's University of Technology Thonburi, Thailand

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Abstract: 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.

Keywords: variable parameters; simplicial depth rank; quality control; principal components analysis; economic design (search for similar items in EconPapers)
Date: 2015
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