A One-Class Classification-Based Control Chart Using the 𝐾-Means Data Description Algorithm

Algorithm 1

%Let Q be the (n  ×  m) matrix of quality variables where n is the number

%of observations and m the number of quality variables in the training phase.

%Define the target class.

T=target_class(+Q);

%Use the KMDD algorithm to fit a sphere around the defined target class above,

%where c1 is a fraction error on the target class and c2 is a parameter

%defining the number of clusters.

w = kmeans_dd(T,c1,c2);

%Show the results of KMDD classifier.

W=+w;

%Phase I of the KM-chart:

%Compute the Euclidean distance of each training observation and the UCL.

n = size(T,1);

D_training = [sqrt(min(sqeucldistm(+T,W.w),[],2)) repmat(W.threshold,n,1)];

%Phase II of the KM-chart:

%Let now R be the (k x p) matrix of quality variables where k is the number

%of observations and p the number of quality variables in the testing phase.

%In Phase II we repeat the same computation as in Phase I but here we use

%test data and compare it with the UCL to detect out-of-control states.

%Compute the Euclidean distance of each test observation.

m= size(R,1);

D_test = [sqrt(min(sqeucldistm(+R,W.w),[],2)) repmat(W.threshold,m,1)];

y1=D_training(:,1); y2=D_training(:,2);x1=(1:n)’;

y3=[D_training(:,1); D_test(:,1)];

y4 =[D_training(:,2); D_test(:,2)];x2=(1:n+m)’;

%Display the KM-chart for Phase I and II.

figure;

SUBPLOT(2,1,1), plot(x1,y1, ‘-o’, x1,y2, ‘-’); title(‘Phase I of the KM-chart’)

SUBPLOT(2,1,2), plot(x2,y3, ‘-o’, x2,y4, ‘-’); title(‘Phase II of the KM-chart’)