A control chart pattern recognition system using a statistical ...

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210 J.-H. Yang, M.-S. Yang / Computers & Industrial Engineering 48 (2005) 205–221 Fig. 4. Unnatural reference patterns. (b) Upward and downward shift patterns ( 0 before shifting xðtÞ Z nðtÞ Cud u Z 1 after shifting ; (4) where d is the shift quantity randomly taken from 1 to 2.5 for upward shift and from K1toK2.5 for downward shift. (c) Upward and downward trend patterns xðtÞ Z nðtÞGdt (5) where d is the trend slope randomly selected from 0.05 to 0.12 for upward trend and from K0.05 to K0.12 for downward trend. (d) Cyclic pattern xðtÞ Z nðtÞ Cd sin 2pt (6) U where d is the amplitude randomly selected from 0.5 to 2.5 and U is the cycle length taken as UZ8 here.
(e) Systematic pattern J.-H. Yang, M.-S. Yang / Computers & Industrial Engineering 48 (2005) 205–221 211 xðtÞ Z nðtÞ CðK1Þ t d (7) where d is the amplitude randomly selected from 0.5 to 2.5. As mentioned in Section 1, larger mean shifts decrease ARL values and may lose the essence of doing the control chart pattern recognition because of out-of-control signals appearing sooner and often. Thus, a principle for choosing abnormal disturbance level d (i.e. shift, slop and amplitude) is to keep the mean not more than 3s. Moreover, the pattern length n used in the generated samples for each pattern is important. We will discuss and demonstrate latter. Thus, the training algorithm is described as follows: Training Algorithm Step 1: Determine the pattern length n and the sample number N. Step 2: First, select a pattern sample generator and a disturbance level d from (4)–(7). Generate a pattern vector x 1 with a pattern length n. Second, change the disturbance level d until N samples x 2 ,.x N are generated from the chosen pattern. Step 3: Estimate the reference pattern vector by using P NiZ1 x EðxÞ Z i : N We repeat the training algorithm until all six reference pattern vectors are generated for upward shift, downward shift, upward trend, downward trend, cyclic and systematic patterns. Our final generated reference pattern vectors are shown in Fig. 4. We would regard these six generated reference patterns as the prototypes to recognize input patterns. The purpose of our training algorithm is to obtain six prototypes for recognizing input control chart patterns. The Step 3 in the training algorithm with a mean vector E(x) ofN samples for each pattern is used to obtain a reference vector as a representation of the unnatural pattern. After we finish the training stage, it is necessary to use Eqs. (3)–(7) to generate samples for testing. A threshold, h, is created for qualifying the winner whether it matches enough or not. If the similarity measure is smaller than h, the winner is not similar enough. We will classify it as a normal pattern. The mechanism will further help us to identify these normal conditions and continue until an unnatural pattern is recognized. Thus, a classification algorithm is created as follows: Classification Algorithm Step 1: Determine a threshold h. Step 2: A processing data sequence containing recent n points is regarded as the pattern size to be recognized. Step 3: Input the data sequence to the recogniser and calculate its statistical correlation coefficient using (2) with six reference vectors to obtain outputs r u.s. , r d.s. r u.t. , r d.t. , r cyc , r sys for upward shift, downward shift, upward trend, downward trend, cyclic and systematic patterns, respectively.
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