Abstract
This paper focuses on the design and development of an expert system for on-line detection of various control chart patterns so as to enable the quality control practitioners to initiate prompt corrective actions for an out-of-control manufacturing process. Using this expert system developed in Visual BASIC 6, all the nine most commonly observed control chart patterns, e.g., normal, stratification, systematic, increasing trend, decreasing trend, upward shift, downward shift, cyclic, and mixture can be recognized well, employing an optimal set of seven shape features. Based on an observation window of 32 data points, it can plot the control chart, compute the control limits, identify the control chart pattern, calculate the process capability index, determine the maximum run length, and identify the starting point of the maximum run length. After pattern recognition, it can also inform the users about various root assignable causes associated with a particular pattern along with the necessary pre-emptive actions. It opens up wide opportunities for quality improvement and real-time applications in diverse manufacturing processes. This developed expert system is built for a vertical drilling process and its recognition performance is tested using simulated process data.
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Appendix
Appendix
1.1 Equations for generation of various patterns in a given normal process
Suppose, the value of a standard normal variate at ith (i = 1,2,…,32) time point is r i , and the observed value at ith time point is y i . Then, various patterns of length 32 for a normal process with mean μ and standard deviation σ can be generated using the following equations:
where,
- σ′:
-
random noise for stratification pattern
- a :
-
amplitude of cyclic variation
- g :
-
magnitude of gradient for the trend pattern
- d :
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magnitude of the systematic pattern
- k :
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parameter determining the shift position
- s :
-
magnitude of the shift
- i :
-
discrete time point at which the pattern is sampled
- T :
-
period of a cycle
- m :
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magnitude of the mixture pattern
- w :
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a binary integer value dependent on a random number p (0 < p < 1) and a pre-specified probability value b = mp, which determines the shifting between distributions. The value of b is fixed as 0.4, and thus, w = 0 if p < 0.4 and w = 1 if p ≥ 0.4.
In this paper, for simulation of various patterns, the values of different process parameters are chosen as follows: μ = 80, σ = 5, 0.2σ ≤ σ′ ≤ 0.4σ, 1σ ≤ d ≤ 3σ, 0.05σ ≤ g ≤ 0.1σ (for UT), −0.1σ ≤ g ≤ −0.05σ (for DT), 1.5σ ≤ s ≤ 2.5σ (for US), −2.5σ ≤ s ≤ −1.5σ (for DS), P = 9, 17 or 25, 1.5σ ≤ a ≤ 2.5σ, T = 8 or 16, 1.5σ ≤ m ≤ 2.5σ, and 0 ≤ p ≤ 1.
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Bag, M., Gauri, S.K. & Chakraborty, S. An expert system for control chart pattern recognition. Int J Adv Manuf Technol 62, 291–301 (2012). https://doi.org/10.1007/s00170-011-3799-z
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DOI: https://doi.org/10.1007/s00170-011-3799-z