Stability Assessment of a Manufacturing Process Using Grey Relationship Theory Based on Two Unsorted Data Series

Xintao Xia, Liang Ye, Zhen Chang

Based on grey system theory, which is used to analyze two unsorted data series produced during the manufacturing process, the stability of a manufacturing system can be evaluated. First, two unsorted data series with the original order maintained are acquired from a manufacturing system. The grey relationship of the two data series without sorting can be established based on the distribution features of data series. Grey confidence level is calculated to evaluate the stability of a manufacturing process dynamically. A simulation experiment and an actual case were studied by analyzing two unsorted data series produced during the manufacturing process to evaluate the stability of manufacturing systems. In the simulation experiment, a normal distribution with unsorted data sequence was added with a linear error distribution sequence with the same number of data points. The result of simulation experiment showed that the grey confidence level P = 69.5% < 90% when the weight f =0.5. Therefore, two unsorted data series did not have the same properties, indicating that the manufacturing process was not stable. In the actual case, a sine function distribution was added to a triangular distribution with the same number of data points to generate a systematic error. The result of actual case showed that the grey confidence level P = 89.5% < 90% when the weight f =0.5, indicating that the manufacturing process was not stable. The stability assessment model is proven to be able to be used to analyze the system property of two unsorted data series under the condition of poor information, which is beyond the constraints of grey relational sequence space in original grey system theory and is the expansion of the grey system theory.