Abstract
Abstract: Interpreting an out-of-control signal is a crucial step in monitoring categorical processes. For the Chi-Square Control Chart (CSCC), an out-of control situation does not specify if it was a process deterioration or a process improvement. For this reason, a weighted chi-square statistical control chart WSCC is proposed with different weighting categories in order to enable an accelerated disclosure of a control situation after a shift due to a deterioration of quality and on the other hand, decelerate an out of control situation after a shift due to a quality improvement. Furthermore, in comparison with Marcucci’s method, the new procedure provides an accurate and easier way to interpret several signals. In other words, the WSCC allows a faster detection of an out-of control situation in the case of a quality deterioration, however, an out-of control situation is not quickly detected in the case of a quality improvement. Indeed, comparative studies have been performed to find the best control chart for each combination. Concluding remarks with comments and recommendations are given based on Average Run Length (ARL) and standard deviation run length (SDRL).
Highlights
Throughout the years, the importance of measurement and improvement of quality was enhanced in the investigation of continuous improvement of products and services
A close examination of the data related to those samples, indicated that despite sample 5 represents an improvement of the quality, the Chi-Square Control Chart (CSCC) consider it as out of control, but the proposed Weighted Sum of the Chi-square Control Chart (WSCC) was able to differentiate that it was an improvement of the quality and interpreted the signal as in-control
Processes with multiple categories can be modeled as multinomial processes
Summary
Throughout the years, the importance of measurement and improvement of quality was enhanced in the investigation of continuous improvement of products and services. If the product can only be categorized as defective or non-defective, control chart by attributes is applied. The attribute control chart is applied if the quality cannot be measured with numerical scale, such as appearance, softness, color, etc. Nelson (1987) investigated chi-square control chart for several proportions and Woodall (1997) discussed construction methods of control charts based on attribute data. The previous studies do not provide an idea about which category is responsible for the out-of-control situation and could not detect if it is a process deterioration or not For this reason, a new chart using a Weighted Sum of Chi-squares that express the relative importance of all categories and with known quality proportions is proposed.
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