Abstract
Abstract: Marcucci (1985) proposed a chi square goodness of fit statistic based generalized p-chart for multinomial process monitoring. A chi square distribution quantile was considered as a control chart limit. A weighted chi square goodness of fit statistic-based control chart is proposed for multinomial process monitoring in this paper, where more important weights are advocated to poor quality categories. The statistic distribution is approximated by a well-known linear combination of chi squares distribution. The approximation is assessed through a simulation, an extreme percentile of the approximated distribution is used as an upper control chart limit and a comparison is carried out with a chi square goodness of fit statistic-based control chart. The average run length is used as a benchmark and the comparison is performed using simulations considering two process shifts scenarios. Under some restrictions, the weighted statistic-based control chart allows an earlier detection of process shift in case of deterioration and postpones out of control signals in case of improvement. This benefit is clearer when the process is improved by a decrease in the poor quality probability category and an increase in the best quality category probability.
Highlights
Control charts for attributes are used when focus is on the classification of product units into categories rather than quality characteristic measurements
Qi is considered as the control chart positive statistic and a one-sided control chart is the appropriate choice. in what follows, Qi distribution is approximated by a linear combination of chi squares as the exact distribution is not known (Equation 4)
A simulation is implemented in order to compare between the (Marcucci, 1985) χ2 control chart and the Q statistic-based control chart with a UCL approximated by a linear combination of independent chi squares distribution quantile
Summary
Control charts for attributes are used when focus is on the classification of product units into categories rather than quality characteristic measurements. The inspected units are generally classified into conforming or nonconforming units; different criteria of nonconforming classification could be used following defect seriousness A probabilistic approach is considered in this paper as no classification ambiguity is considered It is based on the work of (Duncan, 1950) who developed a chi square chart for controlling a set of percentages and (Marcucci, 1985) who introduced a one-sided generalized p-chart for multinomial process monitoring. (Perry, 2019) used an EWMA control chart for categorical processes where weighted category counts were used as a control chart statistic. The proposed control chart is based on a weighted chi-square goodness of fit statistic and aims at earlier detection of process deterioration and delay improvement detection.
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