Control charts for monitoring multinomial variables
Cartas de control para monitorear variables multinomiales
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Background: The control as a tool for monitoring the quality of a product, allows to study the stability of processes over time, contrasting two hypothesis, which states that the process is in stable condition and the other denies it. Its use has been massive for continuous variables but not for categorical variables, why it is imperative to design such tools for such variables. Objective: To propose two (2) control charts for variables multinomial processes based on the p-value test result for homogeneity of proportions using the chi square test for uniform processing variables and approximation Wilson - Hilferty for variables chi square. Methods: The performance of proposed charts via simulation is estimated considering a Phase II process and considering the first category increments of 2%, 4% and 6% in the control stage. Results: The multinomial control chart using Wilson-Hilferty approximation for variables chi square, from the transformation of value-p, has poor performance compared to the control charts using p-value processing and using chi-square p-value, as they have less ability to detect small changes. Conclusion: We propose two control charts to monitor multinomial variables and once studied via simulation, based on the average run length (ARL) and the probability of rejecting the null hypothesis of equal proportions, we recommend the control chart using value-p, or equivalently, the control chart processing using chi square p-value.
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