The Use of Simulation to Compare Parametric and Nonparametric Multivariate CUSUM Charts under Different Statistical Distributions.
DOI:
https://doi.org/10.31272/jae.i151.1480Keywords:
Multivariate Multi-Chart Cumulative Sum (MCUSUM) Chart, Kernel Estimator, Average Run Length (ARL) CriterionAbstract
Statistical quality control is one of the important statistical tools used for monitoring and analyzing the quality of production and service processes. Its main objective is to provide early detection of any deviations that may occur in the process under study. In this research, a simulation approach was employed to study the performance of the parametric multivariate cumulative sum (MCUSUM) control charts (MC1, MC2) and the nonparametric charts based on the kernel estimator, under three different distributions: the multivariate normal, gamma, and chi-square distributions.
The efficiency of both charts was evaluated using the proposed Composite Average Run Length (CARL) criterion under various mean shifts. The results showed that the nonparametric chart using the kernel estimator was more capable of detecting small and moderate shifts, while the parametric chart was slower in detecting deviations and process changes.
Furthermore, the comparison among the three kernel functions (Gaussian, Laplace, and Epanechnikov) indicated that the Gaussian kernel achieved the highest efficiency in detecting small shifts, followed by the Epanechnikov kernel, whereas the Laplace kernel was the least efficient in this regard. These findings demonstrate that the choice of statistical distribution and kernel function significantly affects the performance of the chart, emphasizing the importance of employing nonparametric methods when the data do not follow a normal distribution, when the true distribution form is unknown, or when they follow other types of distributions.
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