ENBIS-21 Online Conference

Constructing nonparametric control charts for correlated and independent data using resampling techniques

14 Sept 2021, 17:05

20m

Room 5

Quality Quality 3

Speaker

Ms Priscila Guayasamín (Dep. de Matemática, Escuela Politécnica Nacional)

Description

Non-parametric control charts based on data depth and resampling techniques are designed to monitor multivariate independent and dependent data.

Phase I

Dependent and independent case

1. The depths $ D_F (X_i) $ ordered in ascending order are obtained.
2. The lower control limit $ (LCI) $ is calculated as the quantile at the $ \alpha $ level of the observations under null hypothesis such that the percentage of false alarms are approximately equal to $ \alpha $.
3. If $ D (X_i) \leq LCI $ then the process is out of control.

For the estimation of the quantile, smoothing bootstrap, stationary bootstrap have been applied for independent and dependent case.

Phase II

1. From the reference sample $ \{X_1, ..., X_n \} $ the depth of the data $ D(X_i) $ is calculated with $ i = 1, ..., n $ and based on this the depths of the monitoring sample $ D(Y_j) $ are obtained with $ j = n + 1, ..., m $ based on the calibration sample
2. Monitor the process, if you have observations $ D (Y_j) \leq LCL $ then the process is out of control.
3. Calculate the percentage of rejection as the average of observations under the lower control limit.

The simplicial depth in general has a better performance for all sample sizes. It is noted that as the sample size increases, the Tukey and Simplicial measures yield better results.