Statistical Quality Control and Capability Process on Non-Normally Distributed Data

Generally, multivariate control charts are only capable of multivariate normal distributed data. In 2005, Chen and Thaga proposed the Max-MCUSUM control chart, which is able to monitor the mean vector and covariance matrix simultaneously. Based on the study conducted by Chen and Thaga, this diagram performs better compared to the MaxMEWMA control chart proposed by Xie which is also more sensitive to detect small shifts. The Max-MCUSUM control chart is implemented in the water quality case study at PDAM Surabaya by dividing the data into two phases. It is obtained that both phases have not been statistically controlled since a shift in the mean and variability process was found. The analysis of univariate process capability using the C_Np index in the water quality case study shows that residual chlorine fails to meet company's specifications due to a lack of precision. According to the level of accuracy based on the C_Npk index, residual chlorine and turbidity do not perform well enough. Meanwhile, multivariate measurement using the weighting average approach found that the process is not yet capable because the process performance does not have good enough overall accuracy in fulfilling company specifications.