A New Nonparametric Tukey MA-EWMA Control Charts for Detecting Mean Shifts

Abstract

Control charts are a type of statistical tool used to control a production process in order to obtain the quality products that can fulfill the demands of both the manufacturer and the consumers. In this paper, we propose the Tukey Moving Average-Exponentially Weighted Moving Average control chart (MME-TCC) to detect the change of average of the process with symmetric and asymmetric distribution and to compare the efficiency in detecting the change of the MME-TCC to the MA, MME, MEM, MA-TCC and MEM-TCC at the various change levels of the parameter. The criteria to measure the efficiency were average run length (ARL), standard deviation of run length (SDRL), and median run length (MRL) which evaluated by using Monte Carlo simulation (MC), The research results showed that the proposed control chart has the highest efficiency in detecting the change when the change level was at -0.75 ≤ δ ≤ 0.75. However, if the change of parameter increased (δ ≥ 1.00), the MME had more efficiency. In the case where the observation was logistic distributions, the MA-TCC had more efficiency to detect the change. Moreover, from applying the proposed control chart to two sets of real data, the mine explosion period in the UK during 1875-1951 and data of diameter of the workpiece from an industrial factory, it was found that the MME-TCC was able to more quickly detect the change than the other control charts.

Keywords

• Mixed control chart
• Tukey moving average-exponentially weighted moving average control chart (MME-TCC)
• average run length (ARL)
• Monte Carlo simulation (MC)