Explicit Formulas of Average Run Length for Triple Moving Average Control Chart to Monitor Changes in Mean Parameter of Normal and Non-normal Process

In this research, a formula is presented for calculating the average run length of a triple moving average (TMA) control chart, which is used to measure control chart performance and determine control chart width. To apply appropriately to data in various processes, a TMA control chart is used to detect small changes in a process by finding the average value of the data over a specified period of time (w). However, determining measure control chart performance and control chart width is difficult because the formula for calculation is not created. The performance of the control charts is measured using the standard normal distribution probability properties and compared with the moving average (MA) control charts and the double moving average (DMA) control charts. The analysis results show that TMA is very effective at detecting small changes, when w is set to have a small value. The study determines that the data within the process are normally and non-normally distributed. Detecting changes on real data by TMA charts has the best detection performance compared to MA and DMA.