Efficient control charting methodology based on Distance Weighted Mean for normal distribution

Abstract

This research suggests a Distance Weighted Mean (DWM) based control chart under normal distribution implementing Simple Random Sampling (SRS). The control limits are calculated using the quantile point method. The control chart's performance is assessed using the Average Run Length (ARL) statistic. The numerical findings are illustrated using samples of sizes 3 and 5. The ARL1 values are determined using Monte Carlo Simulation for increasing and decreasing shifts in the location parameter ranging from 5% to 30%. Using the ARL1 measurement, the proposed DWM control charts are compared to the existing Shewhart control charts. According to the comparison analysis, the suggested DWM control chart surpasses the competing Shewhart control chart. The real-life application of the proposed DWM control chart is also shown by using the lifetime of the light bulb (in hours). The results suggest that the proposed DWM control chart can be a useful tool for monitoring process mean shifts, especially when the sample size is large, and the magnitude of the shift is significant.