The exponentially‐weighted control charts for geometrically moving averages

Abstract

AbstractThis article is a sequel to the previous entitled “A Further Note on the Exponentially‐Weighted Moving Average Control Charts for Monitoring Gradual Shifts in a Process Mean” where the constant sample size n was equal to 1 in each subgroup. We have now generalized the results of the previous article first to the case of constant sample size n > 1 in each subgroup, and then to varying sample sizes; although, the average run length for the most general case of varying sample sizes is a weighted approximation. In our Section 2, we are proposing an estimator of process standard deviation (STD) σX that is more accurate than all previously available in statistical literature only if the targeted average, μ0, is the required standard process mean.