A partitioned weighted moving average control chart.

Abstract

A partitioned weighted moving average (PWMA) chart is developed by partitioning the samples (or observations) into two groups, calculating the groups' weighted average and adding them. This partitioning gives more control over weight distribution in the most recent j (= 2, 3, …) samples. The PWMA, exponentially weighted moving average (EWMA) and homogenously weighted moving average (HWMA) charts are compared. For zero state, the PWMA chart outperforms the EWMA and HWMA charts for most (n, λ, δ) values and the outperformance of the former over the two latter charts increases with the time period (j), employed in the partitioning. Here, λ is the charts' smoothing constant and δ is the shift size (multiples of standard deviation). For steady state, the PWMA chart (regardless of j) generally outperforms the EWMA chart in detecting a small shift (δ = 0.25) when the smoothing constant λ ≥ 0.2 for the sample size n = 1; while a larger λ is needed for n = 5. Moreover, for steady state, the PWMA chart outperforms the HWMA chart in detecting small and moderate shifts (0.25 ≤ δ ≤ 1), regardless of (λ, n, j). The PWMA chart demonstrates robustness to non-normality and estimated process parameters.