Triple Homogeneously Weighted Moving Average Charts for Monitoring Process Dispersion

Abstract

Homogeneously weighted moving average ( $\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}$ ) charts have recently achieved popularity for monitoring small changes in process parameters (location and/or dispersion). Furthermore, the $\mathrm{D}\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}$ (double $\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}$ ) and $\mathrm{T}\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}$ (triple $\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}$ ) are the advanced versions of the $\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}$ charts. The $\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}$ chart for the process dispersion is designed to detect only the upward (one-sided) shift (i.e., process deterioration). Employing a two-sided chart for concurrently detecting both process improvement and process deterioration is an important aspect of statistical process monitoring. By taking this point as motivation, one and two-sided $\mathrm{T}\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}$ charts (symbolized as the $\mathrm{T}\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ ) are proposed for monitoring the process dispersion. The Monte Carlo simulations are performed to investigate the performance behavior of the $\mathrm{T}\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ charts in terms of certain performance indicators, including $\mathrm{A}\mathrm{R}\mathrm{L}$ , $\mathrm{S}\mathrm{D}\mathrm{R}\mathrm{L}$ , $\mathrm{E}\mathrm{Q}\mathrm{L}$ , $\mathrm{R}\mathrm{A}\mathrm{R}\mathrm{L}$ , and $\mathrm{P}\mathrm{C}\mathrm{I}$ . The comparison among the $\mathrm{T}\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ versus existing charts ( $\mathrm{D}\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ , $\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ , $\mathrm{T}\mathrm{E}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ , $\mathrm{D}\mathrm{E}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ , and $\mathrm{E}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ ) indicates that the $\mathrm{T}\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ charts outperform the existing charts. Finally, a dataset is also analyzed to illustrate the implementation of the $\mathrm{T}\mathrm{H}\mathrm{W}\mathrm{M}\mathrm{A}\mathrm{V}$ charts.