A Six Sigma tool that helps to screen factors by using graphical techniques to logically subgroup multiple discrete X's plotted against a continuous Y is known as a _____________Chart.

A Multi-Vari chart is a graphical Six Sigma tool used to identify the sources of variation in a process. It plots a continuous output variable (Y) against multiple discrete input variables (X's), which are logically subgrouped to represent different potential sources of variation (e.g., positional, cyclical, temporal). By visualizing the data in this structured way, the chart helps to screen various factors and pinpoint which ones contribute most significantly to the overall process variation, making it a key tool in the Analyze phase of DMAIC.

A. SIPOC: This is a high-level process mapping tool (Suppliers, Inputs, Process, Outputs, Customers) used in the Define phase; it does not graphically analyze variables.
C. Box Plot: A Box Plot summarizes the distribution of a continuous variable and is useful for comparing groups, but the Multi-Vari chart is specifically designed for analyzing nested sources of variation.
D. Whisker: This is a component of a Box Plot (representing the data range outside the central box), not an independent type of chart.

1. Montgomery, D. C. (2020). Introduction to Statistical Quality Control (9th ed.). Wiley. In Chapter 5, Section 5-3.3, "The Multi-Vari Chart," it is described as a graphical technique for assessing the different components of variability in a process by systematically sampling and plotting data from different sources (e.g., within-unit, between-unit, time-to-time).

2. Pyzdek, T., & Keller, P. A. (2018). The Six Sigma Handbook (5th ed.). McGraw-Hill Education. Chapter 21, "Exploring and Analyzing Data," explains that the "multi-vari chart is a very useful tool for graphically displaying... sources of variation" by plotting the response variable against different factors.

3. Breyfogle III, F. W. (2003). Implementing Six Sigma: Smarter Solutions Using Statistical Methods (2nd ed.). John Wiley & Sons. In Chapter 15, "Process Analysis and Discovery," the Multi-Vari chart is presented as a method to "graphically show the magnitude of variation that is associated with three or four variables" (p. 289), confirming its role in screening multiple discrete X's against a continuous Y.