Which control chart pair is commonly used to monitor stability when subgroups have more than one observation?

Which control chart pair is commonly used to monitor stability when subgroups have more than one observation?

• A. P chart and NP chart
• B. I-MR chart
• C. X-bar and R chart
• D. S chart

Answer: (C)

When you have subgroups with more than one observation, you want to track both where the process is centered and how much its values vary within each subgroup. The standard pairing uses a chart for the subgroup means (the X-bar chart) to monitor the center, and a chart for the subgroup ranges (the R chart) to monitor dispersion. The X-bar chart shows if the process average is drifting, while the R chart detects changes in variability inside each subgroup. Together they give a clear picture of stability: if both charts stay in control, the process is stable; if either shows signals, you know there’s a shift in either mean or spread. Other options are suited to different data scenarios. Proportion charts (P and NP) are for attribute data, not measurements. The I-MR chart is used when you’re dealing with individual observations without subgroups. A dispersion chart using standard deviation (S chart) is another valid choice, but it’s typically preferred when subgroups are larger and you want a more precise measure of variability; for most small-to-moderate subgroup sizes, X-bar and R is the standard, robust pairing.

When you have subgroups with more than one observation, you want to track both where the process is centered and how much its values vary within each subgroup. The standard pairing uses a chart for the subgroup means (the X-bar chart) to monitor the center, and a chart for the subgroup ranges (the R chart) to monitor dispersion. The X-bar chart shows if the process average is drifting, while the R chart detects changes in variability inside each subgroup. Together they give a clear picture of stability: if both charts stay in control, the process is stable; if either shows signals, you know there’s a shift in either mean or spread.

Other options are suited to different data scenarios. Proportion charts (P and NP) are for attribute data, not measurements. The I-MR chart is used when you’re dealing with individual observations without subgroups. A dispersion chart using standard deviation (S chart) is another valid choice, but it’s typically preferred when subgroups are larger and you want a more precise measure of variability; for most small-to-moderate subgroup sizes, X-bar and R is the standard, robust pairing.