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Field Book · Chapter 4 of 8 · The X-bar and R chart

Read the Chart

Plot the data in production order, set control limits from a stable stretch, and read the signals: a point beyond the limit and a run of eight. A worked X-bar and R example.

By Chris Martin, quality manager. 2 minute read. Free, no signup.

Set control limits from a stretch you trust, not from the print, then read the chart in production order. A mean beyond a control limit, or eight in a row on one side of the center line, is a signal. Here the run starts at 9:40 and the first point beyond the limit comes at 11:00, while every part is still in tolerance. The range chart shows the spread did not change, so the whole process moved.

The lathe has been charted all shift: five consecutive pieces every 20 minutes, 19 subgroups from 6:00 to noon. Now plot them in production order and ask two questions. When did it change, and is it a real signal or normal variation?

Set the limits from a stretch you trust

Control limits come from the process itself, not from the print. Take a stretch you believe was stable. Here that is subgroups 1 to 11, from 6:00 to 9:20, which is 55 pieces.

  • Average of the 11 subgroup means: 24.0040.
  • Average of the 11 subgroup ranges: 0.00764.
  • For subgroups of five, A2 is 0.577 and D4 is 2.114.
  • Upper control limit: 24.0040 plus 0.577 times 0.00764, which is 24.0084. Lower control limit: 23.9996.
  • Upper limit on the range chart: 2.114 times 0.00764, which is 0.0162.

Read it in order

Subgroup means 12 to 19, from 9:40 to noon, in order: 24.0042, 24.0046, 24.0080, 24.0070, 24.0094, 24.0108, 24.0124, 24.0124.

Two things stand out. Subgroup 16, at 11:00, is the first mean above the upper limit of 24.0084. And subgroups 12 to 19 are all above the center line, a run of eight, which completes at noon. Either one is a signal. Normal variation scatters points on both sides of the center line inside the limits. It does not climb for two hours.

When did it change? The run starts at subgroup 12, 9:40. Write that time down. Chapter 6 needs it.

The range chart tells you the other half. The largest range all shift is 0.012, well under the limit of 0.0162. The spread inside each subgroup did not change. The whole group of pieces moved up together.

Read more: SPC control charts for beginners.

The mistake to avoid

Reading the chart against the print tolerance. The limits on the chart are the process's own voice, and the tolerance is the customer's. This chart was signaling at 11:00, while every part was still far inside tolerance.

ON THE FLOOR MONDAY
  • Pull one live control chart and check the limit lines are drawn on it.
  • Check the limits came from a stable stretch, not from the print.
  • Count the last eight points. Are they all on one side of the center line?

Open the printable Monday Board

Want every tool on this trail in one purchase? The Process Trail Bundle has all 13.

The part, the machine, the shift and every number in this book (shaft SH-3306 on Lathe 3) are a made-up example. The tool sidebars show ShopFloorOps tools, which I make and sell. Every chapter teaches the step itself, so you can use your own forms. New to a term? See the quality glossary.