Sigma (σ) is the standard deviation, a single number that describes how widely measurements scatter around their average. For capability work you want the short-term sigma, the scatter you see inside small groups of parts made close together. Within a group of five consecutive shafts, the tool has barely worn and the coolant has barely changed, so the only scatter left is the machine's inherent noise.
Collect subgroups of consecutive parts, usually 3 to 5 pieces, at regular intervals. For each subgroup calculate the range (R), which is simply the largest value minus the smallest. Average all the ranges to get R-bar. Then divide R-bar by a constant called d2, which depends only on subgroup size: 1.693 for n = 3, 2.059 for n = 4, 2.326 for n = 5. The result is your estimate of short-term sigma.
Standard Procedure
- 1Decide a subgroup size (3 to 5 consecutive parts) and a sampling interval, such as every 30 minutes.
- 2Measure each subgroup and record the range (maximum minus minimum).
- 3Collect at least 20 subgroups, then average the ranges to get R-bar.
- 4Divide R-bar by the d2 constant for your subgroup size to get the short-term sigma.
Lesson Summary
- ✓Subgroups of consecutive parts isolate the machine's inherent noise from slow drifts like tool wear.
- ✓σ = R-bar / d2 is the standard short-term estimate; look up d2 by subgroup size.