Read spread before the subgroup average

Read spread before the subgroup average

A rational subgroup is intended to expose short-term variation while preserving meaningful changes between samples. For this example each subgroup contains five readings taken under comparable conditions. The range chart helps assess whether that within-subgroup spread is behaving consistently. Review it before interpreting the average chart, whose limits depend on that variation estimate. Constants must match the subgroup size and the chosen method. The displayed points illustrate reading the charts; they do not establish the historical baseline. Do not delete awkward samples merely to obtain attractive limits. Document investigations and use an authorized approach when the underlying process changes.

Follow the method

1. Read range first
2. Within-subgroup range (mm)
3. Sample in time order
4. Center: 0.5
5. LCL: 0
6. UCL: 1.0575
7. Then subgroup average
8. Subgroup mean (mm)
9. Center: 20
10. LCL: 19.7115
11. UCL: 20.2885

Read range, then mean, then record the response

Fictional case: a width process samples five consecutive units per subgroup. A prior reviewed baseline is supplied as grand mean 20.00 mm and average range 0.50 mm. The core charts show six illustrative subgroup means and ranges; those six points are not used to estimate the baseline. Technician Imani checks the calculations and prepares a response record.

Follow the method

1. Mean limits
2. Range limits
3. Six range points
4. Six mean points

A quiet average can hide an abnormal range

Apply supplied subgroup baseline constants, interpret spread before the mean, and record a signal response without confusing limits with specifications.

Fictional case: a width process samples five consecutive units per subgroup. A prior reviewed baseline is supplied as grand mean 20.00 mm and average range 0.50 mm. The core charts show six illustrative subgroup means and ranges; those six points are not used to estimate the baseline. Technician Imani checks the calculations and prepares a response record.

Role: SPC technician with the process owner

Normal condition

Subgroup size is five; measurement and subgroup rationale remain appropriate; historical limits are clearly identified and applied to later observations.

The gap

The draft report recomputes limits from the six demonstration points and reads the mean chart first. That changes the stated evidence and can hide a spread problem.

• Supplied baseline adequacy is an exercise assumption, not newly demonstrated by these six points.
• No product specifications or automatic release criteria are supplied.

1. Confirm the subgroup meaning

   Imani verifies that each point summarizes five consecutive units under the stated collection design and that units are millimetres. She keeps subgroup identity and raw readings available.

   Why: Five values collected across unrelated conditions are not automatically a useful subgroup. The collection design is part of the interpretation, not a chart-format preference.

   Evidence: n=5 and the source of each subgroup are explicit.

2. Calculate limits from the supplied baseline

   She uses 20 ± .577×.50 for mean limits 19.7115 and 20.2885 mm. Range limits are 0×.50=0 and 2.115×.50=1.0575 mm.

   Why: The constants correspond to subgroup size five. Replacing the historical averages with the six plotted examples would silently answer a different question.

   Evidence: Calculation record identifies the historical baseline and constants.

3. Review the range chart first

   She compares each displayed range with 0 and 1.0575 mm. The six supplied ranges show no point beyond these limits under the stated point rule.

   Why: The mean-chart interpretation depends on a suitable within-subgroup spread estimate. An abnormal spread should not be ignored because the means look quiet.

   Evidence: The record describes the observed range comparison without claiming a new baseline study.

4. Then examine subgroup means

   The six displayed means lie between 19.7115 and 20.2885 mm. Imani records the rule examined and avoids claiming that six points establish control or capability.

   Why: Absence of an observed signal is weaker than proof of future stability. A mean within control limits also says nothing by itself about individual product conformance.

   Evidence: No beyond-limit mean point in the illustrative sequence; product limits not supplied.

5. Plan the signal response

   She prepares a record for subgroup identity, raw values, measurement checks, relevant changes and authorized containment/investigation. Limits stay frozen unless a justified baseline review approves a change.

   Why: Widening a limit to absorb a signal would conceal the condition. Investigation must preserve the original signal and distinguish correction from learning about its cause.

   Evidence: The reaction record names the process and quality owners and the next verification.

Range signals while mean stays near center

A later fictional subgroup has mean 20.02 mm and range 1.20 mm.

Record the range signal because 1.20 exceeds 1.0575; preserve the subgroup data and follow the authorized response before treating the near-center mean as reassuring.

A normal-looking average can hide increased within-group spread. The mean does not cancel the range signal.

The signal record includes the 1.20 mm range and original historical limit.

Run a practice session

Materials

• Baseline card
• Calculator
• Blank signal record

1. Identify the source of limits · 5 minutes

   Which numbers are supplied rather than estimated here?

2. Calculate and read spread · 8 minutes

   What can a near-center average hide?

3. Complete the 30 mm case · 10 minutes

   Which point signals and under what rule?

4. Debrief response · 5 minutes

   What would be wrong with widening the limit?

Debrief

• Ask for units on every limit.
• Distinguish no observed point signal from demonstrated long-run control.

Work both charts on paper and write the reaction before revealing the answer.

Transfer into the work

Owner: SPC owner with station quality lead

Record: Baseline revision, subgroup record and signal investigation

Review: At each defined subgroup and after reviewed process changes

Evidence: Traceable data and verified response with unchanged justified limits

Investigate measurement/process conditions; revise the baseline only through the authorized evidence review.