How do control charts with warning and action lines monitor a process?
Sample means are less spread than individual values; control charts for sample mean, median or range; warning lines at two standard deviations and action lines at three; the action to take when a value falls outside a limit.
A focused answer to Edexcel GCSE Statistics (Higher tier) on quality assurance, covering why sample means are less spread than individual values, control charts for the sample mean, median or range, warning lines at two standard deviations and action lines at three, and the action to take when a value falls outside a limit.
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What this dot point is asking
Edexcel Higher tier codes 2g.01 and 2g.02 require you to know that a set of sample means is less spread than the individual values from the same population, and to use warning and action lines on a control chart for the sample mean, median or range. You must know that warning lines are at standard deviations and action lines at standard deviations of the sample mean from the expected value, and the action to take when a value falls outside each limit.
Why sample means vary less
For example, the mean heights of school classes vary far less than the heights of individual students, because each class mean smooths out the tall and short pupils. This is the foundation of quality control: monitoring sample means gives a stable, sensitive signal of whether a process is drifting.
Control charts
In a manufacturing setting, samples are taken at intervals and the chosen statistic is plotted. As long as the points stay within the lines, the process is judged to be in control. The chart for the range monitors the spread (consistency), while the chart for the mean or median monitors the central value.
Warning and action lines
Because of the Normal pattern of sample means, about of means fall within the warning lines, so only about in fall outside them by chance, and almost all (about ) fall within the action lines. A point outside a line is therefore a meaningful signal, not just routine variation.
The action to take
The lines define a clear response:
- Inside the warning lines: the process is in control; carry on.
- Between a warning line and an action line: this is unusual (about in ), so take another sample to check whether the process is drifting; do not stop yet.
- Outside an action line: the process is out of control, so stop and adjust (or investigate) the process before continuing.
Knowing exactly which action matches which region is the most heavily tested point in this topic.
Exam-style practice questions
Practice questions written in the style of Pearson Edexcel exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Edexcel 1ST0 20214 marksA machine fills bottles to a target mean of ml. On a control chart for the sample mean, the warning lines are at ml and ml and the action lines at ml and ml. A sample mean of ml is plotted. (a) State which lines this value falls between. (b) State what action, if any, should be taken.Show worked answer →
(a) ml lies between the upper warning line ( ml) and the upper action line ( ml).
(b) Because it is beyond the warning line but inside the action line, the action is to take another sample (and continue to monitor) to check whether the process is drifting; the machine is not stopped yet.
Markers reward identifying it as between the warning and action lines, and the action of taking a further sample rather than stopping the machine.
Edexcel 1ST0 20224 marksOn a control chart, warning lines are set at standard deviations and action lines at standard deviations of the sample mean from the target. (a) Explain why a set of sample means varies less than the individual items. (b) State what should happen if a sample mean falls outside an action line.Show worked answer →
(a) A sample mean averages several items, so unusually high and low individual values partly cancel out. This makes the set of sample means more closely clustered (less spread) than the individual values from the same population.
(b) If a sample mean falls outside an action line, the process is judged to be out of control: the machine should be stopped and adjusted (or investigated) before production continues.
Markers reward the idea that averaging reduces variation, and the action of stopping or adjusting the process when outside an action line.
Related dot points
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Sources & how we know this
- Pearson Edexcel GCSE (9-1) Statistics (1ST0) specification — Pearson Edexcel (2017)