Quality Assurance and Control Charts
Quality assurance uses control charts to check whether a production process stays consistent over time, plotting a sample statistic, usually the mean, against warning and action limits set around a target value. A point beyond the warning limits (2 standard deviations from the mean) suggests closer monitoring; beyond the action limits (3 standard deviations) means the process should stop for correction.
Before you start
Make sure you're comfortable with these topics first:
Method
- Take regular samples from the production process and record a statistic for each, usually the sample mean.
- Plot each sample statistic on a control chart against time or sample number.
- Draw a central line at the target (or process) mean, using data from when the process was working correctly.
- Draw warning limits at 2 standard deviations above and below the mean, and action limits at 3 standard deviations above and below the mean.
- If a point falls outside the warning limits, treat it as a signal to keep a closer eye on the process.
- If a point falls outside the action limits, or several consecutive points fall on the same side of the mean, stop the process and investigate the cause.
Worked example
A machine fills bottles with a target mean volume of 500 ml and a standard deviation of 4 ml. Find the warning limits and action limits for a control chart monitoring this process.
- Warning limits are set at mean plus or minus 2 standard deviations: 500 +/- (2 x 4) = 500 +/- 8.
- This gives warning limits of 492 ml and 508 ml.
- Action limits are set at mean plus or minus 3 standard deviations: 500 +/- (3 x 4) = 500 +/- 12.
- This gives action limits of 488 ml and 512 ml.
- Final answer: warning limits are 492 ml and 508 ml; action limits are 488 ml and 512 ml.
Practice questions
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Q1A process has a target mean of 100 g and a standard deviation of 3 g. Find the upper and lower warning limits (mean plus or minus 2 sd).Show answer
Answer: 94 g and 106 g.
Q2Using the same process (mean 100 g, sd 3 g), find the upper and lower action limits (mean plus or minus 3 sd).Show answer
Answer: 91 g and 109 g.
Q3A sample mean is plotted just outside the warning limit on a control chart, but inside the action limits. What should the operator do?Show answer
Answer: Keep a closer watch on the process (take another sample soon) but not stop the process yet.
Q4A sample mean falls outside the action limits on a control chart. What should happen to the process?Show answer
Answer: The process should be stopped and investigated or corrected.
Q5A control chart has a central line at 250 ml and action limits at 238 ml and 262 ml. Find the standard deviation used to set these limits.Show answer
Answer: 4 ml (since 3 sd = 12, sd = 12/3 = 4).
Q6Explain why several consecutive sample means falling on the same side of the central line, even within the limits, can be a warning sign.Show answer
Answer: It suggests the process mean may have shifted, or there is a systematic trend, rather than just random variation.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A crisp packing machine has a target mean weight of 150 g with a standard deviation of 2 g. Find the warning limits and the action limits for a control chart.
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A control chart has warning limits of 96 and 104, with a central line of 100. State the value of the standard deviation used.
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A soft drink company fills bottles with a target volume of 330 ml and a process standard deviation of 2.5 ml. (a) Find the action limits for a control chart. (b) A sample mean of 337 ml is recorded. State, with a reason, what action the company should take.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the quality assurance and control charts worksheet pack - 17 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 3 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
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