Quality Assurance and Control Charts - Worksheets, Questions and Revision

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H08 Quality Assurance and Control Charts

EDEXCEL 1ST0 · Calculator allowed · about 80 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Quality assurance is the process a factory uses to check that the items it makes meet the required standard throughout production, not just at the end.
(a)State what is plotted on the vertical axis of a control chart used to monitor a manufacturing process.(1)
(b)Give two reasons why a factory monitors sample means using a control chart throughout production, rather than only checking the finished items at the very end.(2)
(Total for Question 1 is 3 marks)
2
A quality inspector explains some of the vocabulary used with control charts.
(a)State what the central (mean) line on a control chart represents.(1)
(b)State what is plotted on the horizontal axis of a control chart.(1)
(Total for Question 2 is 2 marks)
3
For each statement about warning limits and action limits on a control chart, write down whether it is True or False.
(i)A point that lies beyond an action limit means the process should be stopped and investigated immediately.(1)
(ii)A point that lies beyond a warning limit but within the action limits always means the machine must be shut down immediately.(1)
(iii)Warning limits are always closer to the mean than action limits.(1)
(Total for Question 3 is 3 marks)
4
A factory machine cuts steel bolts to a target shaft diameter of 25 mm. When the machine is working correctly, the population standard deviation of the diameters it produces is 0.8 mm. Workers take samples of 16 bolts at regular intervals and plot the mean diameter of each sample on a control chart.
(a)Work out the standard error of the sample mean.(2)
(b)Work out the warning limits for this control chart.(2)
(c)Work out the action limits for this control chart.(2)
(Total for Question 4 is 6 marks)
5
A drinks company fills plastic bottles with milk to a target mean volume of 1000 ml. Samples are taken regularly, and the standard error of the sample mean has been calculated as 5 ml.
(a)Work out the warning limits for the control chart.(2)
(b)Work out the action limits for the control chart.(2)
(Total for Question 5 is 4 marks)
6
A factory fills bottles of fizzy drink to a target mean volume of 330 ml. The control chart shows the mean volume, in ml, of each of 6 samples taken during one shift. The warning limits are 326 ml and 334 ml; the action limits are 324 ml and 336 ml.
320322324326328330332334336338340 MeanWarnWarnActionAction 123456 Sample number Sample mean volume (ml)
(a)Write down the mean volume of sample 3.(1)
(b)Write down whether the mean volume of sample 4 lies within the warning limits.(1)
(c)Write down the number of the sample whose mean volume lies beyond an action limit.(1)
(d)State the action the factory should take as a result of the point identified in part (c).(1)
(Total for Question 6 is 4 marks)
7
A machine fills bags of sugar. The target mean weight is 500 g, and the standard error of the sample mean has been calculated as 3 g. Samples of 4 bags are weighed every hour. The control chart shows the mean weight, in grams, of each of the first 12 samples taken.
488491494497500503506509512 MeanWarnWarnActionAction 123456789101112 Sample number Sample mean weight (g)
(a)Work out the warning limits for this control chart.(1)
(b)Work out the action limits for this control chart.(1)
(c)Write down the mean weight of sample 5.(1)
(d)Write down the number of the sample whose mean weight lies beyond an action limit.(1)
(e)State the action that should be taken as a result of the point identified in part (d).(2)
(f)The mean weight of sample 8 is 507 g, which lies beyond the warning limit but not beyond the action limit. Explain how the action taken for sample 8 should differ from the action taken for sample 12.(3)
(Total for Question 7 is 9 marks)
8
A chocolate factory wraps bars with a target mean weight of 250 g. On the control chart provided, the mean (target) line, the warning limits (246 g and 254 g) and the action limits (244 g and 256 g) have already been drawn. Five samples of 4 bars were weighed. The individual weights, in grams, are shown in the table.
SampleBar weights (g)
1248, 251, 249, 252
2253, 250, 254, 251
3247, 249, 246, 250
4256, 254, 255, 255
5260, 257, 258, 257
242244246248250252254256258260 MeanWarnWarnActionAction 12345 Sample number Sample mean weight (g)
(a)Work out the mean weight of each of the 5 samples.(2)
(b)Plot the five sample means on the control chart.(2)
(Total for Question 8 is 4 marks)
9
A crisp factory fills bags with a target mean weight of 150 g. The warning limits are 146 g and 154 g; the action limits are 144 g and 156 g. The control chart shows the mean weight, in grams, of each of 10 samples.
142144146148150152154156158 MeanWarnWarnActionAction 12345678910 Sample number Sample mean weight (g)
(a)Write down the number of samples on the chart whose mean weight lies beyond a warning limit.(1)
(b)Despite this, a quality controller says the chart shows a warning sign that the process may need investigating. Identify the run of consecutive points that supports this, and state whether they lie above or below the mean.(2)
(c)Explain why a long run of points on the same side of the mean can be a warning sign, even though no individual point has breached a limit.(2)
(Total for Question 9 is 5 marks)
10
A soup factory uses two separate quality-control methods.

Method 1: During production, a control chart plots the mean weight of samples of 5 tins, taken every 30 minutes.

Method 2: After a batch of 2000 tins has been produced, a random sample of 40 tins is tested against a tolerance (specification) limit of 400 g ± 8 g. If more than 2 tins in the sample fall outside this tolerance, the whole batch is rejected.
(a)State the name usually given to the second quality-control method described above (Method 2).(1)
(b)Give two ways in which acceptance sampling of the finished batch (Method 2) is different from monitoring the process with a control chart (Method 1).(2)
(c)In a sample of 40 tins tested from one batch, 3 tins are found to weigh outside the tolerance limits of 400 g ± 8 g. Using the factory's rule, state with a reason whether this batch should be accepted or rejected.(2)
(Total for Question 10 is 5 marks)
11
A paint factory investigates whether its tin-filling machine is working correctly, using the statistical enquiry cycle. The machine has a target mean fill volume of 5000 ml, with a process standard deviation of 40 ml. Every 30 minutes, a sample of 4 tins is measured.
(a)Plan: Give one reason why the factory samples tins every 30 minutes throughout the day, rather than testing tins only once at the start of the day.(1)
(b)Collect: Give one reason why the tins in each sample should be selected using a consistent method every time (for example, always testing the tins filled immediately after the sampling time).(1)
(c)Process: Work out the standard error of the sample mean.(1)
(d)Process: Work out the warning limits.(1)
(e)Process: Work out the action limits.(1)
(f)Interpret: One sample has a mean fill volume of 4935 ml. Interpret what this shows, and state the action that should be taken.(2)
(Total for Question 11 is 7 marks)
12
A trainee quality inspector at a cereal factory is setting up a control chart. The machine has a target mean box weight of 750 g and a process standard deviation of 12 g. Samples of 9 boxes are weighed at a time. Here is the trainee's working:

Standard error = 12 (used the standard deviation directly, without dividing by the square root of the sample size)
Warning limits = 750 ± 2 x 12 = 726 g and 774 g
Action limits = 750 ± 3 x 12 = 714 g and 786 g
(a)Identify the mistake in the trainee's working.(1)
(b)Work out the correct standard error, and the correct warning and action limits.(3)
(Total for Question 12 is 4 marks)
13
Two identical machines, A and B, fill jars of honey with a target mean weight of 340 g. Both machines have the same process standard deviation of 8 g. Machine A is monitored using samples of 4 jars; Machine B is monitored using samples of 16 jars.
(a)Work out the standard error of the sample mean used for each machine's control chart.(2)
(b)Hence work out the warning limits used on each machine's control chart.(2)
(c)Explain why Machine B's control chart is able to detect a smaller shift in the process mean than Machine A's chart.(2)
(Total for Question 13 is 6 marks)
14
A factory tests the lifetime, in hours, of a sample of light bulbs taken from its production line each day. The process has a target mean lifetime of 1200 hours, with a process standard deviation of 30 hours. Samples of 9 bulbs are tested each day.

On one day, the 9 bulbs tested had these lifetimes, in hours:

1185, 1190, 1200, 1195, 1215, 1180, 1205, 1210, 1175
(a)Work out the mean lifetime of this sample of 9 bulbs.(2)
(b)Work out the standard error of the sample mean.(2)
(c)Work out the warning limits and the action limits for this control chart.(2)
(d)State, with a reason, whether the sample mean from part (a) would trigger any action on the control chart.(2)
(e)The factory's contract states that a day's batch of bulbs can only be shipped if no more than 1% of a random acceptance sample of 200 bulbs from that batch has a lifetime below 1150 hours. In a sample of 200 bulbs taken from this day's batch, 3 bulbs had a lifetime below 1150 hours. Determine, with justification, whether this day's batch should be shipped, and give one reason why passing this acceptance sample does not guarantee that every individual bulb in the batch lasts at least 1150 hours.(3)
(Total for Question 14 is 11 marks)
15
A control chart for a paint-can filling process has a target mean fill volume of 2000 ml. The process standard deviation is 24 ml. The action limits on the chart are set at 1976 ml and 2024 ml.
(a)Use the action limits and the target mean to work out the standard error of the sample mean used for this chart.(2)
(b)Given that the process standard deviation is 24 ml, work out the sample size used for each sample on this chart.(2)
(c)The factory wants to narrow the gap between the warning and action limits without changing the process itself. State whether the factory should increase or decrease the sample size, and explain why.(2)
(Total for Question 15 is 6 marks)
Mark scheme · H08 Quality Assurance and Control Charts

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15