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MSc in PHARM QA
(2015-16)
(Please note that while the use of computer software is encouraged for performing calculations, a ‘bare’ computer printout of results will
not be deemed acceptable for the purposes of your assignment submission. The rationale for choosing a particular statistical test should be
given and the results of the test fully discussed.)
1. (a) Quality control records show that the average tablet weight to be 501 mg with a standard deviation of 5.3. There are sufficient
data so that these values may be considered known parameters (population mean and std. dev.). A new batch shows the following weights from a
random sample of six tablets: 500, 499, 493, 497, 504 and 495 mg . Do you believe that the new batch has a different mean from the process
average?
(b)Two batches of tablets were prepared by two different processes. The potency determinations made on six tablets from each batch were as
follows: batch A: 5.1, 4.9, 4.6, 5.3, 5.5, 4.7; batch B: 4.8, 4.8, 5.2, 5.0, 4.5,4.4
Test to see if the means of the two batches are equal.
(c)What is the answer to part (a) if the variance was unknown. Place a (i) 95% and (ii) 99% confidence interval on the true average weight.
[25 marks]
2. The following analytical data were obtained for a spectrophotometric analysis:
Conc.(mg dm3) Absorbance
10 0.105, 0.090
20 0.201, 0.188
50 0.495, 0.513
100 0.983, 1.120
200 1.964, 2.013
(i) compute r and r2, and explain what their values indicate,
(ii) find the regression equation of absorbance on concentration,
(iii) predict the concentration , if the absorbance was 0.730.
(iv) plot the residuals from the regression analysis against the concentration. What does the resulting pattern indicate?
[25 marks]
3. The number of days since the appearance of a tumour in an animal, and the size of the tumour, are shown below:
Days 14 16 19 21 23 26 28 30 33
Size(cm3) 1.25 1.90 4.75 5.45 7.53 14.5 16.7 21.0 27.1
Construct the best regression that you can find, and use the model to estimate the size of the tumour after 24 days.
[25 marks]
4.
(a) Test the hypothesis that the average dissolution time is 20 seconds, using the random sample of dissolution times below.
Dissolution time (secs): 23 19 26 22 18 27
(b) Two different instruments were used to make a number of replicate measurements. The results were:
Instrument A: 12.06 12.14 12.03 12.09 12.05
Instrument B: 14.62 14.97 14.60 14.51 14.01 14.11
Do these results indicate that either instrument is more precise?
[25 marks]
5. A batch of finished products comprised of 150,000 units.
AQLs are agreed and set at 0.40 % for major defects and 1.5 % for minor defects by the customer.
There have been no prior quality issues noted with the production.
Indicate an appropriate sampling plan outlining the following:
a. The sampling level.
b. The sample size code letter.
c. The number of samples to be taken for a double sampling regime.
d. The allowable accept and reject numbers of defects for each of the AQLs.
[20 marks]
6. A team in one operating unit is interested in improving the yield from a given batch reaction. The team decides to use a control
chart to determine if the process is in statistical control. The team also decides that the control chart will be used in the future to
help monitor the process over time. Once any assignable causes are eliminated, the control chart can be used to monitor attempts at process
improvement. Five batches of product are made each day. This provides frequent data plus a method of rationally subgrouping the data.
The team decides to use a subgroup size of n = 5. Data from the past 25 days are available. The team decides to use this historical data
for the control charts. The data for percent yield from the last 25 days are given below.
Subgroup
(Day) Sample % Reaction Yield Results (n = 5)
Number 1 2 3 4 5
1 81.3 80.4 78.6 83.1 81.8
2 74.3 76.4 82.4 77.8 82.5
3 78.7 77.4 79.4 81.6 81.0
4 80.4 81.7 81.4 79.7 80.2
5 79.4 75.6 80.3 80.2 77.4
6 85.0 75.4 73.8 75.8 78.6
7 78.5 86.2 77.1 73.3 76.4
8 81.7 84.0 80.2 78.6 80.9
9 84.5 82.4 78.8 83.2 83.0
10 82.7 80.5 85.9 82.7 84.0
11 78.4 83.1 80.1 78.5 86.6
12 82.9 82.4 78.9 78.2 78.4
13 75.6 80.1 81.1 78.3 80.4
14 78.2 76.4 82.3 81.7 85.1
15 81.8 80.6 79.1 79.3 83.6
16 75.2 82.2 79.6 83.6 81.9
17 78.6 80.1 80.6 79.3 80.4
18 82.3 80.8 79.7 76.5 85.6
19 83.0 83.6 75.2 83.3 81.3
20 77.6 79.1 78.7 80.8 80.2
21 75.0 81.0 82.9 80.0 81.9
22 82.7 78.8 81.2 74.8 81.7
23 76.9 82.5 82.5 81.4 84.4
24 78.1 82.9 73.7 81.5 75.9
25 79.9 78.7 81.3 80.0 78.5
(Please note that the above data can be copied and pasted directly into a Minitab Worksheet – there is no need to manually input the data).
Use these data to construct the Xbar-R chart for reaction yield. Give the value for the process mean, μ, and the values for the LCL and UCL.
Is the process in control? Comment.
[20 marks]
7. A pharmaceutical company produces tablets that have a specified target tablet weight of 62.5 mg and tolerance limits of +/- 2.0
percent of specified target weight. Every 15 minutes, 5 tablets are selected for testing. The table below presents the weights of tablets
obtained for 29 subgroups of n = 5.
Sample Weight1 Weight2 Weight3 Weight4 Weight5
1 62.9 63 62.8 62.6 62.7
2 62.6 62.5 62.4 63 62.9
3 62.8 62.9 62.4 62.4 62.4
4 62.5 62.4 62.2 62.6 62.4
5 62.6 62.6 62.6 62.9 61.7
6 62.1 62.5 62.6 62.4 62.5
7 62.7 62.6 62.5 62.4 62.1
8 62.7 62.4 62.7 62.6 62.5
9 62.4 63.1 62.6 62.7 62.6
10 62.8 62.7 62.8 62.8 63.1
11 63.1 62.6 62.7 62.4 62.4
12 62.7 61.9 62.3 62.6 62.5
13 62.7 62.7 62.6 62.8 63.1
14 62.8 62.9 62.8 62.8 62.9
15 62.6 62.7 62.1 62.8 61.8
16 62.2 62.7 62.5 62.9 62.3
17 62.7 62.7 62.4 62.2 62.6
18 62.7 62.6 62.9 62.3 62.5
19 62.5 62.4 62.7 62.3 62.3
20 62.3 62.5 62.4 62.8 62.5
21 62.6 62.7 62.6 62.9 62.7
22 63.1 62.7 62.9 62.6 62.5
23 63 62.9 62.4 62.1 62.8
24 62.7 62.9 62.2 62.3 62
25 62 62.3 62.3 62.8 62.7
26 62.8 62.5 62.7 62.9 62.8
27 62.8 62.7 62.9 62.7 62.9
28 62.7 63 62.7 62.7 62.8
29 62.7 63 62.2 62.2 62.6
(Please note that the above data can be copied and pasted directly into a Minitab Worksheet – there is no need to manually input the data).
Construct an Xbar-R chart for these data. By inspection of both charts determine if the process is in a state of statistical control.
Explain your reasoning.
If the process is stable, determine the values for Cp and Cpk and give a histogram showing the data spread (include the LSL and USL)
.
Is the process capable and centred? Explain your reasoning.
[40 marks]
8. The following readings have been taken from hourly in process measurements of the thickness of an extruded drug delivery device. The
product specification is that the average thickness must be 70um +/- 5 um. No individual reading can be outside of 70um +/- 15um.
Is the process in control? Is the output of the process in specification?
Explain your reasoning.
(Please note that the above graph is not a control chart. You are required to construct one from the data in the table)
[20 marks]
