Maths and Stats

Question 1

How are statistics used in the review of PQRs?

Question 2

What standard would you use to set a sampling plan for a delivery of bottles?

Question 3

What inspection level would you use?

Question 4

What statistics are important and how would you use them.?

Question 5

MDI cans come into site. Suggest a sampling plan/ inspection.

What would be your AQL categories, what levels would you set these at and give examples of defects in each category.

Cans have scratches and dents - what do you do?

Question 6

Sachet packaging line - problem with poor seals. What would you look at?

What would you use to statistically sample the sachets?

Define different defects definitions.

Give examples of defects.

What AQL would you use for defective seals on sachets?

Question 7

Explain pK studies – what they are for, how they are conducted, what is sampled?

Question 8

A key part of the PQR is a review of process control. Cp and Cpk are two tools that can be used for this. Can you explain what these are and how they help you describe a process as part of PQR?

Question 9

What statistical tests would you complete on assay transfer and explain how you would do it?

Answer 9

the use of statistics will build objectivity into the data analysis and allow unbiased comparison of the data sets.
The T-test and two one sided T test (TOST) are distinct approaches for assessing a difference or equivalence in data. Statistical and nonstatistical approaches to data evaluation may be acceptable however, decision whether to use statistics must be part of the test plan.

These tests would be performed by suitably trained analytical development scientists using a recignised computerised statistics package- e.g. minitab and subject to review as part of the assay transfer report review/approval.
How:
Key points: use same protocol/method, ensure adequate training of personnel (communication is key).
1. Perform the analysis as prescribed in the method.
2. Get the results (at least 5 to be statistically significant)
3. Compare the data obtained between the 2 labs - test for reproducibility of the method) using T-test.
T-test test for: ‘are the 2 sets of data, from different populations, equal?’ (Null hypothesis) - if the 2 populations are the same, there is no statistically significat difference between the groups.
4. Calculate the difference between the means (natural approach: large differences in the population means might suggest that they differ whilst small differences reflect equality) and divide the diference by its standard deviation - this yields a test-statistic whose distribution is known when the null hypothesis is true.
5. From this, we can compute the probability of obtaining as different as the observed data if the null hypothesis is true - procedure called Hypothesis testing, in effect to accept or reject the truth of the null hypothesis. The computed probability is called the p value of the test. We accept often p of 0.05 as the least acceptable value (significance level of the test). If p<0.05 we reject the null hypothesis (we cannot be confident that the samples come from populations with the same means) and if p>0.05 we accept it.
Note: follows a t-distribution (because we only have standard deviation of the sample and not the population) and the t-value can be taken from t-tables or from computer software

Question 10

In statistics, what is a
‘P value’?

Answer 10

Probability of an event occuring by chance.
Data sets with p values less <0.05 are statistically significant, and those with p values > 0.05 are not.

Question 11

What is a ‘T- Test’

Answer 11

The purpose of a t-test is to compare the means of a continuous variable in two research samples in order to determine whether or not the difference between the two observed means exceeds the difference that would be expected by chance from random samples.

Question 12

What statistical process control methods might you use for trending of micro EM data?

Answer 12

Moving average and range charts. Cussum graphs <show deviations from ‘normal’>

Question 13

What is the ‘Central Limit Theorum’?

Answer 13

Mean values follow a normal distribution as long as sample size is large enough

Question 14

What is SPC and what are example tools?

Answer 14

SPC= Statistical Process Control (collecting data, converting to meaningful information and using it to manage processes). It is used to assess Quality in an ongoing production process and it is concerned with the application of data processing in support of the quality of the product

Examples:
- Control Charts
- Fishbone diagrams
- Pareto Charts
- Process Capability

Question 15

What are control charts suitable for monitoring? Give some examples

Answer 15

Performance of continuous data (e.g. weight of tablets) and also attribute data (e.g. whether or not pack contains a chipped tablet).

Examples:
Variable data (X bar and range charts. X bar and moving range charts, Cusum charts)
Attribute data (P chart, NP chart, C chart, U chart)

Question 16

What are types of variation in a process?

Answer 16

1. Common cause (always inherent. Likely to create variation in future. Lots of them. Hard to remove/ reduce) e.g machine wear
2. Special cause (occassionally exists in process. Less likely to happen again. Relatively rare & easy to correct) e.g. breakdown

Question 17

What are some example rules for special cause removal in SPC data?

Answer 17

GE rules, Nelson rules
e.g. - points byond control limit, - unusual patterns - seven consecutive points on 1 side of mean or that rise and fall.

Question 18

What are measures of capability?

Answer 18

Cp = compares tolerance to the spread (USL-LSC)
Cpk= looks at drift from nominal (is it still in specification?)

Capable process: Cpk >1.5
Marginal Process: Cpk >1.0 but <1.5
Incapable Process: Cpk <1.0

<6 sigma process has Cpk= 2.0> <Stable ≠ Capable!>

Question 19

Describe ‘six sigma’

Answer 19

Problems solving process (DMAIC)- Define, Measure, Analyse, Improve, Control
used as a parameter and benchmark <99% right is not good enough! 6 sigma = 99.999%>

Question 20

Describe some statistical sampling plans

Answer 20

ISO 2859 (BS6001): Inspection by Attributes. (For batch to batch inspection- can’t be used for continuous & limited for micro)
Measures an attribute <ie.>. Classify: Critical/ Major/ Minor
Agree an 'Acceptable Quality Level' AQL: Acceptable level of defects for customer. (lowest AQL in ISO 2859 is .010 i.e. 1 in 10,000 defects. Still not good enough for some markets!)</ie.>

Single sampling plan
For a given AQL, use tables which specify the size of sample (n) and # defects (c) acceptable.

Double sampling plan
After 1st sample collected, if # defects is questionable (i.e. not small enough to accept, not large enough to reject) take a 2nd sample. Decision is based on both samples as per rules in the guide. Principle can be further extended to multiple sampling plans. «level 2 most appropriate unless otherwise authorised by regulatory authorites- i.e. special levels for small smaple sizes»

Reduced and Tightened modes: Sampling plans can accommodate changes in the sample size according to past performance of previous batches- i.e. normal mode -> reduced mode….problem! -> tightened mode….problem gone-> Normal mode
(follow ‘switching rules’)

other sampling practices?
- Base on experience with product, process, supplier & consumer
- 100% inspection <not always successful!>

Question 21

What statistical test would you use for 3 or more samples?

Answer 21

ANOVA- Analysis of Variance
<Measures variability across groups and within groups. If these are the same, shows no statistical difference>
only do the comparison test is P value from ANOVA is <0.05

(cant use 2 sample t tests as would be bad practice to split groups and comapare each)

Question 22

What is a ‘type I ‘ or ‘type II’ error?

Answer 22

Type I error: Reject null hypothesis when true <false> :(e.g. Reject batch when batch is good, e.g. telling a man he is pregnant)
Type II error: Accept null hypothesis when false <false> :(e.g. accept batch when batch is defective, e.g. telling a pregant women she is not)</false></false>

Question 23

Give an example of an outlier test and how this could be used

Answer 23

Dixons test
- takes into account how improbable the suspected outlier is.
- Put values in increasing or decreasing order. Suspected outlier first. Perform calculation and if the r-value is in excess of the cut off calue for the specified sample size, then the probability of it occurring is considered <0.05 = evidece of outlier

• if ommitting a value you need justifiicable reason and auditable procedures. If values are very close to the threshold, err on side of caution.

Question 24

What statistical techniques can you use to determine shelf life?

Answer 24

ICH guidlines: ICH Q1-E Regression Analysis
Example Setting shelf life:
- Gather data at regular intervals over period of stability <long term, Intermediate & Accelerated>
- Linear regression analysis is carried out on the data and the lower single-sided 95% confidence limit calculated .
- Shelf life estimated where this lower limit intersects with the label claim (graphically or mathematically)

<each year at least 1 batch of each type and strength should be randomly selected for regression analysis to determine any trend in stability. Exact # of batches should allow for trend analysis>

Question 25

What kinds of stability study design can be used?

Answer 25

ICH Q1;
Full Study Design: e.g. 0,3,6,9,12,18,24 + 36 mths. All conditions, All batch strength, allpack sizes and fill.
Reduced Bracketing Study Design: e.g. 0,3,6,9,12,18,24 + 36 mths. All conditions, All batch strength,ONLY EXTREME pack sizes and fill.
Reduced Matrix Study Design: e.g. 0,3,6,9,12,18,24 + 36 mths. All conditions, All batch strength, allpack sizes and fill.
Reduced Bracketing Study Design: e.g. all factor combinations collected at start and end timepoints, tested at 12 months. Data available from at least 3 timepoints. Select sampels to ensure design is balanced and representative <95% prediction interval>

Question 26

What Confidence Intervals mean?

Answer 26

Confidence interval for the mean provides an estimate of the mean for the entire population (‘batch’) - puts error bounds on either side of the estimate to give an interval which we can say it contains the true mean. The smaller the CI are, the more likely it is certain that it will contain the true mean.

Question 27

What is Standard Error?

Answer 27

The mean of a population for sample means does not change however the standard deviation gets smaller as the sample size increases - standard error, which gives us the spread of the means.

Question 28

What are SPC (Shewhart) charts?

Answer 28

SPC charts are used to measure and monitor the performance of ongoing processes in real time, to identify if special cause of variation is present.

Question 29

What are Cusum charts?

Answer 29

monitors a process through cumulative summation (continuous data). V masks applied to chart

Question 30

Differences between Cusum and Shewhart (SPC) charts

Answer 30

Cusums are better at identifying a small drift
Shewhart charts are useful in detecting large/abrupt changes and unusual patterns

Question 31

Define process capability

Answer 31

Process capability - Looks at the spread of the results against the specification:
- Cp (process capability)
- Cpk (Should be at least 1.33 to 1.5)

Question 32

What does it mean if the cpk is 1?

Answer 32

Means that the process is not ideal:
1) Ensure testing is not contributing
2) Widen specification limits - Reg Affairs implication
3) Reduce common cause variation
4) Remove special cause variation

Question 33

Define DMAIC

Answer 33

Six sigma (process knowledge/improving).
D - Define: (KPIs)
M - Measure: (charts/capability performance)
A - Analyse: (FMEA, 5 why’s)
I - Improve: (FMEA)
C - Control: (control charts, capability/performance indicators)

Question 34

What is ISO2859

Answer 34

Sample plans for attributes-to decide the batch should be accepted or rejected.

Question 35

Define A.Q.L.

Answer 35

Acceptable Quality Level - percent defects considered satisfactory as a process average. Agreement between the producer and customer

Question 36

Define O.C. curve

Answer 36

Operating Characteristics Curve - relation between the percent of batches accepted and the percent defective. It is a graph that shows what any particular sampling plan can be expected to do in terms of accepting and rejecting the batches - each plan has its own curve.
Note: the probability of accepting a batch with AQL = 0 is 100%. Real OC Curve is a high probability of accepting a batch if it is better than the AQL.

Question 37

What is the purpose if ISO 2859?

Answer 37

1) To provide a sound statistical basis for determining how large a sample is needed for an inspection;
2) How to find the Acceptance and Rejection limits for any stated AQL based on the sampling.

Question 38

What are the uses of ISO 2859?

Answer 38

1) Raw materials and components;
2) In process and finished product;
3) Quality assessments during validation / qualification
NOTE: It cannot be used for characteristics that can be measured, i.e weight, length - variables (ISO 3951)

Question 39

10 drums of tablets inspected: 8 are acceptable and 2 fail inspection. What are the options / next steps?

Answer 39

If failures are from 2 consecutive drums: potential for special cause variation, potential for segregation & acceptance of part of the batch (depending if cause is identified and the nature of the cause). If no special cause is identified: the whole batch fails. Each inspection must pass for the batch to pass, unless there is a speific event that explains the sample’s failure.

Question 40

What is Cp?

Answer 40

Cp tells us how close the process is running to the specification limits. Relates to process spread to the specification spread, it does not consider the location of the process mean so it tells us what capability the process could achieve if centered.

Question 41

What is Cpk?

Answer 41

Cpk tells us how close the process is running to the specification limits and how consistent it is around the mean. If the process is centered, Cp = Cpk. Incorporates information about both the process spread and the process mean, so it is a measure of how the process is actually performing. It considers the location of the process mean - K is the centralising factor.

Question 42

SPC (Statistical Process Control)- what uses in your company, and the relevance of results.

Answer 42

• Identification and Data gathering * Prioritizing * Pareto Charts * Analysis Of Selected Problem * Cause-and-Effect or Fishbone Diagram * Flowcharting 1 * Scatter Plots * Data Gathering And Initial Charting * Check Sheets * Histograms * Probability Plot * Control Charts * Attribute Data Charts * Process Capability Charts

Control charts help determine whether special-cause variation is present implying that action needs to be taken to either eliminate that cause if it has a detrimental effect on the process or to make it standard operating procedure if that cause has a beneficial effect on the process. If no special-cause variation is found to be present, SPC helps define the capability of the stable process to judge whether it is operating at an
acceptable level.

Examples:
1) Variable Data Control Charts (e.g. weight, volume, temperature)- e.g. X -R control chart to monitor the in-process quality control of the tablet compression process- use tablet hardness as a critical quality attribute for demonstration.
Attribute Data- based on data grouped and counted as present or not- e.g. Acceptable vs. non-acceptable, PI’s completed with errors vs. without.

Question 43

Correlation Coefficient – what is this and can you explain the r2 value?

Answer 43

The quantity r, called the linear correlation coefficient, measures the strength and the direction of a linear relationship between two variables.

The coefficient of determination, r^2, is useful because it gives the proportion of the variance (fluctuation) of one variable that is predictable from the other variable. It is a measure that allows us to determine how certain one can be in making predictions from a certain model/graph.

The coefficient of determination is the ratio of the explained variation to the total variation.
The coefficient of determination is such that 0 < r ^2 < 1, and denotes the strength of the linear association between x and y.

Question 44

Can you explain a T test and how you would use it? Give examples.

Answer 44

A T-test is a statsitical approache for assessing a difference or equivalence in data- e.g. this is commonly used when comparing and evaluating data between laboratories as part of assay transfer activities. Another example: in evaluating clinical trial data for a cancer medication, evaluating life expectancy results of the control group to find out if the results are repeatable for an entire population.

A t-test is commonly used to determine whether the mean of a population significantly differs from a specific value (called the hypothesized mean) or from the mean of another population. To determine whether the difference is statistically significant, the t-test calculates a t-value. (The p-value is obtained directly from this t-value.)

These tests would be performed by suitably trained analytical development scientists using a recignised computerised statistics package- e.g. minitab and subject to review as part of the assay transfer report review/approval.

Question 45

What is a p-value and what does it tell you about the data?

Answer 45

All statistical tests produce a p-value and this is equal to the probability of obtaining the observed difference, or one more extreme, if the null hypothesis is true. To put it another way - if the null hypothesis is true, the p-value is the probability of obtaining a difference at least as large as that observed due to sampling variation.
Consequently, if the p-value is small the data support the alternative hypothesis. If the p-value is large the data support the null hypothesis.

Conventionally a p-value of <0.05 (5%) is generally regarded as sufficiently small to reject the null hypothesis- i.e. demonstrates there is probability that the data results show a statistically significant difference.

If the p-value is >0.05 we fail to reject the null hypothesis.

The 5% value is called the significance level of the test. Other significance levels that are commonly used are 1% and 0.1%. Some people use the following terminology:

Question 46

How would you decide on the warning and action limits for Shewhart charts?

Answer 46

In setting up control charts, may be based upon 3 sigma/ 2 sigma limits (Shewart set these as 3 sigma)
For process control, Alert and action levels should be based on historical data, wherever available. It is good practice to reestablish and recalculate these figures on a periodical basis, particularly following a significant change.

Background: Shewhart divided variation in a process into two categories: controlled variation and uncontrolled variation. The control chart he developed allows us to determine what type of variation we are dealing with. If your process has variation that is consistent and predictable (controlled), the only way to improve this process is to fundamentally change the process. But, if the process has unpredictable variation, the special cause responsible for the unpredictability should be identified. If the special cause hurts the process, the reason for the special cause needs to be found and eliminated. If a special cause helps the process, the reason for the special cause should be found and incorporated into the process.
This concept of common and special causes is the foundation of the control charts Shewhart developed. Shewhart’s choice of 3 sigma limits considered probability and the simple fact that 3 sigma limits provide effective action limits when applied to real world data)

Question 47

15. What statistical tool or approach would you use to set control limits?

Question 48

A) What is a Shewhart Process Control Chart?
B) Tell me five things that you would expect to see in a PQR?
C) What is CpK?

Answer 48

A)used to measure and monitor the performance of ongoing processes in real time, to identify if special cause of variation is present.

B) A review of:
- starting materials including packaging materials used in the product,
- critical in-process controls and finished product results.
- all batches that failed to meet spec and their investigation.
- all significant deviations + investigations
- CC’s
- MA variations
- stability programme + adverse trends
- complaints + returns
- qualification of equipment
- TA’s

C) Cpk tells us how close the process is running to the specification limits and how consistent it is around the mean.

Question 49

When do you see statistics used as a QP and how are they useful to you?
Describe a T‐test?
Describe sampling plans?
How would you apply this to incoming carton testing for IMPs?

Answer 49

A) Cpk, shewhart, t-tests, Dixons outlier test
B)

Question 50

What is your understanding of ISO 2859?
a) Where would you use this within your company?
b) Can you give me examples of critical, major, minor defects for a tablet?
c) When would ISO 2859 not be suitable for use?

Answer 50

Sample plans for attributes-to decide the batch should be accepted or rejected.
A) raw material sampling, IPC’s, end product or supplies in storage
B) critical defect example - hazardous or unsafe usage - metal in tablets
major defect example - failure of the unit or reduce usability - efficacy of tablet reduced
minor defect example - not likely reduce usability on effective use of unit - aesthetically not pleasing
C) NOT used for Continuous production

Question 51

A) Tell me about the structure of a PQR?
B) What do they tell you about the performance of the product?
C) At what frequency would you expect to produce PQRs?
D) What statistics would you use in a PQR?

Answer 51

A) defined in Chapter 1 of GMP, covers review of:
- starting materials including packaging materials used in the product,
- critical in-process controls and finished product results.
- all batches that failed to meet spec and their investigation.
- all significant deviations + investigations
- CC’s
- MA variations
- stability programme + adverse trends
- complaints + returns
- qualification of equipment
- TA’s
B) What changes have been made, summary of recurring issues etc
C) Annually
D) Cpk, shewhart, t-tests