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3 Sigma Formula for Trend Analysis Limits


Alert and action limit for trend analysis in pharmaceuticals is a mandatory requirement for cGMP. These limits are obtained using 3 sigma formula.
All observations related to the water system and environmental monitoring are subject to trend analysis. Trends are prepared but its limit always remains a point of discussion because all regulatory guidelines provide single limit for the tests. No alert and action limit is given.

Trend Chart
There are many formulas to determine the in-house alert and action limits but 3 sigma formula is more reliable and widely used formula.

To determine these limits first of all standard deviation of the result values is calculated and then it is added in average of all values. For example:

If you have 10 user points of purified water having the official limit 100 cfu/ml and has a data of 15 days, calculate the alert and action limits in following way.

Sampling Point
Results of Different Days
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
11th
12th
13th
14th
15th
SP01
05
08
11
06
08
05
12
06
06
10
12
11
06
13
17
SP02
08
13
06
11
08
09
07
10
08
06
13
11
07
09
06
SP03
12
19
08
12
13
09
07
15
12
10
10
13
09
07
12
SP04
18
10
09
13
06
09
11
10
12
08
12
08
06
11
09
SP05
12
08
11
08
04
15
09
06
12
10
07
13
16
10
12
SP06
05
12
08
06
06
19
12
10
09
11
08
08
08
12
16
SP07
10
13
09
16
12
08
11
10
14
24
18
21
16
12
16
SP08
16
18
08
11
22
12
09
14
12
06
10
16
20
11
13
SP09
09
18
22
09
14
06
13
09
14
12
07
13
16
09
11
SP10
15
22
08
12
09
13
17
20
14
08
08
13
11
19
22

Average of all results = 11.28
Standard deviation (Sigma) = 4.16
Alert Limit = Average+(2xSigma)
=11.28+(2x4.16)
=20 cfu/ml

Action Limit = Average+(3xSigma)
=11.28+(3x4.16)
=24 cfu/ml


Results should not exceed the alert limit and investigation should be done whenever it exceeds. Result exceeding the action limit shows the serious problem in the water system and must be rectified immediately.
Note: Sufficient data should be available to determine the alert and action limits by 3 sigma formula. Alert and action limit of water system and environmental monitoring should be calculated with minimum one year data because results vary in different seasons of the year.

WHO (TRS-970 page-85) also suggests establishing the alert and action limits for water system and trending should not exceed 2 sigma. An investigation for the results exceeding the alert limit should be done for the root cause. Appropriate corrective action should be taken to prevent the cause.
Download 3 sigma formula in excel calculation sheet.
Ankur Choudhary is India's first professional pharmaceutical blogger, author and founder of Pharmaceutical Guidelines, a widely-read pharmaceutical blog since 2008. Sign-up for the free email updates for your daily dose of pharmaceutical tips.
Email: .moc.enilediugamrahp@ofni Need Help: Ask Question


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