3 Sigma Formula for Trend Analysis Limits : Pharmaceutical Guidelines

# 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.

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
=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.

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.

#### 1 comment:

1. As per TRS-970 established action and alert limit for water system should be exceed 2 sigma. what is the meaning of 2 sigma and 3 sigma calculation.

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