by Andrew W. Jones, Technical Manager, KMI/PAREXEL LLC
Determine the Confidence Interval as compared to +/- 3S.D. With the +/- 3 S.D. ranges determined, it can be considered important to evaluate what confidence there is that the next data point will fall within this range. The rationale for determining this level is to justify that the +/- 3 S.D. range provides a confidence that 99% of the data is within that range. Similar to the +/- 3 S.D. range, the confidence interval is a range between which the next measurement would fall. This level is typically 99% or greater. Thus a 99% confidence interval means, "there is 99% insurance that the next value would be in the range." To calculate a 99% Confidence Interval, one needs to consider the area under the standard normal curve, the mean, the standard deviation, and the population size. Determining this level can be done using the formula in Figure 7. The confidence interval can be added to our previous example and is displayed in Figure 8.
Figure 8: Trend Chart with +/- 3 S.D. and Confidence Interval.
Figure 7: Definition of Confidence Interval Formulas.
Following our example:
Confidence Interval (99.9%) = 6.23 ± snc ( 0.151202/(30) 1/2)
Confidence Interval (99.9%) = 6.95 to 6.02
The confidence interval at 99.9% is slightly more narrow than the +/- 3 S.D. range which follows the trend if the +/- 3 S.D. range provides that 99% of the data will be within the range if the data is normally distributed.
As can be seen in the trend charts, the data fits well within the +/- 3 S.D. range, and therefore the confidence level is very high that the next data point that is collected will be within this range. Therefore this range may be appropriate to use as acceptance criteria based on the statistics. If the confidence level was wider than the +/- 3 S.D., then the data would have to be analyzed such to investigate if there were errors in calculating the degree of normality, the +/- 3 S.D., the confidence level, the outliers, or errors in the sampling technique to show that it was not computational error.
Another method to setting ranges to be used as acceptance criteria are the Process Capability Indices defined by:
CPu = (USL - µ) / s (or in our example 3 S.D.)
CPl = (µ - LSL) / s (or in our example 3 S.D.)
USL = Upper Specification Limit
LSL = Lower Specification Limit
An industry accepted standard CP would be 1.33.1 This would mean that only 0.003% of the testing results would be out of the specification or 99.997% would be within the specification. This is a similar concept to confidence level.
Recording the maximum and minimum values in the data is important because it is a quick way to see if the data is all within the +/- 3 S.D. range. Additionally, if the maximum and minimum are within the +/- 3 S.D. range, than there is an additional level of confidence since all of the data would be within the range. Lastly, the data may be determined to be non-normally distributed and in such case, confidence may predict to high a possibility for failure at the +/- 3 S.D. range so in the interim, the maximum, and minimum values can be selected to be the range until further data can be collected to define the range (this refers back to increasing the sample size in order to approach a more normal distribution).
Using all of the above analysis techniques, knowledge of the process and agreement on by a cross-discipline committee, acceptance criteria ranges can be assigned for the critical parameters and attributes. A general course of action would be to start by recording all the data at a given point in a spreadsheet, calculating the mean, S.D., population size, +/- 3 S.D., 95% and 99% confidence intervals, plotting the trend charts with appropriate ranges, and then deciding on which range makes the best sense. When selecting the acceptance criteria, a cross-functional committee should be utilized with backgrounds of QA, Manufacturing, Validation, R&D, and Engineering present. The
ranges should be selected and justified by scientifically sound data and conclusions. The ranges should be within the PAR for the product, which means that if +/- 3 S.D. is selected, the range should be checked at the upper and lower limits to verify that acceptable product is prepared. This should be done prior to a final agreement on the range and incorporation into the validation protocol. A report should be written to document the ranges with the rationale for selecting them and the justification for determining the limits as well as any determination that the ranges are within the PAR. Additionally, those ranges which are not to be included should be discussed within the report to justify why they are not to be recorded. A process validation protocol should be prepared with theses ranges for acceptance criteria and the process should be run at a target within the acceptance criteria ranges at least three consecutive times using identical procedures to verify that the process is valid.
Since the ideal case of validating a process during its implementation does not always exist in the pharmaceutical, biopharmaceutical, biotechnology or medical device industries, it may be important to determine a way to validate these processes using historical data. The historical data can be found in a variety of places as long as it is approved (e.g. approved and completed BPRs or quality control release documents, etc). A cross-functional team should perform a risk assessment on the parameters and attributes to determine which ones would be included in the process validation. A range establishing study for the attributes and parameters should be performed to evaluate historical data and analyze the data set for the concepts of normality, variation (standard deviation), and confidence. With a high degree of confidence, acceptance criteria ranges should be set for each parameter and attribute and a process validation protocol should be written with the appropriate ranges. This protocol should be approved and executed at target settings within the acceptance criteria ranges, from the start of the manufacturing process to the finish using qualified equipment, approved SOPs, and trained operators. In a final report for the process validation, the degree to which the process is valid would be determined by the satisfaction of the approved acceptance criteria.
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Page last updated: 5 March 2009