In its industry guidance to companies that manufacture drugs and biological products for people and animals, the Food and Drug Administration (FDA) recommends three stages for process validation. While my last post covered statistical tools for the Process Design stage, here we will focus on the statistical techniques typically utilized for the second stage, Process Qualification.
Stage 2: Process Qualification
During this stage, the process design is evaluated to determine if it is capable of reproducible commercial manufacture. Successful completion of Stage 2 is necessary before commercial distribution.
Example: Evaluate Acceptance Criteria with Capability Analysis
Suppose the active ingredient amount in a tranquilizer needs to be between 360 and 370 mg/mL and you need to assess the quality level, where a minimum Cpk of 1.33 is defined as the acceptance criteria. To assess process performance and determine if measurements are within specification, you can use capability analysis, available in Minitab Statistical Software.
Five samples are randomly selected from 50 batches and the amount of active ingredient is measured. The data is then analyzed relative to the 360 mg/mL minimum and 370 mg/mL maximum.
The capability analysis reveals a Cpk of 0.53, which fails to meet the acceptance criteria of 1.33. The active ingredient amounts for this tranquilizer are not acceptable. So how can we improve it? The Cp value of 1.41 and the graph both reveal that, although the variability is acceptable with respect to the width of the specification limits, the process average needs to be shifted to a higher mg/mL in order to achieve an acceptable Cpk.
Example: Conduct Variation Analysis across Batches
Suppose we want to assess content uniformity, a critical quality characteristic, across 3 batches at 10 locations. To visualize the intra-batch (within-batch) variation and the inter-batch (between-batch) variation, we can create boxplots for each batch.
A boxplot can help us visually assess both the intra- and inter-batch variation, and identify any outliers. This specific graph shows a homogeneous dispersion of measurements both within each batch and between batches. And there are no outliers, which Minitab would flag with an asterisk (*).
Although boxplots are useful tools to conduct a visual assessment, we can also statistically assess if there is a significant difference in the between batch variation using an equal variances test. The test reveals a p-value greater than an alpha-level of 0.05 (or whatever alpha-level you prefer), which supports the conclusion that there is consistency between batches.
Example: Various Applications for Tolerance Intervals
Another useful tool for Process Qualification is the tolerance interval. This tool has multiple applications. For example, tolerance intervals can be used to compare your process to specifications, profile the outcome of a process, or establish acceptance criteria.
For a given product characteristic, a tolerance interval provides a range of values that likely covers a specified proportion of the population (for example, 95%) for a specified confidence level (like 99%).
For example, suppose we want to know how the active ingredient values in the manufacturing process compare to our specification limits. Based on a dose-response study, the limits are 360 to 370 mg/mL.
For this particular data set, Minitab reveals that we can be 99% confident that 95% of the units will be between 362.272 and 367.468 mg/mL. The process bounds therefore indicate that we can meet the requirements of 360 to 370, and we can conclude with high confidence that the process variation is less than the allowable variation, defined by the specification limits.
Or perhaps we need to assess content uniformity using 99% confidence and 99% coverage. We sample 30 tablets and calculate a tolerance interval, revealing that we can be 99% certain that 99% of the tablets will have a content uniformity within some range, calculated using Minitab.
And that’s how you can use various statistical tools to support Process Qualification. In the final post in this series, we’ll explore the Continued Process Verification stage!