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One of the key features of the Closure Moisture Analyzer (CMA) is to provide the operator with a real time frequency distribution of the capacitance of elastomer closures used to protect lyophilized products. The frequency distribution provides the operator, on a real time basis, with the display of the (M) or average value of the capacitance and the standard deviations. Anyone who has attempted to examine a large number of values in a set of data to create a frequency distribution will tell you it is indeed an arduous and time consuming task. The fact that the CMA can non-destructively and rapidly measure the effect of moisture on the dielectric properties of an elastomer closure is a real advantage but to process the data makes this instrument truly remarkable
This tutorial is designed as a very basic means for those using the CMA to take advantage of the display of the data in statistical terms and how to use such information to evaluate the risk of using closures that could prove harmful to the stability of their lyophilized products. This tutorial is by no means meant as a substitute for the many texts written on statistics that are commonly available in the literature and after reviewing this tutorial the reader is encouraged to consult other texts for a more definitive description of the field of statistics.
I. Why should I use statistics to evaluate the moisture in elastomer closures that will be used in sealing lyophilized pharmaceutical products?
There are a number of reasons why you would want to apply statistics to evaluating your closures but let me just outline a few for you at this time.
- No matter what the mass of your lyophilized cake may be - but more importantly if the mass is less than 100 mg - the moisture from the outgassing of water vapor could have an adverse affect on the stability of the product.
- Many lyophilized products require the closures to be sterilized and steam sterilization is the sterilization process most often used. The exposure of the closures to steam at 15 psi and 121 C for some period of time will have the effect of increasing the moisture content.
- You may use a drying process to remove the moisture from the closures but there may be some degree of uncertainly as to just how effective is the drying process. The question may be asked as to what is the risk that some of the closures could contain sufficient moisture that could affect the stability of the lyophilized product during its shelf life.
- Even if the closures that are used in your formulation do not require steam sterilization or are sterilized by other means like radiation, they will still contain a range of moisture values that could prove injurious to the lyophilized product's stability.
Now you have to understand from the very beginning that statistics in itself cannot prove anything but is a valuable tool for allowing you to assess the risk that moisture from the closures may affect the stability of the lyophilized product. The following will give you a basic introduction as to how using statistics can enable you to evaluate if the closures you are using in your container closure package pose a risk to your product.
II. Sample size
The first question that you need to ask yourself is how many closures will you need to measure to assess, with some defined degree of confidence, if any of the dried closures could pose a threat to the stability of your lyophilized product.
The apparent answer to this question is a sample size that will be representative of the distribution of moisture in the closures that you will be using in making a given batch of lyophilized product. While the answer is correct it does not give you any insight as to how you can judge the size of such a sample.
In order to give you perhaps a better understanding let us take as our example a large pot (100 liters) of vegetable soup. The soup will be made up of say 50% water and the other 50% will be vegetables. Our task is to determine if the soup has the desired composition. We want to make sure the soup contains the correct number of peas, carrots, beans, corn, celery and potatoes. One way we could to this is to determine the total water content in the soup and take an actual count of the each individual vegetable. However, to do that for a soup that has a volume of 100 liters would accurate but far too time consuming. We could still achieve our objective if were to examine a sample of the soup that would be representative of the total contents of the soup.
The first thing we would do is to be sure that the sample we use is really representative of the actual contents of the soup. In order to do this we must make sure the soup was well stirred before taking the sample.
Stirring the soup was not a difficult problem but now we must decide on the sample size. At first we could use a teaspoon to sample the soup. In our analysis of what we find on the teaspoon is that the soup contained only 30 % water, one potato, a few peas and one bean. Our common sense tells us that our sample is not representative of the content of the soup. We therefore should try a larger sample volume.
We next select a tablespoon to obtain the sample. This time our results are much better and we find the water content has increased to 41% and we once again found peas and beans and now even some corn and celery but no potatoes. While our results are a bit better, we find from our analysis that we have excess peas and corn and low amounts of beans and celery. Accounting to our results there are no potatoes and carrots in the soup. Once again we come to the realization that we are not selecting a large enough sample.
Now let us take a larger sample of the soup, e.g., 500 ml ( a cup). Now with this sample we find the water content is 51% and we found all the vegetables were present in nearly the right portion. While our results did not give us an exact analysis of the soup's composition, the results are close enough that we had confidence that composition of the soup is within acceptable limits and we did not have to measure the contents of the entire 100 liters.
The main point of the soup example is that sample size plays a key role in use of statistics and is something we have to take into careful consideration. Unfortunately, such a consideration is not often followed today in the pharmaceutical industry.
Now in the case of the soup, we could distinguish each of the ingredients but that is not the case with elastomer closures. For the closures they will all have the same color and dimensions and thus appear to the eye to be indistinguishable. But unfortunately there could be major differences in the moisture content of the closures and some closures may contain a sufficient amount of moisture that could affect the stability of a lyophilized product. Thus there is a need to be able to distinguish - the otherwise indistinguishable closures - with respect to their moisture content.
The CMA provides a rapid means for distinguishing the moisture content in closures from the change in their dielectric properties. Thus as in the example of the soup were we were able to separate the water content and the number of individual vegetables, the CMA can separate the closures according to their capacitance. However, we are still faced with the problem of determining an adequate sample size (n).
Since we cannot rely on common sense as in sampling the closures we must make use of statistical considerations to ascertain the sample size (n), namely the desired Confidence Level and Confidence Interval for our measurements.
In simple terms, the Confidence Level is that percentage of the tested closures you wish to fall within the mean value (M). Are you satisfied with only those capacitance values that are within 90 % of the M or would you want to include more data in your analysis with capacitance values that are within 95 % or 99 % of the arithmetic mean?. Most researchers are often satisfied with a Confidence Level of 95 % but given the PAT guide lines a Confidence of 99 % would now be preferred.
Since one of our main focuses will be in the change in the mean value of the capacitance as the closures are exposed to either steam sterilization or a drying process, we next must select the range to which we expect this value to fall. Would we be satisfied with the mean value to have a range of 10 % or would we wish to have greater confidence in the mean capacitance value by reducing the range to say 5 % to even 3%.
What you must keep in mind is that the values that we select for the Confidence Level and Confidence Interval will greatly influence the sample size needed to perform the test. You can determine the sample size "n" by going to the following web site and select the Confidence Level, Confidence Interval for a given lot size of the closures.
III. Interpretation of the CMA Data
a. Arithmetic Mean Capacitance Value
The CMA provides a real time value of the M or average value of the capacitance data as they are received from the closure manufacturer. This value will increase as a result of steam sterilization and decrease upon drying.. The mean value M represents a benchmark upon which one can compare samples of closures as they are received from the manufacturer, after steam sterilization or drying. However, as we will soon see, knowing just M provides only one part of the information needed to interpret the results of the CMA data.
b. Standard Deviation (sigma)
In the most simplistic of terms, the standard deviation (sigma) is a measure of how the values of a set of data will be dispersed about the arithmetic mean (M). While there are well defined mathematical expressions for calculating sigma, such expressions may not help the reader grasp the significant role that sigma will play in assisting them in evaluating if the moisture in any of their closures could affect the stability of the lyophilized product. In order to assist the reader in understanding the role of s for a given M, consider the two frequency distributions shown in Figure 1.
Figure 1 shows the frequency distribution for two sets of data having equal M values but significantly different values for sigma. Notice in plot A, which has a sigma value of 2, that the capacitance values of the sample are closely dispersed about M. However, for plot B, the value of sigma is given as being 10 and it is clear to see that the capacitance values in the distribution are more dispersed about the arithmetic mean.
Now the question arises how do I use a given value of M and sigma to ascertain if a given lot of dried closures would pose a risk to the stability of the lyophilized product? And, in addition, how many defective closures can I expect to find in such a lot? It should be made clear now that statistics alone cannot provide the answers to those questions.
To answer such a question let us examine the frequency distribution shown in Plot B in Figure 1. Because the CMA is a non-destructive test method, our capacitance measurement will not in any way affect the moisture content in the closure. As a result, we are able to select closures with a given range of
Figure 1 A plot of two distributions having the same M but with
different sigma values
capacitance values and test the affect that these closures will have on the stability of the lyophilized product. If the selected range of closures affects the stability of the closure then we will deem these closures to be defective with respect to their use with that given lyophilized product.The following will provide the reader with general guideline for establishing the effectiveness that a lot dried closures will have on the stability of a given lyophilized product and what would be the anticipate number of closures out of every million closures tested that would be deemed defective, i.e., moisture from these closures would adversely affect the stability of the lyophilized product.
Let us assume that Plot B in Figure 1 represents a frequency distribution of dried closures. We will select a portion of the closures defined by a given range of capacitance values and ascertain how many closures will be considered defective for every million closures that are dried.
Figure 2 shows, by the black area, are those dried closures that have capacitance values greater than M.
Should all of those closures shown by the black region of Figure 2 adversely affect the stability of the lyophilized product then the number of defective closures for every million closures dried would amount to 500,000 (1). But if not all those in the black area were shown to affect the lyophilized product's stability, then we might want to change the range of capacitance values and start with sigma=1.
Figure 2. Those dried closures in the frequency distribution with capacitance values greater than M.
The closures with capacitance values starting with sigma=1 are illustrated by black area under the frequency distribution in Figure 3.
Should all of those closures shown by the black region of Figure 3 adversely affect the stability of the lyophilized product then the number of defective closures for every million closures dried would amount to 158, 655. But if not all those in the black area were shown to affect the lyophilized product's stability, then we might want to change the range of closures with capacitance values starting with sigma=2 as seen in Figure 4.
Figure 3. Those dried closures in the frequency distribution with capacitance values greater than sigma=1 are represented by the black area under the curve.
The closures with capacitance values starting with sigma=2 are illustrated by black area under the frequency distribution in Figure 4.
If all of those closures shown by the black region of Figure 4 adversely affect the stability of the lyophilized product then the number of defective closures for every million closures dried would amount to 22, 750. But if not all those in the black area were shown to affect the lyophilized product's stability, then we might want to change the range of capacitance values and start with sigma=3 as seen by Figure 5.
Figure 4. Those dried closures in the frequency distribution with capacitance values greater than sigma=2 are represented by the black area under the curve.
The closures with capacitance values starting with sigma=3 are illustrated by black area under the frequency distribution in Figure 5.
Should all of those closures shown by the black region of Figure 5 adversely affect the stability of the lyophilized product then the number of defective closures for every million closures dried would amount to 1, 350. But if not all those in the black area were shown to affect the lyophilized product's stability, then we might want to change the range of capacitance values and start with sigma=4 as seen by Figure 6.
Figure 5. Those dried closures in the frequency distribution with capacitance values greater than sigma=3 are represented by the black area under the curve.
The closures with capacitance values starting with sigma=4 are illustrated by black area under the frequency distribution in Figure 6.
Should all of those closures shown by the black region of Figure 6 adversely affect the stability of the lyophilized product then the number of defective closures for every million closures dried would amount to 32. But if not all those in the black area were shown to affect the lyophilized product's stability, then we might want to change the range of capacitance values and start with sigma=4.5 as seen by Figure 7
Figure 6. Those dried closures in the frequency distribution with capacitance values greater than sigma=4 are represented by the black area under the curve.
The closures with capacitance values starting with sigma=4.5 are illustrated by black area under the frequency distribution in Figure 7.
If all of those closures shown by the black region of Figure 6 adversely affect the stability of the lyophilized product then the number of defective closures for every million closures dried would amount to just 3.4 and is the quantity of defects often referred to as six sigma.
Figure 7. Those dried closures in the frequency distribution with capacitance values greater than sigma=4.5 are represented by the black area under the curve
IV. Summary
Some main points to remember concerning the use of the CMA
The CMA provides a rapid and non-destructive means for assessing the affect that moisture has on the dielectric properties (capacitance) of elastomer closures.
The software of the CMA provides a statistical analysis of the collected data on a real time bases.
Just how effective the CMA will be in providing reliable statistical data will depend on not only the sample size but also if the sample is truly representative of the entire lot of closures.
While the value of M is an important consideration when examining a frequency distribution, one should be particularly concerned with frequency distributions having relatively large values of s, i.e., s > 10.
Using the ability of the CMA to selectively choose a range of dried closures, based on a range of their capacitance values enables one to ascertain just how effective their drying process is and project the number defective closures (those closures having suffice moisture content to affect the stability of the lyophilized product) per million of closures that were processed.
V. Reference:
1. http://www.engin.umich.edu/class/eng401/003/Stats/ppm_tabl.htm
For an oven that is specifically designed and constructed to dry elastomer closures with Pat in mind.
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Febuary 2007