Limits of alert and action for the environmental microbiological control – practical solution (página 2)

USE OF THE GAMMA DISTRIBUTION FOR THE DETERMINATION OF THE LIMITS

Discarded the possibility of using the Poission distribution to approximate the behavior of the historical data, other statistical distributions were analyzed.

This search lead to the Gamma probability distribution (5), which is defined by:

Figure 3 shows the graphs of the function of distribution for some pairs of parameters ( and (.

We took the previous sampling point (Ag – Packaged of nonsterile Liquids in bottles), and we made the test of kindness of adjustment for the Gamma distribution:

Hypothesis Test

Ho: The data adjust to a Gamma distribution with a = 0.80 (#)

(#): The election of the value of a is made in empirical form, choosing that value that better fits the function of distribution with respect to the true results.

Ji-square test:

The calculated value is compared with the reduced which is tab, for a level of significance (a) =0,05 and 3 degrees of freedom (n):

Reduced : 7,81

The calculated is smaller to the reduced then the null Hypothesis is admitted: "is accepted that the data follow a Gamma distribution "

In agreement with the found thing, we see that the same population of data that did not adjust to the Poission distribution, if it does to a Gamma distribution.

This agreement between the observed data and the theoreticians can be observed with greater clarity in figure 4.

Considering the previous thing, it is possible to be calculated the action and alert limits using percentiles of this distribution.

In our case, we decided to use percentiles 90 and 95, that in agreement with the experience gathered they were apt for the objective of the environmental control:

• Limit of Alert = P90: 14

• Limit of Action = P95: 19

Of the way it deciphers previously have been made analysis for the different sampling points. The application of this distribution in each one of them is possible because the form of the function is not rigid, but that it depends on the parameter (, which can determine so that the function adapts to the followed one by the evaluated historical data.

In figures 5-12 are the comparative graphs in the control of bacteria and fungi (UFC/Plate) in the same Area of Packaging of nonsterile Liquids in bottles by Sedimentation, with a time of sampling of 1 hour.

For each one of the points, corresponding hypotheses tests was also made, giving satisfactory results.

From observed in the graphs and hypothesis tests, it is deduced that the function of probability distribution Gamma represents in suitable form the distribution of the results obtained in the microbiological control.

In agreement with the indicated thing, the limits of alert and action for the rest of the sampling points of the Area of Packaging of nonsterile Liquids in bottles calculated, using percentiles 90 and 95 of the corresponding Gamma distributions, according to it is indicated in table 12.

Therefore, we have obtained own limits for each point of sampling, that they adjust to a suitable statistical analysis.

In this way it is based, of reasonable way, the necessity to carry out an investigation on the conditions from the area when surpassing itself these values, and to take the actions necessary to reestablish the microbiological load at the accepted levels.

CONCLUSIONS

The evaluation of the collected historical data during the environmental microbiological control by means of the function of Gamma distribution, is a useful statistical form, consistent and practical for the determination of the limits of alert and action in the different sampling points of the controlled areas.

This way, the established limits turn out appropriate to identify if the conditions during the control move away of the historical tendency.

REFERENCIAS

• (1) Sidney H. Willig – James R. Stoker, Good Manufacturing Practices for Pharmaceuticals – A Plan for Total Quality Control, Volume 52, 91-92 (1992)

• (2) James Wilson – "Environmental Monitoring: Misconceptions and Misapplications", PDA Journal of Pharmaceutical Science Technology, 185-190, Volume 55, No. 3, May/June 2001

• (3) Anthony M. Cundell, "Utilización de análisis microbiológicos en procesos asépticos", Pharmaceutical Technology Sudamérica 69, 17-24 (2004)

• (4) Jay Devore, Probabilidad y Estadística para Ingeniería y Ciencias, 4° Edición, 159-162 (1998)

• (5) Jay Devore, Probabilidad y Estadística para Ingeniería y Ciencias, 4° Edition, 566-570 (1998)

Autor:

Lic. Diego Alberto Diaz

Quality Assurance

Laboratorios Bagó S.A. –La Plata Plant

Colaboration:

Lic. Claudia Lagares

Microbiology Department

Laboratorios Bagó S.A. –La Plata Plant