Acceptable quality level statistics

Two sets of standards are set for empty capsules, analytical and functional. Capsules, like all other pharmaceutical preparations, must comply with cGMP norms and must be made of materials that comply with pharmacopeial chemical and microbiological standards. However, these tests do not indicate whether a capsule will run well on a filling machine. Series of functional tests are applied by the manufacturers. The critical dimensions of a capsule (the lengths and diameters of the caps and bodies) are checked. It is a continuous production process, and there will be a very small proportion of visually defective capsules. Standard statistical sampling methods are used to estimate quality from samples. The manufacturers and users agree on acceptable quality levels (AQL). The faults are... 

American Pharmaceutical Association Animal and Plant Health Inspection Service Acceptable quality level AIDS-related complex Adult respiratory distress syndrome Applied Research Ethics National Association American Statistical Association Administrative Systems Automation Project (FDA)... 

Industry has accepted a default release specification for the active substance of the label claim 5 %. This would imply that in the long run, given a label claim of 100 %, a real content between 95 % and 105 % is warranted in a pre-specified proportion of the products at release. This proportion is called producer s risk and should be between 5 % and 10 % (in the example 10 %) as is usually accepted within the Statistical Quality Control (SQC) community. The corresponding content limits are thus identical to the acceptable quality level or AQL as defined above. The producer may propose to loosen these limits, when the active substance is e.g. hygroscopic, electrostatic or otherwise difficult to handle, or when the active substance is degrading considerably within the shelf life permitted. 

A sampling plan for attributes is a method to overcome this problem. An example of such a plan is the Accepted Quality Level system (AQL) (See Sect. 24.5.4. for a more complete description of AQL and Sect. 20.4.5 for a statistic background). In order for the AQL system to be successful an extensive and statistically planned random sample has to be selected. The defects that are found are classified into levels, for example critical, major, minor. Within each level the system defines an acceptable quality level . When a quality level is exceeded, then a batch should be rejected. This method of testing requires time and expertise. Sampling has to be performed from a large number of containers from the same batch. Within the pharmaceutical industry it is often necessary for such tests to be carried out by the container manufacturer. For smaller enterprises such as pharmacies quality control can be undertaken by the wholesaler or an independent laboratory. Within a (hospital) pharmacy the quality control is often limited to a visual comparison to reference samples and a check of the presence of the supplier s statement that the containers comply with the agreed specifications [46]. 

The AQL-system is a sampling and assessment system frequently used to check cOTitainers. It is a type of attribute assessment, see Sect. 20.4.5 for statistical background. AQL means Acceptable Quality Level. The AQL-value is the percentage of rejected units accepted by a supplier or buyer to approve the crmcemed batch. Tables are available which describe, for a certain batch size N and an agreed AQL-value, how large the test sample n should be and how many units of that sample are allowed to show a specific defect The AQL-system classifies defects in classes ... 

Acceptance Testing. With increased emphasis on quality control and quality assurance, raw materials or intermediates are subjected to a series of tests of relevant properties to ensure that they match the producers specification. The acceptance quality level, which is the percentage which is acceptable to the buyer, is usually specified, and compliance checked by testing and statistical analysis of the results. BS 3921 lays down a detailed sampling scheme for building bricks. 

Alert and Action Levels. Validated and established systems should be periodically monitored to confirm that they continue to operate within their design specifications and consistently produce water or air of acceptable quality. Monitored data may be compared to established process parameters or product specifications. A refinement to the use of process parameters and product specifications is the establishment of alert and action levels, which signal a shift in process performance. Alert and action levels are distinct from process parameters and product specifications in that they are used for monitoring and control rather than accept or reject decisions. The levels should be determined based on the statistical analysis of the data obtained by monitoring at the PQ step. 

A laboratory QA/QC program is an essential part of a sound management system. It should be used to prevent, detect, and correct problems in the measurement process and/or demonstrate attainment of statistical control through QC samples. The objective of QA/QC programs is to control analytical measurement errors at levels acceptable to the data user and to assure that the analytical results have a high probability of acceptable quality. 

For example, a 95% probability that a batch is as good as the AQL does not exclude other probabilities that the batch is worse (for example the 10% probability level, sometimes called the lot tolerance per cent defective (LTPD) or unacceptable quality level, can be several percentage points worse than the AQL). It is the relationship of AQL to LTPD that more closely identifies the quality risk in any statistical sampling plan, and illustrates why the use of national plans as simple accept and reject figures fails to tap their full potential. 

In the previous section we described several internal methods of quality assessment that provide quantitative estimates of the systematic and random errors present in an analytical system. Now we turn our attention to how this numerical information is incorporated into the written directives of a complete quality assurance program. Two approaches to developing quality assurance programs have been described a prescriptive approach, in which an exact method of quality assessment is prescribed and a performance-based approach, in which any form of quality assessment is acceptable, provided that an acceptable level of statistical control can be demonstrated. 

What is the importance of the null and the alternative hypotheses They enable us to link the baseline and alternative condition statements to statistical testing and to numerically expressed probabilities. The application of a statistical test to the sample data during data quality assessment will enable us to decide with a chosen level of confidence whether the true mean concentration is above or below the action level. If a statistical test indicates that the null hypothesis is not overwhelmingly supported by the sample data with the chosen level of confidence, we will reject it and accept the alternative hypothesis as a true one. In this manner we will make a choice between the baseline and the alternative condition. 

Two elements of quality assurance are quality control and quality assessment. Quality control is a set of measures implemented within an analytical procedure to assure that the process is in control. A combination of these measures constitutes the laboratory QC program. A properly designed and executed QC program will result in a measurement system operating in a state of statistical control, which means that errors have been reduced to acceptable levels. An effective QC program includes the following elements ... 

Besides analyzing and correlating data by statistical means, the chemical engineer also uses statistics in the development of quality control to establish acceptable limits of process variables and in the design of laboratory, pilot plant, and process plant (evolutionary operation) experiments. In the latter application, statistical strategy in the design of experiments enables the engineer to set experimental variables at levels that will yield maximum information with a minimum amount of data. 

This has been defined (B5) as the smallest single result which, with some assurance, can be distinguished from zero, or, in statistical terms, the smallest single result whose fiducial limits for, say, P = 0.05 do not include zero. This review will be primarily concerned with clinical chemical methods that have acceptable levels of sensitivity, and to which therefore statistical methods of quality control can be applied throughout the range of concentrations which may be encountered in physiological and pathological conditions. To take an extreme example, therefore, the statistical methods of quality control discussed in this review would not be fully applicable to determinations of plasma epinephrine or... 

One of the major uses of statistical distributions of atmospheric concentrations is to assess the degree of compliance of a region with ambient air quality standards. These standards define acceptable upper limits of pollutant concentrations and acceptable frequencies with which such concentrations can be exceeded. The probability that a particular concentration level, x, will be exceeded in a single observation is given by the complementary distribution function F(x) = Prob c > jc =1 — F(x). 

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