Production lots and tests with a specification range of two standard deviations will produce random rejections five percent of the time, as a result of extreme statistical variation. Techniques based on sound statistical reasoning were developed to deal with out-of-specification (OOS) test results. The temptation to bend the rules and lower the reject rate led to abuses, however. The most common of these was to test a sample repeatedly until a passing result was produced. In 1993, Barr Laboratories lost a lawsuit on this and related points and the judge's decision led to new interpretations of FDA rules, including the requirement that an investigation be initiated before a replicate sample can be tested. These rules and others incorporated into FDA guidance documents reflect a misunderstanding of important statistical principles.
This approach to OOS results became a major problem following the 1993 lawsuit between the US government and Barr Laboratories.2 Peculiar judicial conclusions and subsequent US Food and Drug Administration (FDA) actions created a major problem out of a minor quality control (QC) problem. In this article, we trace this history with an emphasis on the 15 years since the Barr Decision. A key part of the story is that poor training in mathematics and a lack of statistical thinking combine to confuse workers.
Before discussing the history of the out-of-specification (OOS) problem, it is useful to examine some basic tenets underlying lot release testing and the use of statistics.
All Measurements are Approximate
Scientists realize that all measurements are uncertain at some level and are taught that the standard deviation is the parameter that estimates the degree of this uncertainty. For the pharmaceutical analyst, this idea is very important when making quality control (QC) measurements because the analyst must balance the cost of making measurements against the needed level of certainty.
Unlike their counterparts in academia, industrial QC analysts are not expected to produce test results that are accurate and precise to the maximum number of significant figures that are possible. In most cases, the analyst's supervisors will not provide the equipment or the time to make measurements of that type, but will only provide what is necessary to determine if a product lot meets specifications.
Of course, the occurrence of OOS results also raises the question of whether the specifications themselves have been properly set. If the specifications are set improperly, we will consistently see OOS results, because the manufacturing process itself cannot meet the specifications that were set for it. This article does not deal with such circumstances, however; the OOS problem addressed here applies to stable and controlled processes with realistic requirements, in which an OOS result is a rare event.
Variability Can be Measured
The experienced QC scientist knows, when setting specifications, that individual units of a product will vary because of process variations that affect both samples and whole lots. In addition, variation in the test method itself is layered on top of process variations. Therefore, the result of a single test is affected by multiple sources of variation, and may be misleading unless the degree of variation arising from the different sources is understood. That is why a specification has ranges.