C Two types of errors when using SPC
Classifying variation into common cause or special cause is the primary focus of statistical process control methodology. In practice, this classification is subject to two types of error which can be compared to an imperfect screening test that sometimes shows a patient has disease when in fact the patient is free from disease (false positive), or the patient is free from disease when in fact the patient has disease (false negative).
Error 1 (false positive): Treating an outcome resulting from a common cause as if it were a special cause and (wrongly) seeking to find a special cause, when in fact the cause is the underlying process.
Error 2 (false negative): Treating an outcome resulting from a special cause as if it were a common cause and so (wrongly) overlooking the special cause.
Either mistake can cause losses. If all data were treated as special cause variation, this maximises the losses from mistake 1. And if all data were treated as common cause variation, this maximises the losses from mistake 2. Unfortunately, in practice it is impossible to reduce both mistakes to zero. Shewhart concluded that it was best to make either mistake only rarely and that this depended largely upon the costs of looking unnecessarily for special cause variation. Using mathematical theory, empirical evidence, and pragmatism, he argued that setting control limits to ± three standard deviations from the mean provides a reasonable balance between making the two types of mistakes.