Process Analysis Sampling Plans - Alpha and Beta Error Probabilities
To return to the piston rings example, there are two types of mistakes that we can make when inspecting a batch of piston rings that has just arrived at our plant. First, we may erroneously reject H0, that is, reject the batch because we erroneously conclude that the piston ring diameters deviate from target specifications. The probability of committing this mistake is usually called the Alpha error probability. The second mistake that we can make is to erroneously not reject H0 (accept the shipment of piston rings), when, in fact, the mean piston ring diameter deviates from the target specification by a certain amount. The probability of committing this mistake is usually called the Beta error probability. Intuitively, the more certain we want to be, that is, the lower we set the Alpha and Beta error probabilities, the larger the sample will have to be; in fact, in order to be 100% certain, we would have to measure every single piston ring delivered to our company.