Quality Control and Acceptance Sampling

Abstract

Consider a mass production line for a single “part” and let us center our interest on a single “dimension” of the part. There will always be some variability in the dimension because of the sum of several variables whose causes are not usually understood and whose effects might not be controllable if they were. The dimension of the part is thus a random variable, but one whose mean and variance can change with time as something goes wrong with the “machinery” producing the part. If the process is stable and only the “usual” system of chance causes is operating (which implies that the mean θ and variance σ² of the process are constant), we say that the process is in statistical control and that it has an inherent variability σ². If the mean or variance wanders from those stable values, we say that an assignable cause is operating, meaning that it can be understood/controlled. The term quality control refers to control of quality by any means, but statistical quality control refers to the control of quality through the use of certain statistical tools to be described shortly. The best known of those tools is the Shewhart Control Chart, which is used to demonstrate statistical control and to detect the presence of assignable causes. There are control charts for the mean, range, standard deviation, fraction defective, and number of defects per unit. Three horizontal lines plus the data make up the control charts. The 3 lines are a centerline, an upper control limit, and a lower control limit. (One of the control limits may be omitted if there is no interest in it.) The centerline is an “average” of the statistic being plotted, and the control limits are at distances of 3 standard deviations (of the statistic) above and below the centerline.