Quality associates, inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes.

in one particular application a client gave quality associates a vast sample of 10,000 observations taken during a time in which the client’s process was operating satisfactorily. the standard deviation of this sample was 0.21; hence with so much data, the population standard deviation was assumed to be 0.21.

quality associates then suggested that random samples of size 30 be taken hourly to monitor the process on an ongoing basis. by analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. when the process was not operating satisfactorily, corrective action could be taken to eliminate the problem.