A camera manufacturer receives shipments of 3,600 lenses several times a week. The quality team takes samples of 259 lenses from each shipment and measures the thickness to determine whether to accept or reject the entire lot of lenses. A defective lens is one that is thicker than 0.415 inch, which is the upper specification limit (USL), or thinner than 0.395 inch, which is the lower specification limit (LSL).
From the lot of 3,600 lenses, the manufacturer and its supplier agree to set the acceptable quality level (AQL) to 100 defectives per million and the rejectable quality level (RQL) to 600 defectives per million. Using a producer's risk (alpha) of 0.05 and a consumer's risk of 0.10, Minitab determines that an appropriate sampling plan is to randomly select and inspect 259 of the 3,600 lenses. The critical value is approximately 3.4 and the maximum standard deviation is approximately 0.003.
The quality team collects data from the most recent shipment to determine whether to accept or reject the entire lot of lenses.
The quality team randomly selects and measures the thickness of 259 lenses from the current shipment of 3,600 lenses. If the Z-values are greater than the critical distance and the standard deviation is less than the maximum standard deviation, the team will accept the lot. For this shipment, the Z-values are less than the critical distance. The standard deviation is greater than the Maximum Standard Deviation (MSD). Both of these conditions lead the team to reject the entire lot.