# Example of Variables Acceptance Sampling (Accept/Reject Lot)

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 3.44914, and the maximum standard deviation is 0.0027533.

The quality team collects data from the most recent shipment to determine whether to accept or reject the entire lot of lenses.

1. Open the sample data, CameraLensThickness.MTW.
2. Choose Stat > Quality Tools > Acceptance Sampling by Variables > Accept/Reject Lot.
3. In Measurement data, enter Thickness.
4. In Critical distance (k value), enter 3.44914.
5. In Lower spec, enter 0.395.
6. In Upper spec, enter 0.415.
7. Click OK.

## Interpret the results

The quality team randomly selects and measures the thickness of 259 lenses from the current shipment of 3,600 lenses. From these measurements, Minitab determines the mean and standard deviation to calculate the Z-values:
• Z.LSL = (mean – lower spec) / standard deviation = 0.172803
• Z.USL = (upper spec – mean) / standard deviation = 0.253452
The Z-values are less than the critical distance (3.44914), and the standard deviation (0.0469204) is greater than the MSD (0.0027533). Thus, the team rejects the entire lot.

### Acceptance Sampling by Variables - Accept/Reject Lot

Make Accept or Reject Decision Using Thickness Sample Size 259 Mean 0.403108 Standard Deviation 0.0469204 Lower Specification Limit (LSL) 0.395 Upper Specification Limit (USL) 0.415 Z.LSL 0.172803 Z.USL 0.253452 Critical Distance (k Value) 3.44914 Maximum Standard Deviation (MSD) 0.0027533 Decision: Reject lot.
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