Acceptance Sampling by Variables - Compare

User-Defined Plans - Sample Size and Critical Distance

  

You can compare other plans by varying the sample size, the critical distance, or both together.

If the sample average is closer to the specification than the critical distance (k), this is evidence that there are more items in the tail of the distribution beyond that specification than our AQL allows. So the critical distance (k) represents the smallest distance from the specification (in Z units) that will produce an acceptable quality level for the lot. It therefore represents a Z-score cut-off for accepting the lot.

Example Output

Compare User Defined Plan(s)

 

 

 Sample     Critical   Defectives  Probability  Probability

Size(n)  Distance(k)  Per Million    Accepting    Rejecting    AOQ     ATI

    100      3.44914          100        0.854        0.146   83.0   612.3

    100      3.44914          600        0.224        0.776  130.8  2815.1

 

    150      3.44914          100        0.899        0.101   86.1   500.1

    150      3.44914          600        0.172        0.828   98.8  3007.3

 

    200      3.44914          100        0.928        0.072   87.6   444.7

    200      3.44914          600        0.135        0.865   76.3  3142.0

 

 

Sample     Critical     Maximum         At Defectives

  Size  Distance(k)  StDev(MSD)   AOQL    Per Million

   100      3.44914   0.0027533  145.6          369.7

   150      3.44914   0.0027533  138.5          288.9

   200      3.44914   0.0027533  136.7          256.4

 

Z.LSL = (mean - lower spec)/standard deviation

Z.USL = (upper spec - mean)/standard deviation

Accept lot if standard deviation ≤ MSD, Z.LSL ≥ k and Z.USL ≥ k; otherwise reject.

Interpretation

Using your specifications for lot size, AQL, RQL, producer's risk (alpha), and consumer's risk, Minitab determines that an appropriate sampling plan is to inspect 259 lenses. You want to investigate the risks associated with sampling 100, 150, or 200 lenses, using the same critical distance of 3.44914 at the AQL and RQL levels.