Decision Tree for Selecting Type of Variables in Sampling Plan

Decision-Tree-for-Selecting-Type-of-Variables-Sampling-Plan

Determine the AQL to use in the Master Table: Since there are standard AQLs used in the Master Tables, you need to convert the AQL per table below:

AQL-Conversion-Table

Determine the Sample-Size Code Letter to use in the Master Table: ANSI/ASQ Z1.9 Table A.2 Formulas for the Q Value:

AQL-Conversion-Master-Table

Formulas for the Q Value:

For Section B – Standard Deviation Method (σ Unknown):

Formulas-for-the-Q-Value

Note: For 2-sided spec limits, an AQL can be assigned to both limits combined, or to each end of the spec limit separately.
Table B-1 Standard Deviation Method Master Table B-1 for Normal and Tightened Inspection for Plans Based on Variability Unknown (Single Specification Limit)

Obtain the k Value from the Master Table:

Obtain-k-Value-from-the-Master-Table

Designing your own Variable Sampling Plan

known-unknown-population-sigma

What would be the variables sampling plan (sigma unknown) for the following conditions? High Pa (α = .05) for a fraction non-conforming (P1) of .005, with a low Pa (β = .05) for a fraction conforming (P2) of .03.

Solution

known-unknown-population-sigma-solution

Note: with the same operating characteristics, an attribute sampling plan would require n = 274.

Example (Method: Population Sigma Known)

A lot of 1500 bobbins is submitted for inspection. Inspection level II, normal inspection, with AQL = .65%, is to be used. The specified minimum yield value for the tensile strength is 25.0 lbs. The variability σ is known to be 2.4 lbs.

The sample size code letter from Table A.2 is K. In Table D-2 (p. 86 in ANSI/ASQ Z1.9-2003), for reduced inspection, the required sample size is 7 and the k value is 1.80. The 7 sample specimen’s tensile strengths are 25.7, 26.4, 26.1, 27.2, 25.8, 28.3, and 27.4. QL = (X̄-LSL)/σ = 24.6 – 25.0 / 2.4 = 0.63

Since QL < k, the lot does not meet the acceptability criterion and should be rejected.

What are the alpha and beta risks for sampling letter K (p. 23 in ANSI/ASQ Z1.9-2003), for an AQL of .65, for various incoming quality levels (P)?

P Pa α β
Relatively Good Quality .25 99.5 .5
.50 96 4
Marginal .75 90 10 90
1.5 62 38 62
Poor 2.00 46 46
3.0 22 22
4.0 10 10
5.0 4.5 4.5

* All values are in Percentages

Why is the lot rejected even though none of the samples were out of spec? (Assuming this is a representative sample, a larger, +/- 3σ distribution would provide some product out of specification; in this case, in the left tail of the distribution.)

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