Tools › Quality › Control › Acceptance Sampling › Example
Montgomery Section 15.2.4: designing a single plan for AQL 1 %, α 0.05, LTPD 6 %, β 0.10
| Tool | Acceptance Sampling |
| Source | Montgomery, D. C. (2013). Introduction to Statistical Quality Control, 7th ed. Wiley, Hoboken, NJ. Section 15.2.4; Cameron, J. M. (1952). "Tables for Constructing and for Computing the Operating Characteristics of Single-Sampling Plans." Industrial Quality Control, Vol. 9, No. 1, pp. 37–39. |
| Level | Undergraduate |
Problem
Find a single sampling plan whose OC curve passes through p1 = 0.01 with Pa = 0.95 and p2 = 0.06 with Pa = 0.10, by exact binomial search and by Cameron's Poisson ratio table, and compare with the nomograph reading of n = 89, c = 2.
Inputs to Enter
- Analysis 'Design a single plan from AQL, α, LTPD, β'
- AQL 1.0 %, producer's risk 0.05, LTPD 6.0 %, consumer's risk 0.10 (default values)
Answers
- Exact binomial search: c = 3, n = 110 is the smallest plan meeting both risks; the c = 2 row needs n = 88 for β but misses α (0.059)
- Nomograph plan n = 89, c = 2 (book): α = 0.0603, β = 0.0919
- Cameron: p2/p1 = 6 lies between R(3) = 4.890 and R(2) = 6.509 → c = 3; n = 1.366/0.01 → 137 (meets α) or 6.681/0.06 → 112 (meets β)
Notes
Switch the Analysis select to the design mode; the risks and quality levels are already the book's. Not the default selection.