If the lot size N changes, the below curves change very little. However, the curves will change quite a bit as sample size n changes. So, basing a sampling plan on a fixed percentage sample size will yield greatly different risks. For consistent risk levels, it is better to fix the sample size at n, even if the lot sizes N vary. Question: If n = 10 & c = 2, what is the alpha risk for a vendor running at p = .02? Answer: Pa is about .55, so alpha is about .45. Question: What is the beta risk if the worst-case quality the customer will accept is 3%? Answer: (about 15%). To lower alpha and beta, you can increase n and c.
Is c = 0 the best plan for the producer and the consumer?
At the 2.8% lot defect rate, both plans give the producer equal protection: Pa = 11%, or Prej = 89%. Which one gives better protection against rejecting relatively good lots, e.g., at the .5% lot defect rate, and why?
For (1), α = about 8% and for (2), α = about 30%.
(1) has a lower α error so less chance of rejecting good lots. With (2), you will reject any lot of 500 if there is even 1 defect in the sample, but it will lead to higher costs.
Is c = 0 the best plan for the producer and the consumer?
At the 2.8% lot defect rate, both plans give the producer equal protection: Pa = 11%, or Prej. = 89%. Which one gives better protection against rejecting relatively good lots, e.g., at the .5% lot defect rate, and why? For (1), α = about 8%; for (2), α = about 30%. (1) has a lower α error so less chance of rejecting good lots. With (2), you will reject any lot of 500 if there is even 1 defect in the sample, but it will lead to higher costs.
Discrimination is the ability of a sampling plan to distinguish between relatively good levels of Quality and relatively bad levels of quality. In other words, having
The Operating Ratio is defined as
R = P2/P1 = Pβ/P1-αExample: R = .03/.005 = 6.0
Derive a plan that comes as close as possible to satisfying two points on the OC curve. The two points are (P1, 1-α) and (P2, β). The derived plan will contain an n and a c value.
Example
Desired α risk of .05 for a P1 of .005, along with a desired risk of .05 for a P2 of .03.
1. Determine R:
R = P2/P1 = .030/.005 = 6.0
2. Enter the Values of Operating Ratio Table with α and β and find the closest R to the calculated value in step 1.
For α = .05 and β = .05, the closest table value is 5.67. This is acceptable since it is slightly more discriminating than 6.0. Note the c value of 3 in the far left column.
3. Obtain the nP1 value in the far right column. Then calculate n from:
n = nP1/P1 = 1.366/.005 = 273.2 or 274.
The acceptance sampling plan is n = 274, c = 3.