Acceptance Sampling
Example:Suppose our company is destructively sampling 40 welds from lots of 1200 welds sent from a supplier. If any of the maximum sustainable pull forces are less than 150 Newton’s, the entire lot is shipped back to the supplier and a
contractually agreed penalty is assessed. What is the technical description of this policy?
Answer:This is single sampling with n = 40 and c = 0.
Example: Is there a risk that a lot with ten nonconforming units would pass through this acceptance sampling control?
Answer: Yes, there is a chance we show how to calculate the probability under standard assumptions, which is approximately 0.7. An OC curve, also described in Chapter 10, could be used to understand the risks better.
Double Sampling
The “double sampling” method involves an optional second set of inspections if the first sample does not result in a definitive decision to accept or reject. This approach is necessarily more complicated than single sampling. Yet the risk verses inspection cost tradeoffs are generally more favorable. The symbols used to describe single sampling are:
1.N is the number of units in the full “lot” of all units about which acceptance decisions are being made.
2.n1 is the number of units inspected in an initial rational subgroup.
3.c1 is the maximum number of units that can be found to be nonconforming for the lot to be declared acceptable after the first batch of inspections.
4.r is the cut-off limit on the count nonconforming after the first batch of inspections.
5.n2 is the number of units inspected in an optional second rational subgroup.
6.c2 is the maximum number of units that can be found to be nonconforming for the lot to be declared acceptable after the optional second batch of inspections.
As for single sampling, there is no universally accepted method for selecting the sample sizes, n1 and n2, of the radical subgroups. Nor is there any universal standard for selecting the parameters c1, r1, and c2. In general, larger samples sizes, n1and n2, and tighter limits on the numbers nonconforming, c1, r1, and c2, decrease the primary risks.
As in single sampling, rejection of a lot generally means returning all units to the supplier or upstream sub-system. This return of units often comes with a demand that the responsible people should completely inspect all units and replace
nonconforming units with units that have been reworked or are new.