From: Stan Hilliard
Date: 8/26/2004
Time: 11:50:37 PM
YOU SAID: "... the risks corresponding to these "two points" of proportion nonconforming on the OC curve tend to be arbitrarily decided in practice, starting off with ambitious values then being significantly compromised when the required sample size "appears" overly sizable and unpalatable."
MY REPLY: I think that more typically, the producer's and consumers' risks are chosen arbitrarily, like 0.05 and 0.05, and then the AQL and RQL are chosen initially with possibly ambitious values.
A person in Manufacturing might want an ambitiously high AQL. A person in Marketing might want an ambitiously low RQL. The result being too high of a sample size.
In my opinion, the practice of compromising ambitious initial values to balance inspection cost with effectiveness is part of the legitimate design process.
I do not object to that because sample design is a judgement call that balances 1) the likelihood of the product having various quality levels, 2) inspection time and cost to detect them, 3) the rejectable quality level and the risk of not detecting such "bad" lots, 4) the acceptable quality level and the risk rejecting such "good" lots, and 5) the consequences of each possible decision.
Some aspects of that judgement call are economic and some are not. Inspection cost is economic and therefore is most often considered. But not such things as anticipating how often in the future the process will go bad. Or contemplating the possible loss of life if it were to go bad and not be detected.
Here is an example of balance some above-mentioned factors. Consider the sampling by an individual of canned food when he/she opens the can and eats the food. If the food were to contain botulism it can result in death. Yet almost everyone chooses a sample size of n=0 tests for botulism. Why? Because they believe that the probability that botulism is in the can is so small.
The oc curve for n=0 is a horizontal line at Pa=100%. So the producer's risk (alpha) is zero and the consumer's risk (beta) is 100%. Yet the plan seems rational -- millions of people use it every day. By their behavior, they agree to a 100% probability of accepting a product that is 100% defective -- even when the potential consequence will be their own death.
The thing that makes a sampling plan rational is that it is designed statistically. That is, the designer of the plan knows its probability of acceptance for any potential quality level -- and accepts responsibility for having drawn that balance.
The design of a sampling plan is a matter of individual judgement -- as some designers are more risk-averse than others. Therefore, it is incorrect to say that there is a "right" sampling plan for a particular situation.