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Re: C=0 Sampling plan from AQL

From: Stan.Hilliard@samplingplans.com
Date: 12 Nov 2002
Time: 01:10:58

Comments

Roland,

You said: No change in producer's or consumer's points.

For n=315, acc=10, rej=11, using software program TP105, the producer's point is (AQL=1.9704%, alpha=0.05,) and the consumer's point is (RQL=5.3253%, beta=0.05).

It is not possible to select a C=0 sampling plan that has the same producer's and consumer's points as your current plan. The oc curve of your current sampling plan has an S-shaped oc curve. The S-shape is which enables the oc curve to go through any two points that you pick. See: samplingplans.com/modern3.htm#EVALUATE

On the other hand, C=0 sampling plans do not have the S-shape. They have oc curves that follow an exponential shape - like a loose rope. For this reason, you can only pick one point on the curve. There is only one C=0 oc curve going through that point, so you can't pick another point. Thus if you pick the consumer's point, you cannot also pick the producer's point, and vice versa.

It is my opinion that the universal C=0 that QS9000 imposes is an irrational approach to the design of sampling plans. I have never met a person who understands the oc curve who can make sense out of choosing Ac instead of choosing points to protect the consumer and the producer. Are you willing to reject a lot containing 35,000 items because one inspector saw one visual defect in a sample? Don't you have inspector to inspector variability?

I believe that you should set AQL no better than process capability. Otherwise you would be frequently rejecting lots of good product.

Example 1: Since your current plan is based on process capability, I suspect that p'~2 percent defective. If you were to change the current C=10 to zero, keeping n=315, the AQL and RQL would change to 0.0163% and 0.9465% respectively. Having this RQL, which is less than process capability, guarantees that most lots from the current process will be rejected. You can get around this by keeping C=0 and reducing the sample size to the point where 2% defective lots will typically pass. The plan is n=2, C=0, (alpha=0.05, beta=0.05, AQL=2.5321%, RQL=77.6393%) In this case, n=3 is too large because AQL=1.6952%, which is better than process capability and will reject an excessive number of lots.

The example above with n=2 will protect you, the producer, from loss due to rejecting current lots. However, in the event that you produce a lot that is off-grade, the RQL does not offer the consumer much protection against passing it.

Example 2: You can keep the current consumer's point for the C=0 plan. Again using software program TP105, n=55, C=0, (alpha=0.05, beta=0.05, AQL=0.0932%, RQL=5.3011%) Here RQL is approximately the same as the current sampling plan, but AQL is far less than current process capability. This will lead to rejection of most lot having current quality levels.

These two examples illustrate that, for C=0, you cannot choose both the producer's point and the consumer's point. Thus, universal C=0 is an irrational criterion. You might ask then why then C=0 is specified in QS9000. I think that the economics rules. The economic need of the producer-company to keep and expand it's customer base outweighs the its need to provide that final guarantee of quality that a good sampling plan would offer. Therefore the producer-company has a very strong incentive to conform to the vision of its customer.

Faced with your dilemma, I would try the following:

1) For variables, use variables sampling plans. These will not be subject to the C=0 rule. Match their oc curves to the current attribute plan.

See: samplingplans.com/modern3.htm#MATCHING Software program TP414 will design variables sampling plans.

2) For Attributes, use a sequential attribute plan. This will allow accepting on zero if there are no early defectives in the sample (at n=85 Ac=0 for your plan) but will require larger n and Ac otherwise. With this approach, you will need to produce a report for QS9000 purposes to demonstrate that the sequential sampling plan and Fixed-n C=0 plans were analyzed and compared using oc curves.

See: samplingplans.com/outputbinomial.htm Software program TP105 will design sequential attribute plans.

Sincerely, Stan Hilliard

PS: I have a four page article that I could fax to you from Quality Progress by R. C. Baker describing expected cost increases with C=0 plans.


Last changed: November 20, 2007