Dodge (1969b, p. 156) has indicated that in the early days of the development of military standards during World War II, a distinction became apparent between acceptance sampling plans, on one hand, and acceptance quality control, on the other. The former are merely specific sampling plans, which, when instituted, prescribe conditions for acceptance or rejection of the immediate lot inspected. The latter may be compared to process quality control, which utilizes various indicators (such as control charts) and strategies (such as process capability studies) to maintain and improve existing levels of quality in a production process. In like manner, acceptance quality control exploits various acceptance sampling plans as tactical elements in overall strategies designed to achieve desired ends. Such strategies utilize the elements of systems engineering, industrial psychology, and, of course, statistics and probability theory, together with other diverse disciplines, to bring pressures to bear to maintain and improve the quality levels of the submitted product. For example, in the development of the Army Ordnance sampling tables in 1942, Dodge (1969b, p. 156) points out that
basically the “acceptance quality control” system that was developed encompassed the concept of protecting the consumer from getting unacceptably defective material and encouraging the producer in the use of process quality control by varying the quantity and severity of acceptance inspections in direct relation to the importance of the characteristics inspected and in inverse relation to the goodness of the quality level as indicated by those inspections.
The resulting tables utilize not just one sampling plan, but many in a scheme for quality improvement.
This book stresses acceptance quality control in recognition of the importance of such systems as a vital element in the control of quality. There is little control of quality in the act of lot acceptance or rejection. While the utilization of sampling plans in assessing lot quality is an important aspect of acceptance sampling, it is essentially short run in effect. The long-run consequences of a well-designed system for lot acceptance can be more effective where applicable. Thus, an individual sampling plan has much effect of a long sniper, while the sampling scheme can provide a fusillade in the battle for quality improvement.
Acceptance Quality Control
Individual sampling plans are used to protect against irregular degradation of levels of quality in submitted lots below that considered permissible by the consumer. A good sampling plan will also protect the producer in the sense that lots produced at permissible levels of quality will have a good chance to be accepted by the plan. In no sense, however, is it possible to “inspect quality into the product.” In fact, it can be shown (Mood 1943) that if a producer continues to submit to the consumer the product from a process with a constant proportion defective, lot after lot, simple acceptance or rejection of the lots submitted will not change the proportion defective the consumer will eventually receive. The consumer will receive the same proportion defective as was in the original process.
This idea may be simply illustrated as follows. Suppose you are in the business of repackaging playing cards. You have an abundance of face cards (kings, queens, and jacks) and so submit an order to the printer for 5000 cards having an equal selection of nonface cards. Any face cards, then, can be considered as defectives if they are found in the shipment. The cards are supposed to come to you in packages of 50 resembling standard 52-card decks. Unknown to you, the printer has mixed up your order and is simply sending standard decks. Your sampling plan is to accept the deck if a sample of one card is acceptable. The lot size is actually, of course, 52.
What will be the consequences? Nearly 12 of the 52 cards in a standard deck are face cards, so the probability of finding a face card on one draw is 12/52 = 0.23, or 23%. This means that in 100 decks examined there should be roughly 23 rejections. Suppose these rejected decks are thrown into the fire, what will be the proportion of face cards in the accepted material? Why 23%, of course, since all the decks were the same. Thus, the sampling plan had no effect on the quality of the material accepted while the process proportion defective remained constant. The proportion defective accepted is the same as if no inspection had ever been performed.
Suppose, instead, the printer had become even more mixed up. The printer fills half the order with ordinary playing cards and the other half with cards from pinochle decks. Pinochle decks are composed of 48 cards, half of which (or 24) are face cards. The printer ships 50 ordinary decks (2600 cards) and 50 pinochle decks (2400 cards). Inspection of the 50 ordinary decks by the same plan will reject about 23%, or about 12 of them. The remaining 38 will pass and be put into stock. Of the 50 pinochle decks, however, half will be rejected and so 25 will go into stock.
Some calculation will show that, with no sampling (i.e., 100% lot acceptance), the stock would consist of
face cards out of a total stock of 5000 cards or
face cards.
Using the sampling plan, simple and ineffective as it was, the stock would consist of
