Reading Assignment:

Download and read Chapter 11 in Essentials of Quality With Cases and Experiential Exercises.  Review the Discussion Questions at the end of the chapter to be sure that you understand what you have read.

Sower, J. Motwani, & M. Savoie. "Are Acceptance Sampling and Statistical Process Control Complementary or Incompatible?"  Quality Progress 26: 8 (September 1993), pp. 85-89.

Consider that you are the quality inspector in a jelly bean factory.  Your job is to insure the quality of the jelly beans produced.  You determine that taste, color, and shape are the important quality characteristics to use.  100% inspection of color and shape is feasible, but 100% inspection for taste would leave no product to sell (i.e. you would have to taste every jelly bean).

Even nondestructive inspection of every unit produced often is not an option due to cost or time constraints.  For example, if the units to be inspected must be taken off-line to a laboratory and subjected to extensive chemical or physical tests in order to determine whether they conform to specifications, time and cost may limit the number of samples that can be tested.  In this situation, attempting to use 100% inspection will result in a backlog of samples to be tested or will ruin the budget.  In any case, 100% inspection is not a guarantee of zero defects. Occasional inattention of inspectors, misinterpretation of standards, the hypnotic effect of performing the same inspection on the same type units over an 8-hour shift, etc. sometimes lead to the inadvertent passing of defective products. (Imagine having the job of visually inspecting jelly beans on a conveyor belt for shape and color 8 hours a day.)

The necessity for 100% inspection of every item is sometimes an indicator of an out of control process which is not receiving appropriate attention or corrective action. Management sometimes uses 100% inspection to "sort out the bad from the good." Then, 100% inspection is actually a crutch used as an inappropriate substitute for corrective action or process improvement.  You cannot inspect quality into a product!  100% inspection may be needed in the short term while a process problem is being identified and resolved, but it should not be used as a substitute for solving the problem.

[NOTE:  Automated testing does afford the opportunity to conduct 100% inspection of key quality characteristics in a cost-effective manner.  For example, soft drink manufacturers can use a simple, two-beam optical device to insure that bottles are filled to the correct level.  If the top beam is blocked, the bottle is too full.  If the bottom beam is not blocked, the bottle is not sufficiently full.  Automated inspection and testing will be discussed in Ch 7]

Acceptance sampling is an approach to sampling a lot to determine the proper disposition of that lot. The lot disposition is determined by inspecting an appropriately sized random sample from the lot. Because acceptance sampling is a statistically valid process, the probability of wrongly accepting a defective lot (Type II error) or wrongly rejecting an acceptable lot (Type I error) can be estimated for each sampling plan using the operating characteristics (OC) curve.

There are standard sampling plans for attributes (ANSI/ASQC Z1.4 or MIL STD 105) and variables (ANSI/ASQC Z1.9 or MIL STD 414) that are based on acceptable quality levels (AQL). There are also sampling plans based on the lot tolerance percent defective (LTPD).  Sometimes management is confused about the difference between AQL and LTPD.  "The AQL is the highest proportion defective that is considered acceptable as a long-run average for the process."  Therefore a lot inspected to a 4.0% AQL may be passed by a Z1.4 sampling plan even if its true proportion defective is 8.0% or higher.  The OC curve for the plan shows the probability of this occurring.  "The LTPD is the highest proportion defective that is considered acceptable for a given lot."  Confusion results when management thinks of AQL as if it were LTPD, accusing a supplier of incompetence (providing a lot with 8.0% defective) when that supplier is simply following the agreed upon (Z1.4 4.0% AQL) sampling procedure.

Note that Z1.4 can be used where the extent of nonconformance of product can be stated in terms of percent nonconforming or in terms of nonconformities per hundred units.  It is possible to have more than one nonconformity in a unit.  Therefore an AQL above 100 is possible.

Consider this telephone call from a Purchasing Manager to a supplier.  "We tracked your last lot of materials through production.  It actually contained 8% defective units.  I thought we were using a 4% AQL sampling plan.  How could this happen???  What are you doing to make sure it never happens again?"  This reflects the Purchasing Manager's lack of understanding of the definition of AQL.  He really doesn't understand what he told the supplier to do in the contract (i.e. Use a 4.0% AQL sampling plan).  He apparently believes that, using that sampling plan, he will receive no lots containing more than 4.0% defective units.  The Quality Manager should show the Purchasing Manager the OC curve for the sampling plan and explain the difference between AQL and LTPD.

The average outgoing quality limit (AOQL) is the maximum average outgoing quality (AOQ) for a given acceptance sampling plan for all levels of lot quality given that non-conforming lots are subjected to 100% inspection with replacement of non-conforming units with confirming units.  Where lots contain low levels of non-conforming units, the probability of rejection is low and the AOQ (proportion of nonconforming units in the outgoing stream) is low.  As the level of non-conforming units increases, the AOQ increases.  As the level of non-conforming units increases further, the probability of a lot being accepted declines.  More and more lots are rejected and subjected to 100% inspection.  These "clean" lots now enter the outgoing stream along with accepted lots thus lowering the AOQ (the accepted lots with high levels of non-conforming units are "diluted" by "clean" lots with no non-conforming units).  The highest point on the AOQ curve is defined as the AOQL (illustrated in Lesson 9 Presentation).  If the level of non-conforming units reaches a high enough point, then virtually all lots will be rejected leading to 100% inspection and an AOQ of 0% (because all non-conforming units have been identified and replaced).

        Answer Discussion Questions 1-16 at the end of Chapter 11of the text.

Do Problems 1-13 at the end of Chapter 11 of the text.

Binder clips are packaged 12 to a box and 12 boxes to a carton.  You have received a lot consisting of 4 cartons of binder clips.  Use ANSI/ASQC Z1.4 (see Fig. 10-12 in Chapter 11) to determine a sampling plan to decide whether to accept or reject the lot.  Use General Inspection Level I, single sampling, and an AQL of 2.5.  In your report include how many and which individual clips are to be inspected (be sure to use random sampling) and also the accept/reject criteria.  If in inspecting your sample you find 3 defective binder clips, what is the disposition of the lot? If the true fraction defective in the lot is 10%, what is the probability of accepting the lot?