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Introduction to Statistical Quality Control, 4th Edition

Chapter 14

Lot-by-Lot Acceptance Sampling for Attributes


14-1. The Acceptance-Sampling Problem

• Acceptance sampling is concerned with inspection and decision making regarding products.

• Three aspects of sampling are important:1. Involves random sampling of an entire “lot”2. Accept and Reject Lots (does not achieve

quality improvement) “Lot sentencing”3. Audit tool



• Three approaches to lot sentencing:

1. Accept with no inspection

2. 100% inspection

3. Acceptance sampling



Why Acceptance Sampling and Not 100% Inspection?

• Testing is destructive• Cost of 100% inspection is high• 100% inspection is not feasible (require

too much time)• If vendor has excellent quality history



14-1.1 Advantages and Disadvantages of Sampling Advantages• Less expensive• Reduced damage• Reduces the amount of inspection errorDisadvantages• Risk of accepting “bad” lots, rejecting “good” lots.• Less information generated• Requires planning and documentation



14-1.2 Types of Sampling Plans • There are variables sampling plans and attribute

sampling plans (this chapter concentrates on attributes)

1. Single sampling plan2. Double-sampling plan3. Multiple-sampling plan4. Sequential-sampling



14-1.3 Lot Formation

• Considerations before inspection:– Lots should be homogeneous– Larger lots more preferable than smaller lots– Lots should be conformable to the materials-

handling systems used in both the vendor and consumer facilities.



14-1.4 Random Sampling• The units selected for inspection should be

chosen at random.

• Random samples are not used, bias can be introduced.

• If any judgment methods are used to select the sample, the statistical basis of the acceptance-sampling procedure is lost.


14-2. Single-Sampling Plans For Attributes

14-2.1 Definition of a Single-Sampling Plan• A single sampling plan is defined by sample size, n, and the

acceptance number c. Say there are N total items in a lot. Choose n of the items at random. If at least c of the items are unacceptable, reject the lot.

• N = lot size

• n = sample size

• c = acceptance number

• d = observed number of defectives

• The acceptance or rejection of the lot is based on the results from a single sample - thus a single-sampling plan.



14-2.2 The OC Curve• The operating-characteristic (OC) curve measures

the performance of an acceptance-sampling plan.

• The OC curve plots the probability of accepting the lot versus the lot fraction defective.

• The OC curve shows the probability that a lot submitted with a certain fraction defective will be either accepted or rejected.



14-2.3 Designing a Single-Sampling Plan with a Specified OC Curve

• Let the probability of acceptance be 1 - for lots with fraction defective p1.

• Let the probability of acceptance be for lots with fraction defective p2.

• Assume binomial sampling (with type-B OC curves) is appropriate.



14-2.3 Designing a Single-Sampling Plan with a Specified OC Curve

• The sample size n and acceptance number c are the solution to

c

0d

dn2

d2

c

0d

dn1

d1

)p1(p)!dn(!d

!n

)p1(p)!dn(!d

!n1



Example• Consider constructing a sampling plan for which

– p1 = 0.01

= 0.05

– p2 = 0.06

= 0.10

– N = 1000

• Using computer software or a graphical approach (using an appropriate binomial nomograph) it can be shown that the necessary values of n and c are 85 and 2, respectively.


14-4. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859)

14-4.1 Description of the Standard• Developed during World War II• MIL STD 105E is the most widely used

acceptance-sampling system for attributes• Gone through four revisions since 1950.• MIL STD 105E is a collection of sampling

schemes making it an acceptance-sampling system


14-4. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) 14-4.1 Description of the Standard• Three types of sampling are provided for:

1. Single2. Double3. Multiple

• Provisions for each type of sampling plan include

1. Normal inspection2. Tightened inspection3. Reduced inspection



14-4.1 Description of the Standard• The acceptable quality level (AQL) is a primary focal

point of the standard• The AQL is generally specified in the contract or by the

authority responsible for sampling.• Different AQLs may be designated for different types of

defects.• Defects include critical defects, major defects, and minor

defects.• Tables for the standard provide are used to determine the

appropriate sampling scheme.



14-4.1 Description of the Standard• Switching Rules

– Normal to tightened– Tightened to normal– Normal to reduced– Reduced to normal– Discontinuance of inspection


14-4. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) 14-4.2 Procedure1. Choose the AQL2. Choose the inspection level3. Determine the lot size4. Find the appropriate sample size code letter from Table

14-45. Determine the appropriate type of sampling plan to use

(single, double, multiple)6. Enter the appropriate table to find the type of plan to be

used.7. Determine the corresponding normal and reduced

inspection plans to be used when required.



Example• Suppose a product is submitted in lots of size

N = 2000. The AQL is 0.65%. Say we wanted to generate normal single-sampling plans.

• For lots of size 2000, (and general inspection level II) Table 14-4 indicates the appropriate sample size code letter is K.

• From Table 14-5 for single-sampling plans under normal inspection, the normal inspection plan is n = 125, c = 2.



14-4.3 Discussion• There are several points about the standard that

should be emphasized:1. MIL STD 105E is AQL-oriented2. The sample sizes selected for use in MIL STD 105E

are limited3. The sample sizes are related to the lot sizes.4. Switching rules from normal to tightened and from

tightened to normal are subject to some criticism.5. A common abuse of the standard is failure to use the

switching rules at all.



14-4.3 Discussion• ANSI/ASQC Z1.4 or ISO 2859 is the civilian standard

counterpart of MIL STD 105E.• Differences include:

1. Terminology “nonconformity”, “nonconformance”, and “percent nonconforming” is used.

2. Switching rules were changed slightly to provide an option for reduced inspection without the use of limit numbers

3. Several tables that show measures of scheme performance were introduced

4. A section was added describing proper use of individual sampling plans when extracted from the system.

5. A figure illustrating switching rules was added.

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Documents

mil std 105e

statistical

military standard

oc curve

sampling plans

sampling plan

sampling problem14

ansiasqc z1