c7 acceptance sampling system

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ACCEPTANCE SAMPLING SYSTEM

UteM DMFD 3582126

CHAPTER NO 7 : ACCEPTANCE SAMPLING SYSTEM

INTRODUCTION

This chapter covers three types of acceptance sampling plans;

a. lot-by-lot acceptance sampling for attributes

b. Continuous production acceptance sampling for attributes

c. Acceptance sampling for variables.

This chapter it is helpful to distinguish among:

a. An individual sampling plan that states the lot size, sample size or sizes, and the

acceptance criteria.

b. A sampling plan scheme that is a combination of sampling plan with switching rules

and possibly a provision for discontinuance

c. A sampling system that is a collection of sampling schemes

LEARNING OBJECTIVES

The objectives of this unit are to :

1. Define an individual sampling plan that states the lot size, sample size or sizes, and the

acceptance criteria.

2. Use a sampling plan scheme that is a combination of sampling plan with switching rules

and possibly a provision for discontinuance.


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7.1 ANSI/ASQ Z1.4 1993

7.1.1 INTRODUCTION

The standard is applicable, but not limited to attribute inspection of the folowing; end

items, components and raw materials, operations, materials in process, supplies in storage,

data or records, etc. Sampling plans of this standard are intended to be used for a

continuing series of lots, but plans may be designed for isolated lots by consulting the OC

curve to determine the plan with desired protection. The standard provides for three types of

sampling; single, double, and multiple. For each sampling plan, provision is made for normal,

tightened or reduced inspection. In this chapter, we only focused on he single sampling plan.

Figure 7.1: Comparison of Normal (N), Tightened (T) and Reduced (R) inspection.

Tightened inspection is used when the producers recent quality history has

deteriorated. Acceptance requirements under tightened inspection are more stringent than

under normal inspection. Reduced inspection is used when the producers recent quality

history has been exceptionally good. Figure X, illustrates the differences among the OC

curves for Normal (N), Tightened (T), and Reduced (R), inspection.

The number inspected under reduced inspection is less than under normal

inspection. The decision as to the type of plan to use (single, double, or multiple) is left to the

responsible authority. Normal inspection is used at the start of inspection with changes to

tightened or reduced inspection being a function of recent quality performance.


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Product is submitted in homogeneous lots with the manner of presentation and

identification designated or approved by the responsible authority (consumer). Samples are

selected at random without regard to their quality. Non-accepted lots are resubmitted after all

nonconforming units are removed or nonconformities corrected. The responsible authority

will determine whether reinspection should include all types or classes of nonconformities or

the particular types or classes of nonconformities that caused initial non acceptance.

7.1.2 ACCEPTABLE QUALITY LEVEL

The Acceptable Quality Level (AQL) is the most important part of the standard

because the AQL and the sample-size code letter index the sampling plan. AQL is defined

as the maximum percent nonconforming (or the maximum number of nonconformities per

100 units) that, for purpose of sampling inspection, can be considered satisfactory as a

process average. The phrase can be considered satisfactory is interpreted as a producers

risk, , equal to 0.05; actually, varies from 0.01 to 0.10 in the standard.

When the standard is used for percent nonconforming plans the AQLs range from

0.010% to as high as 10%. For nonconformity-per-unit plans, AQLS are possible from 0.010

nonconformities per 100 units to 1000 nonconformities per 100 units. The AQLS are in a

geometric progression, each being approximately 1.585 times the preceding one.The AQL is designated in the contract or by the responsible authority. Different AQLs

may be designated for groups of nonconformities considered collectively or for individual

nonconformities. Groups of nonconformities or nonconforming units can have different

AQLs, with lower values for critical ones and higher values for minor ones. AQLs are

determined from (1) historical data; (2) empirical judgment; (3) engineering information, such

as function, safety, interchangeable manufacturing, life testing, etc.; (4) experimentation by

testing lots with various percent nonconforming or nonconformities per 100 units; (5)

producers capability; and, (6) in some situations, the consumers requirements. AQLdetermination is a best-judgment decision. The standard helps to determine the AQL since

only a finite number are available in the standard. It is a frequent practice to use AQL values

of 0.10% or less for critical, 1.00 for major, and 2.5% for minor. The acceptance number for

critical should be zero.

The AQL is a reference point on the OC curve. It does not imply that any percent

nonconforming or nonconformities per 100 units is tolerable. The only way the producer can

be guaranteed that a lot will be accepted is to have 0% nonconforming or to have the

number of nonconforming units less than or equal to the sampling plan acceptance number.


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7.1.3 SAMPLE SIZE

The sample size is determined by the lot size and the inspection level. The inspection

level to be used for a particular requirement will be prescribed by the responsible authority.

Three general inspection levels (I, II, and III) are given in Table 7.1. The different levels of

inspection provide approximately the same protection to the producer but different

protections to the consumer. Inspection level II is the norm, with level I providing about one-

half the amount of inspection and level III providing about twice the amount of inspection.

Thus, level III gives a steeper OC curve and consequently more discrimination and

increased inspection costs. Figure 7.2 illustrates the differences among the OC curves for

inspection levels I, II, and III.

Table 7.1: Sample size code letters (Table 1 of ANSI/ASQ Z1.4-1993)

The decision on the inspection level is also a function of the type of product. For

inexpensive items, for destructive testing, or for harmful testing, inspection level II should be

considered. When subsequent production costs are high or when the items are complex and

expensive, inspection level III may be applicable. The consumer should change the

inspection level as conditions warrant. Four additional special levels (S-1, S-2, S-3, and S-4)

are given in Table 7.1 and may be used where relatively small sample sizes are necessary

and large sampling risks can or must be tolerated.


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Figure 7.2: Comparison of inspection levels, I, II, and III.

Table 7.1 does not immediately provide the sample size based on the lot size and

inspection level but does give a sample-size code letter. The AQL and the sample-size code

letter index the desired sampling plan.

Implementation

The steps required to use the plan are as follows:

1. Determine the lot size (usually the responsibility of materials management)

2. Determine the inspection level (usually level II it can be changed if conditions

warrant).

3. Enter table and find sample-size code letter.

4. Determine the AQL

5. Determine the type of sampling plan (single, double, or multiple)

6. Enter the appropriate table to find the sampling plan

7. Start with normal inspection and change to tightened or reduced based on switching

rules.

Example problems for single sampling plans are given in subsequent sections.


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7.1.4 SINGLE SAMPLING PLANS

The single sampling plans of the standard are given in Table 7.2, 7.3, and 7.4 for

normal, tightened, and reduced inspection, respectively. In order to use the tables, the AQL,

lot size, inspection level, and type of sampling plan are needed. An example problem will

illustrate the technique.

For a lot size of 2000, an AQL of 0.65% and inspection level of III, determine the

single sampling plans for normal, tightened, and reduced inspection.

Normal. Using the lot size N= 2000 and inspection level of III, the sample size code

letter L is obtained from Table 7.1. From table 7.2 (single sampling plans for normal

inspection), the desired plan is obtained for code letter L and AQL 0.65%. It is n = 200, Ac =

3, and Re = 4. Thus, from a lot of 2000, a random sample of 200 is inspected. If 3 or fewer

nonconforming units are found, the lot is accepted, if 4 or more nonconforming units are

found, the lot is not accepted.

Tightened. The sample-size code letter, L, is the same as the one for normal

inspection. From Table 7.3 (single sampling plans for tightened inspection), the desired plan

is obtained for code letter L and AQL 0.65%. It is n = 200, Ac = 2 and Re = 3. Thus, from a

lot of 2000, a random sample of 200 is inspected. If 2 or less nonconforming units are found,the lot is accepted, if 3 or more nonconforming units are found, the lot is not accepted.

Reduced. The sample-size code letter, L, is the same as the one for normal

inspection. From Table 7.4 (single sampling plans for reduced inspection), the desired plan

is obtained for code letter L and AQL 0.65%. It is n = 80, Ac = 1 and Re = 4. Thus, from a lot

of 2000, a random sample of 80 is inspected. If 1 or fewer nonconforming units are found,

the lot is accepted, if 4 or more nonconforming units are found, the lot is not accepted. If 2 or

3 nonconforming units are found, the lot is accepted, but the type of inspection changes fromreduced to normal. A change to normal inspection is also required when a lot is not accepted

In comparing the three plans, notice that the acceptance requirements are most

stringent for tightened than for normal inspection. In fact, a sample with 3 nonconforming

units is accepted under normal inspection but not accepted under tightened inspection. The

sample size for reduced inspection is approximately 40% of the sample size of normal or

tightened inspection, which represents a considerable saving in sampling costs.

If a vertical arrow is encountered, the first sampling plan above or below the arrow is

used. When this occurs, the sample-size code letter and the sample size change. For


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example, if a single sample tightened plan (Table 7.3) is indexed by an AQL of 4.0% and a

code letter D, the code letter changes to F and the sample size changes from 8 to 20. If the

vertical arrow points down, it means that the sample size is too small to make a decision; if

the vertical arrow points up, it means that a decision can be made with a smaller sample

size. In some cases, the sample size will exceed the lot size and, in those cases, 100%

inspection is required.

Normal, Tightened, and Reduced Inspection

Unless otherwise directed by the responsible authority, inspection starts with the

normal inspection condition. Normal, tightened, or reduced inspection will continue

unchanged for each class of nonconformities or nonconforming units, or until the switching

procedures given below require a change.

Normal to tightened. When normal inspection is in effect, tightened inspection shall

be instituted when 2 out of 5 consecutive lots or batches have not been accepted on original

inspection (i.e., ignoring resubmitted lots).

Tightened to normal. When tightened inspection is in effect, normal inspection shall

be instituted when 5 consecutive lots or batches are accepted on original inspection.


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Table 7.2: Single Sampling Plans for Normal Inspection (Table II-A of ANSI/ASQ Z1.4-1993)


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Table 7.3: Single Sampling Plansfor Tightened Inspection (Table II-A of ANSI/ASQ Z1.4-

1993)


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Table 7.4: Single Sampling Plans for Reduced Inspection (Table II-A of ANSI/ASQ Z1.4-

1993)


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Normal to reduced. When normal inspection is in effect, reduced inspection shall be

instituted provided all following conditions are satisfied.

1. The preceding 10 lots or batches have been on normal inspection and all of the lots

have been accepted on original inspection.

2. The total number of nonconforming units (nonconformities) in the samples from the

preceding 10 lots or batches is equal to or less than the applicable number given in

Table 7.5. For example, if the total number inspected for the past 10 lots or batches

is 600 and the AQL is 2.5%, the limit number is 7. Therefore, to qualify for reduced

inspection, the number nonconforming in the 600 inspected must be equal or less

than 7. In some cases, more than 10 lots or batches are necessary to obtain a

sufficient number of sample units for a particular AQL, as indicated by the note of

Table 7.5. This condition is optional.

3. Production is at steady rate. In other words, no difficulties, such as machine

breakdowns, material shortages, or labor problems, have occurred recently.

4. Reduced inspection is considered desirable by the responsible authority (consumer).

The consumer must decide if the savings from fewer inspections warrant the

additional record-keeping and inspector training expenses.

Reduced to normal. When reduced inspection is in effect, normal inspection shall be

instituted provided any of the four conditions below are satisfied on original inspection.

1. A lot or batch is not accepted

2. When the sampling procedure terminates with neither acceptance nor rejection

criteria having been met, the lot or batch is accepted, but normal inspection is

reinstated starting with the next lot.

3. Production is irregular or delayed

4. Other conditions, such as customer desire, warrant that normal inspection will be

instituted.

If 5 consecutive lots or batches remain on tightened inspection, then inspection

should be discontinued pending action to improve the quality of submitted material.


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Table 7.5: Limit Numbers for Reduced Inspection (Table VIII of ANSI/ASQ Z1.4-1993)


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7.2 ANSI/ASQ Standard Q3 - 1988

This standard is to be used for inspection of isolated lots by attributes. It compliments

ANSI/ASQ Z1.4-1993, which is appropriate for a continuous stream of lots. This standard

indexes tables by Limiting Quality (LQ) values and is applicable to type A or type B lots or

batches. These concepts were discussed in the last chapter. The LQ values are determined

by the same techniques used to determine AQL values. There are two schemes. One

scheme, given in Table 7.6, is designed to be used for lots that are isolated or mixed or that

have an unknown history as far as both vendor and vendee know. To use the table that lot

size and LQ value must be known.

Table 7.6: Single Sampling Plans Indexed by Nominal Limiting Quality (LQ)


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Example 1Given a lot size of 295 and an LQ value of 3.15%, determine the sampling plan. From

Table 7.6 the solution is

n = 80

Ac = 0

The nominal values of the LQ are based on = 0.10. Because we are working with

whole numbers, the actual LQ values will vary slightly from the nominal. Note the LQ is given

as a percent.

The second scheme is used when a vendor is producing a continuous stream of lots

and sends one or few to a customer who will consider them as isolated lots. This situation

would frequently occur in the purchase of small quantities of a raw material. Tables are given

for LQ values of 0.5, 0.8, 1.25, 2.0, 3.15, 5.0, 8.0, 12.5, 20.0, and 32.0%. Only the table for

3.15% is reproduced, as Table 7.7. The tables list the process quality in terms of AQL (as

used in ANSI/ASQ Z1.4-1993), which are equivalent to the LQ for different lot sizes.

Example 2Given a lot size of 295, Inspection Level II, and an LQ value of 3.15%, where the

isolated lot is from a vendor with a continuous stream of product, determine the sampling

plan. From Table 7.7 the solution is

n = 125

Ac = 1

Note that the information in the last 5 columns can be used to plot the OC curves.

Also note that the information in Table 7.7 comes from ANSI/ASQ Z1.4. The only difference

is the indexing by LQ values in order to make it easier to use.


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Table 7.7: Single Sampling Plans for Nominal Limiting Quality 3.15%


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SUMMARY

In this chapter we have studied that

1. There are 2 standard can be used; ANSI/ASQ Z1.4-1993 and ANSI/ASQ Standard Q3-1988.

2. Each sampling plan must have the lot size, sample size or sizes, and the acceptance

criteria.

3. There are switching rules as guidance for a sampling plan scheme that is a combination

of sampling plan.

REFERENCES

1. Dale H. Besterfield, (2004), Quality Control, 7th Edition, Prentice Hall.

2. Douglas C. Montgomery, (2005),Introduction to Statistical Quality Control, 5th

Edition, John Wiley and Sons.

3. Frank M. Gryna, Richard C.H. Chua, Joseph A. Defeo, (2007), Jurans Quality

Planning and Analysis, 5th Edition, Mc Graw-Hill.

c7 acceptance sampling system

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