acceptance sampling (1)

Quality Control

Chapter 10- Acceptance Sampling Systems

RMN

Outline

Lot-by-lot acceptance sampling plans for attributes

Acceptance sampling plans for continuous production

Acceptance sampling plans for variables

Learning Objectives

Determine the sampling plan using ANSI/ASQ Z1.4.

Know the switching rules for ANSI/ASQ Z1.4.

Categorize the various sampling plan systems in terms of lot-by-lot, continuous production, attributes or variables.

Learning Objectives-contd.

Describe the various sampling plan systems and know their function (advantages, disadvantages, purpose etc.).

Determine the sampling plan using the Dodge Romig Tables

Construct the OC Curve for a chain sampling plan.

Learning Objectives-contd.

Be able to use the Shainin Lot Plot Method.

Determine the sampling plan ANSI/ASQ S1

Determine whether a lot is accepted or rejected using ANSI/ASQ Z1.9

Lot-by-Lot Acceptance Sampling Plans for Attributes

Devised in 1942 at Bell Labs

Later became MIL-STD-105E

ISO-2859

ANSI/ASQ Z1.4

Wording & terminology changes

Additional tables added

ANSI/ASQ Z1.4

This standard is applicable to:

End items

Components and raw materials

Operations

Materials in process

Supplies in storage

Maintenance operations

Data or records

ANSI/ASQ Z1.4

Intended to be used for a continuing

series of lots, but may be designed for

isolated lots.

Standard provides for single, double, and

multiple sampling plans.

Provision is also provided for normal,

tightened, or reduced inspection.

Plan is specified by the AQL, and sample-

size code.

ANSI/ASQ Z1.4

Normal inspection is used at the start of

inspection with changes being a function of

recent quality history.

Tightened inspection:

Generally used when producers recent

quality history has deteriorated.

ANSI/ASQ Z1.4

Reduced inspection:

Used when the producers recent quality

history has been exceptionally good.

Decision concerning what type of plan to use is

left to the responsible authority.

Nonconformities are classified such as critical,

major

ANSI/ASQ Z1.4

Sample Size Code Letters

Comparison of Inspection levels

III

1086

Percent Nonconforming (100Pa)

100

95

80

60

40

20

0

100=10

= 0.05

Per

cent

of L

ots

Acc

epte

d (1

00P

a)

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II I

I = 1/2 n

II = n

III = 2n

ANSI/ASQ Z1.4

AQL

The AQL is the most important part of the

standard since the AQL and sample size dictate

the plan used.

AQL is defined as the maximum percent

nonconforming that can be considered

satisfactory as a process average.

Satisfactory = Producers risk,

Usually 0.05

ANSI/ASQ Z1.4

AQL

AQL is specified by contract or

responsible authority.

AQL may be determine from

historical data, empirical judgment,

engineering information,

experimentation, producers

capability, consumers

requirements.

ANSI/ASQ Z1.4

AQL

AQL is specified by contract or responsible

authority.

AQL may be determine from historical data,

empirical judgment, engineering information,

experimentation, producers capability,

consumers requirements.

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ANSI/ASQ Z1.4

Sample Size

Determined by lot size and inspection

level

Use of sample-size code

Inspection level is determined by the

responsible authority.

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ANSI/ASQ Z1.4

Sample Size

Different levels of inspection provide

approximately the same protection to the

producer, but different protections to the

consumer.

Plan provides for special levels to be

used where relatively small sample sizes

are necessary and large sampling risks

must be tolerated. (S-1, S-2, S-3, S-4)

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Besterfield: Quality Control, 8th ed.. 2009 Pearson Education, Upper Saddle River, NJ 07458.

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Implementation

Determine lot size

Determine inspection level

Find sample-size code letter in table

Determine AQL

ANSI/ASQ Z1.4

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Implementation contd.

Determine type of sampling plan

Find sampling plan in appropriate table

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

ANSI/ASQ Z1.4

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What an AQL means is that as long as a supplier maintains his/her process average (% defective) at the assigned AQL or lower, there is a very high probability that shipments from that supplier, when inspected using ASQ Z1.4 sampling plans, will be accepted.

AQL

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By the same token, there is a very high probability that shipments, when inspected using ASQ Z1.4 sampling plans, will be rejected if a supplier's process average (% defective) remains higher than the assigned AQL.

AQL

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Single sampling plans

Start by identification of AQL, lot size, inspection level, and type of sampling plan.

Locate appropriate plan parameters in tables.

Double and Multiple Sampling

Similar procedures as single sampling

ANSI/ASQ Z1.4

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Normal, Tightened, and Reduced Inspection

Start with normal inspection

Switching Procedures

Normal to tightened

Institute when 2 out of 5 consecutive lots not accepted on

original inspection

Tightened to normal

Institute when 5 consecutive lots accepted

If not, then discontinue inspection under this plan

ANSI/ASQ Z1.4

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Normal to reduced

Institute when: (all of the following)

Preceding 10 lots on normal inspection have been accepted

Total nonconforming in preceding 10 samples is less than number identified in Table 10-5.

Production is at a steady rate

Reduced inspection is considered desirable by responsible authority

ANSI/ASQ Z1.4

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Reduced to normal

Institute when: (any of the following)

A lot is not accepted

Sampling procedure terminates with neither acceptance or rejection criteria have been met

Production is irregular or delayed

Other conditions

ANSI/ASQ Z1.4

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Standard is designed for use where units of product are produced in a continuing series of lots or batches.

If a sampling plan is desirable for a lot or batch of an isolated nature, it should be chosen based on the Limiting Quality (LQ) and consumers risk, b.

These tables are included in the standard, but not the textbook.

Or use ANSI/ASQ Standard Q3

ANSI/ASQ Z1.4

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Standard is used for inspection of isolated lots by attributes.

Provides indexed tables by Limiting Quality, LQ.

ANSI/ASQ Standard Q3

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Two Schemes:

1. Used for lots that are isolated or mixed or that have an unknown history as far as all parties know.

Lot size and LQ must be known.

Nominal values of the LQ are based on b=0.10


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Two Schemes:

2. Used when a vendor is producing a continuous stream of lots and sends one or a few to a customer who will consider them as isolated lots.

Occurs frequently when purchasing small quantities of raw materials.


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A set of inspection tables for lot-by-lot acceptance sampling by attributes.

Tables are based on Limiting Quality (LQ) and Average Outgoing Quality Limit (AOQL).

Tables for single and double sampling

Advantage that the plan provides a minimum amount of inspection for a given inspection procedure.

Desirable for in-house inspection

Dodge-Romig Tables

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Limiting Quality LQ Based on the probability that a particular lot, which has

percent nonconforming equal to the LQ, will be accepted.

Probability is the consumers risk, = 0.10

LQ plans give assurance that individual lots of poor quality will rarely be accepted.

Dodge-Romig Tables

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Observations about the LQ tables:

As the lot size increases, the relative sample size decreases.

The tables extend until the process average is one-half of the LQ.

As the process average increases, a corresponding increase occurs in the amount inspected.

Dodge-Romig Tables

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Average Outgoing Quality Limit AOQL

Applicable when the inspected lot is a convenient subdivision of a flow of product for materials handling purposes (non-homogeneous)

AOQL plan limits the amount of poor outgoing quality on an average basis, but gives no assurance on individual lots.

Dodge-Romig Tables

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Process average

Obtained by the same techniques as for p-charts

First 25 lots the average percent nonconforming is obtained

Type of nonconformance

Dodge-Romig tables do not provide for different categories or tightened inspection

Different LQ or AOQL values may be used

Dodge-Romig Tables

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A special type of lot-by-lot acceptance sampling plan for attributes designated as Chain Sampling Plan ChSP-1.

Applicable to quality characteristics which involve destructive or costly tests.

Use of small sample sizes

Acceptance number, c=0

Poor shape of OC curve at the producers risk

Chain Sampling Inspection Plan

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Chain sampling uses the cumulative results of several samples

Determination of the value of i, the number of previous samples, is determined by analysis of the OC curves for a given sample size.


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Procedure:

For each lot, select a sample of size n and test each for conformance to specifications.


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Procedure:

If the sample has 0 nonconforming units, accept the lot; if the sample has 2 or more nonconforming units, do not accept the lot; and if the sample has 1 nonconforming unit, it may be accepted provided that there are 0 nonconforming units in the previous

i samples of size n.


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n=5 c=0

Last Lot Second- to-Last

Lot

i previous lots

Current Lot

Accept if 0 Nonconforming Units in n =5 or if 1 Nonconforming Unit

& Zero Nonconforming Units in i Previous Lots

Chain Sampling Diagram

Figure 10-4 Chain Sampling Diagram

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Conditions for use of the Chain Sampling Plan:

1. The lot should be one of continuing series of product that is sampled in substantially the order of production

2. The consumer can normally expect the lots to be essentially the same quality.


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Conditions for use of the Chain Sampling Plan:

3. The consumer has confidence in the producer not to occasionally send an unacceptable lot that would have the optimum chance of acceptance.

4. The quality characteristic is one that involves destructive or costly tests.


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Used for costly or destructive tests

Subgroup size of 1 item by item plan

Sequential sampling is similar to multiple sampling, except sequential sampling can, in theory, continue indefinitely.

In practice, the plan is truncated after the number inspected is equal to three times the number inspected by a corresponding single sampling plan.

Based on the Sequential Probability Ratio Test

Sequential Sampling

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Sequential Sampling Plan

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Designated SkSP-1 and based on AOQL.

A single sampling plan for minimizing inspection costs when there is a continuing supply of lots of raw materials, component parts, subassemblies, and finished parts from the same source.

Applicable to chemical and physical characteristics that require laboratory analysis.

Skip Lot Sampling

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When i consecutive lots are found to be conforming

Begin by inspecting every lot

Discontinue inspection of every lot Inspect a fraction, f, of the lots

In a random manner When an inspected lot is found

nonconforming

Procedure for SkSP-1 Plans

Figure 10-7 Procedure SkSP-1 plans 47


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Provides procedures to reduce the inspection effort when the suppliers quality is superior.

A skip-lot scheme used in conjunction with attribute lot-by-lot plans given in ASQ Z1.4

ANSI/ASQ S1

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Requirements to use ANSI/ASQ S1

1. Have a documented system for controlling product quality and design changes

2. Have instituted a system that is capable of detecting and correcting changes that might adversely affect quality.

3. Not have experienced an organizational change that might adversely affect quality

ANSI/ASQ S1

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Additional requirements of the product:

Be of stable design

Have been manufactured on a continuous basis for at least 6 months unless agreed to a longer period.

Have been on normal and reduced inspection during the qualification period.

Have maintained a quality level at or less than the AQL for at least 6 months.

ANSI/ASQ S1

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Other: The previous 10 or more consecutive lots have been accepted

The min cumulative sample size for the last 10 or more consecutive lots have been met.

The acceptance numbers for the last 2 lots have been met

ANSI/ASQ S1

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Sampling for Continuous Production

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Acceptance sampling for continuous production implies that manufacturing operations do not create lots as part of the normal part of the production process.

Parts are produced by a continuous process on a conveyor or similar system.


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Plans for continuous production consist of alternating sequences of sampling inspection and screening (100%) inspection.

Plans begin with 100% inspection and convert to sampling after a stated number of items are free of nonconformities.

Sampling continues until a stated number of nonconforming units are found, at which time 100% inspection in reinstated.

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CSP-1

Sampling inspection is then instituted

Samples are selected in such a manner as to minimize any bias

If a nonconformity occurs, sampling is discontinued and 100% inspection begins.


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The Screening Crew Inspects 100% of the Units

When i Consecutive Units Are Found Free of

Nonconformities Concerned,

The Screening Crew is Released from 100% Inspection

and the Sampling Inspector Inspects a Fraction, f, of

the Units, Where the Sample Units are Selected in a

Random Manner.

When the Sampling Inspector Finds One of the

Nonconformities Concerned,

Start

CSP-1 and CSP-F Plans

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Inspection is by attributes for nonconforming units using three classes of severity:

Critical

Major

Minor

Each of the plans incorporates a provision for discontinuance of inspection

MIL-STD-1235B

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Shainin Lot Plot

Random sample of 10 subgroups of 5 each

Find average and range

Construct a histogram

Calculate Xdouble bar, R bar

Calculate ULL and LLL

Compare to lot plots in Figure 10-15


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ANSI/ASQ Z1.9-2003 Sampling Procedures and Tables for Inspection by Variables for Percent Nonconforming is an acceptance sampling system to be used on a continuing stream of lots for Acceptance Quality Limit (AQL) specified.


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ANSI/ASQ Z1.9-2003 provides tightened, normal, and reduced plans to be used on measurements which are normally distributed. Variation may be measured by sample standard deviation, sample range, or known standard deviation. It is applicable only when the normality of the measurements is assured.

acceptance sampling (1)

Documents

aql aql

records ansiasq z1

major ansiasq z1

sampling plan ansiasq

lot size

lot acceptance sampling

nansiasq z1

chain sampling plan