12 Sampling Tech 4 - Student

Acceptance Sampling System

by Attributes

Assoc. Prof. Ir. Dr. Cheong Kuan YewSchool of Materials & Mineral Resources Engineering

Engineering CampusUniversiti Sains Malaysia

Topic Outcome:

At the end of this topic, students will be able to:

Use sampling system for lot-by-lot sampling (ANSI/ASQ Z1.4 1993 & Dodge-Romig sampling Tables)

Use sampling system for isolated lot sampling

(ANSI/ASQ Standard Q3 – 1998)

Topic Outline:• Lot-by-lot Acceptance Sampling Plans:

1)AQL Sampling Plans (ANSI/ASQ Z1.4 1993)

- An Introduction.

- Inspection Level

- Types of Sampling Plans.

- Switching Procedures

- AOQL factors

- LQ

- ASN

• Isolated lot Acceptance Sampling Plan ANSI/ASQ Standard Q3

- 1998

Refresh:

• Sampling plan, scheme, & system

Lot-by-lot Acceptance Sampling Plans

AQL Sampling Plans – ANSI/ASQ Z1.4 – 1993LQ Sampling PlansAOQL Sampling Plans

Dodge-Romig Sampling Tables

ANSI/ASQ Z1.4 – 1993

An Introduction ANSI/ASQ Z1.4 – 1993 ASQ = American Society for Quality A sampling plan for lot-by-lot inspection by attributes for

use by US government & industries1942 (@Bell Telephone Lab) – JAN-STD-105Since that time, there have been 5 revisions (MIL-

STD-105E).1973 – adopted by ISO (International Organization for

Standardization) and designated International Standard ISO/DIS-2859.

1993 – modifications were made by ASQ under designation ANSI/ASQ Z1.4 all tables and procedures remain unchanged, but with 3 basic changes:

ANSI/ASQ Z1.4 – 1993

1) Nonconformity (tak kesesuaian) and nonconforming (tak sesuai) unit are substituted for the words defect (cacat) and defective (kecacatan).

2) The switching rule that used a limit number for one of the reduced inspection criteria is an option.

3) Additional tables for AOQL,LQ,ASN,and OC curves are added. These tables reflect scheme performance, which is the combination of switching among normal, tightened, and reduced sampling plans.

The most widely used acceptance sampling plan in the world.

Quality Index is AQL.

In Malaysia Malaysian Standard, MS 567: Part 1 & 2 – 1978.

Inspection Level

Inspection level determines relationship between lot size (N) and sample size (n).

The levels of inspection offered are (Table 1: Sample size code letters (abjad)):

Level II – Normal Level, designated as N.

Level III – Tightened Level (tahap diperketat), designated as T.

Greater discrimination is required. Introduced when

there is deterioration of process capability.

Level I – Reduced Level (tahap dipermudah), designated as R.

Less discrimination is required. Introduced when there

is an improvement of process capability or no rejected

lots for a specified period.

4 additional special levels are given in the same table:S-1S-2S-3S-4

May be used where relatively small sample sizes are necessary and large sampling risks can be tolerated.

Types of Sampling Plans

This Standard offers:Single Sampling PlansDouble Sampling PlansMultiple Sampling Plans

Single Sampling Plans

Only a number of sample is taken per plan.

Double Sampling Plans

An initial sample is taken.

Based on the information, a decision is made to

A) Accept the lot,

B) Reject the lot, or

C) Take a second sample.

If the 2nd sample is taken, the information from 1st and 2nd is combined to reach a decision to accept or reject the lot.

Multiple Sampling PlansThis is an extension of the double sampling

concept.More than 2 samples are drawn to reach a

decision either to reject or accept the lot.

Summary of Advantages & Disadvantages of Various Types of Sampling Plans

SINGLE DOUBLE MULTIPLE

Acceptability to Producer

One chance to pass

Better chance to pass

Indecisive

Number to be Inspected

Greatest10% to 50%

less than Single Sampling Plans

30% less than Double

Sampling Plans

Cost Lowest Fair Greatest

Information Most Less Least

Simplicity Easiest Hard Hardest

Estimation of Quality

Good Fair Fair

How to use this Standard for Single Sampling Plans?

The steps are:

1) Decide on AQL.

2) Decide on the inspection level.

3) Decide on the type sampling plan to be used SINGLE

4) Decide whether normal, tightened, or reduced inspection is to be used.

5) Determine Lot size (N).

6) Use Table 1 to find the sample size code letter.

7) Use the appropriate table to obtain the plan (Table II.A to II.C).

8) Look at OC curve.

Q & A

1) Determine a single sampling plan if AQL = 1.0%, the inspection level is II and the Lot size is 2500.

Table 1- Sample size code letter KTable II.A – Single sampling plans for normal inspection

(Master table) n=125, Ac=3, Re=4.

Q & A

2) Determine a single sampling plan if AQL = 0.4%, the inspection level is I and the Lot size is 230.

3) Determine a single sampling plan if AQL = 0.015%, the inspection level is III and the Lot size is 120.



Switching Procedures

This standard has provision for switching of sampling

plan to a tighter sampling plan when the supplier’s (or

producer’s) quality has deteriorated.

It is also provides for a switch to reduced inspection

when the product quality has improved.

NORMAL to TIGHTENEDTightened inspection is instituted where 2 out of 5

consecutive lots have been rejected on original

inspection.

TIGHTENED to NORMALWhen tightened inspection is in effect, normal

inspection shall be reinstated when 5 consecutive lots

have been accepted on original inspection.

NORMAL to REDUCEDTo qualify for reduced inspection, the following

conditions must be satisfied:

10 consecutive lots have been accepted on

normal and original inspection.

The total number of nonconforming in the 10

samples is equal or less than the limit number.

Production is at steady state.

Reduced inspection is considered desired by

inspecting authority.

REDUCED to NORMALWhen reduced inspection is in effect,normal inspection

is reinstated when:

A lot is rejected.

Sampling terminates without either acceptance or rejection criteria having been met. The lot is considered acceptable but normal inspection is reinstated.

Production becomes irregular or delayed.

Other conditions warrant that normal inspection shall be re-instated.

Summary of Switching Rules

• Preceding 10 lots Accepted with total nonconforming less than limit number,

• Steady production, and• Approval from

responsible authority.

• Lot not accepted, or• Lot accepted but

nonconformities found lie between Ac and Re of the plan, or

• Irregular production, or• Other conditions

warrant.

• 2 out of 5 consecutive lots not accepted

• 5 consecutive lots accepted

• 10 consecutive lots Remain on Tightened

• Discontinue inspection

NORMAL TIGHTENEDREDUCED

START

How to use this Standard for Double Sampling Plans?

Schematic Operation of a Double Sampling.

Inspect a 1st sample of n1 pieces

If the number of nonconforming found in the 1st sample

Exceeds c1, but does not exceed r1

Does not exceed c1 Exceed r1

Inspect a 2nd sample of n2 pieces

If the number of nonconforming found in the 1st and 2nd samples combined

Does not exceed c2 Equal or exceed r2

Accept the Lot Reject the Lot

The steps are:

1) Decide on AQL.


3) Decide on the type sampling plan to be used DOUBLE




7) Use the appropriate table to obtain the plan (Table III.A to III.C).


Q & A

1) Determine a double sampling plan if AQL = 1.0%, the inspection level is II and the Lot size is 2500.

Table 1- Sample size code letter KTable III.A – Double sampling plans for normal inspection (Master table) n1=80, cumulative sample size=80

n2=80, cumulative sample size=160

AQL=1.0%

Ac Re

First

Second

1 4

4 5

Q & A

2) Determine a double sampling plan if AQL = 0.4%, the inspection level is I and the Lot size is 230.

3) Determine a double sampling plan if AQL = 0.015%, the inspection level is III and the Lot size is 120.



How to use this Standard for Multiple Sampling Plans?

Schematic Operation of a Multiple Sampling.

Inspect a 1st sample of n1 pieces

If the number of nonconforming found in the 1st sample

Exceeds c1, but does not equal or exceed r1

Does not exceed c1 Exceed r1

Inspect a 2nd sample of n2 pieces

If the total number of nonconforming found in the 1st and 2nd samples

combined

Does not exceed c2

Equal or exceed r2

Accept the Lot

Do not Accept

the Lot*


Does not exceed c3

Equal or exceed r3

Accept the Lot


Inspect a 3rd sample of n3 pieces

If the total number of nonconforming found in the first three samples

combined

Do not Accept the Lot*Etc.

* Some of these plans continue to the ‘bitter end’, i.e., the taking of samples continues if necessary until the lot is fully inspected, unless the plan has meanwhile ‘made up its mind’.

The steps are:

1) Decide on AQL.


3) Decide on the type sampling plan to be used MULTIPLE




7) Use the appropriate table to obtain the plan (Table IV.A to IV.C).


Q & A

1) Determine a multiple sampling plan if AQL = 1.0%, the inspection level is II and the Lot size is 2500.

Table 1- Sample size code letter KTable IV.A – Multiple sampling plans for normal inspection (Master table)

sample Sample size Cumulative sample size

AQL=1.0%

Ac Re

First

Second

Third

Fourth

32

32

32

32

32

64

128

160

# 3

0 3

1 4

2 5

# acceptance not permitted at this sample size.

Q & A

2) Determine a multiple sampling plan if AQL = 0.4%, the inspection level is I and the Lot size is 230.

3) Determine a multiple sampling plan if AQL = 0.015%, the inspection level is III and the Lot size is 120.



Average outgoing quality limit factors Tables V-A and V-B.

Limiting Quality (LQ)

Tables VI-A and VI-B. (for consumer’s risk of 0.10) Tables VII-A and VII-B (for consumer’s risk of 0.05) A sampling plan for isolated lots can be obtained that will

come close to both the producers’ and consumers’ criteria. It is much easier to use ANSI/ASQ standard Q3 – 1988. Table VIII. (for reduced inspection)

Average Sample Number(ASN) Table IX – Average sample size curves for double and

multiple sampling. Assumption: no curtailment of inspection and are

approximate to Poisson distribution, and the sample size for double and multiple sampling are assumed to be 0.631n and 0.25n.

Arrow indicates the location of the AQL.

ANSI/ASQ Standard Q3 - 1988

ANSI/ASQ Standard Q3 - 1988 It is used for inspection of isolated lots by attributes.

It complements ANSI/ASQ Z1.4-1993 (for continuous stream of lots).

Indexes tables by Limiting Quality (LQ).Limiting Quality (LQ).

1st scheme:

It is designated to be used for lots that are isolated or mixed or that have an unknown history as far as both vendor and vendee know.

Lot size and LQ value must be known.

Table 10-6

Q & A:Q: Lot size = 295, LQ=3.15%, determine the sampling

plan.A: n=80, Ac=0

2nd scheme:

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 (purchasing of small qualities of purchasing of small qualities of

a raw materiala raw material).

Example of Table for LQ=3.15%

Table 10-7

The last 5 columns can be used to plot the OC curves.

Q & A:Q: Lot size = 295, inspection level II, LQ=3.15%, where

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

A: n=125, Ac=1

12 Sampling Tech 4 - Student

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