ACCEPTANCE SAMPLING - PowerPoint Presentation

Slide1

ACCEPTANCE SAMPLING

BPT2423 – STATISTICAL PROCESS CONTROLSlide2

CHAPTER OUTLINE

Fundamental Concepts

Types of Sampling Plans

Single, Double, Multiple and Sequential

Statistical

Aspects

Lot-By-Lot

Acceptance Sampling Plans for Attributes

Acceptance Sampling Plans For :

Continuous Production

VariablesSlide3

LESSON OUTCOMES

Know the advantages and disadvantages of sampling

Understand the types of sampling plans and selection factors

Determine the Operation Characteristic (OC) curve for a single sampling plan and the propertiesSlide4

FUNDAMENTAL CONCEPT

Lot-by-lot acceptance sampling by attributes is the most common type of sampling

A predetermined number of units (sample) from each lot is inspected by attributes

If the number of nonconforming units is less than the prescribed minimum, the lot is accepted;

if not, the lot is not accepted

Acceptance sampling can be used either for the number of nonconforming units or for nonconformities per unit

Example :

Lot size, N = 9000

Sample size, n = 300

Acceptance number, c = 2Slide5

Acceptance sampling is most likely to be used in one of five situations:When the test is destructive, sampling is necessary; otherwise, all of the units will be destroyed by testingWhen the cost of 100% inspection is high

in relation to the cost of passing a nonconforming unitWhen

there are many similar units to be inspected

; with manual inspection, fatigue and boredom cause a higher percentage of nonconforming material to be passed than would occur on the average using a sampling plan

When

information concerning producer’s quality

, such as X-Bar and R, p or c charts and

C

pk

is not availableWhen automated inspection is not available

FUNDAMENTAL

CONCEPTSlide6

AdvantagesDisadvantagesMore economical (fewer inspectors and less handling)

Upgrades the inspection job (piece-by-piece to lot-by-lot)Applies to destructive testing

Stronger motivation for improvement (entire lots are not accepted rather than the return of a few nonconforming units)

Certain risks of not accepting conforming lots and accepting non-conforming lots

More time and effort is devoted to planning and documentation

Less information is provided about the product

There is no assurance that the entire lot conforms to specifications

FUNDAMENTAL

CONCEPTSlide7

Lot Formation can influence the effectiveness of the sampling plan:Lots should be homogeneousLots should be as large as possibleThe sample units selected for inspection should be representative of the entire lot – random sampling

There are a number of courses of action that can be taken on the non-accepted lots

:

Passed to the production facilities and the non-conforming units sorted by production personnel

Rectified at the consumer’s plant by personnel from either the producer’s or the consumer’s plant

Returned to the producer for rectification

FUNDAMENTAL

CONCEPTSlide8

TYPES OF SAMPLING PLANS

Single

– one sample is taken from the lot and a decision to accept or not accept the lot is made based on the inspection results of that sample

Double

– on the initial sample, a decision, based on the inspection results, is made whether:

To accept the lot

Not to accept the lot

To take another sample

If the quality is very good, the lot is accepted on the first sample and a second sample is not taken; if the quality is very poor, the lot is not accepted on the first sample and a second sample is not taken

Only when the quality level is neither very good nor very bad is a second sample takenSlide9

TYPES OF SAMPLING PLANSSlide10

Multiple – is a continuation of double sampling in that three, four, five or as many samples as desired can be established. Sample sizes are much smallerSequential – items are sampled and inspected one after another. A cumulative record is maintained and a decision is made to accept or not accept the lot as soon as there is sufficient cumulative evidenceRemarks:

All four types of sampling plans can give the same results. Thus, the type of plan for a particular unit is based on factors other than effectivenessThese factor are simplicity, administrative costs, quality information, number of units inspected and psychological impact

TYPES OF SAMPLING PLANSSlide11

STATISTICAL ASPECTS

Operation Characteristic (OC) Curve for Single Sampling Plans

In judging a particular sampling plan, it is desirable to know the probability that a lot submitted with a certain percent nonconforming, 100p

o

, will be accepted – the OC curve will provide this information

When the percent nonconforming is low, the probability of the lot being accepted is large and decreases as the percent nonconforming increases

In graphing the curve with the variables 100P

a

(percent of lots accepted) and 100p

o (percent nonconforming), one value, 100po

, will be assumed and the other calculatedSlide12

Construction of an OC CurveAssume po valueCalculate npo value

Attain Pa

values from the Poisson table using the applicable c and

np

o

values

Plot point (100p

o

, 100P

a)Repeat 1,2,3 and 4 until a smooth curve is obtained

OC Curve for the Single Sampling Plan

STATISTICAL ASPECTSSlide13

Calculation:

STATISTICAL ASPECTSSlide14

OC Curve PropertiesAcceptance sampling plans with similar properties can give different Operation Characteristic (OC) curve:

Sample size as a fixed percentage of lot size

Fixed sample size

STATISTICAL ASPECTSSlide15

As sample size increase, the curve becomes steeperAs the acceptance number decrease, the curve becomes steeper

OC Curve Properties (cont.)

STATISTICAL ASPECTSSlide16

Consumer-Producer RelationshipThere is a conflicting interest between the consumer and the producer when using acceptance samplingIdeal OC curve that is a vertical line can satisfy both – can be achieved only with 100% inspectionSampling carries risks of not accepting lots that are acceptable and of accepting lots that are unacceptableAcceptance Quality Limit (AQL)

“Is the quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling. It is a reference point on the OC curve and is not meant to convey to the producer that any percent nonconforming is acceptable. It is a statistical term and is not meant to be used by the general public”

STATISTICAL ASPECTSSlide17

Consumer-Producer Relationship (cont.)Producer’s RiskRepresented by the symbol α, is the probability of non acceptance of a conforming lotThis risk is frequently given as 0.05, but it can range from 0.001 to 0.10 or more

It cannot be located on an OC curve unless specified in terms of the probability of acceptance

This conversion is accomplished by subtracting from 1

Thus, P

a

= 1 –

α

and for

α

= 0.05, Pa = 0.95

STATISTICAL ASPECTSSlide18

Consumer-Producer Relationship (cont.)Limiting Quality (LQ)“Is the percent nonconforming in a lot or batch for which, for acceptance sampling purposes, the consumer wishes the probability of acceptance to be low” Consumer’s RiskRepresented by the symbol

β, is the probability of acceptance of a nonconforming lot

This risk is frequently given as 0.10

STATISTICAL ASPECTSSlide19

Consumer-Producer Relationship (cont.)Example:AQL = 0.7%There are 0.7% nonconforming will have a non-acceptance probability of 5% or in other words; 1 out of 20 lots that are 0.7% nonconforming will not be accepted by the sampling plan

LQ = 2.6%

There are 2.6% nonconforming will have a 10% chance of being accepted or in other words; 1 out of 10 lots that are 2.6% nonconforming will be accepted by this sampling plan

STATISTICAL ASPECTSSlide20

ACCEPTANCE SAMPLING PLANS

Attributes

Was first devised in 1942 by a group of engineers at Bell Telephone Laboratories for use by the US government

It was designated JAN-STD-105 and adopted by the ISO and designated ISO/DIS-2859

Have been revised 5 times (MIL-STD-105E) and modified by American Society for Quality (ASQ) under the designation ANSI/ASQ Z1.4 – all tables and procedures remain unchanged Slide21

Attributes (cont.)

ACCEPTANCE SAMPLING PLANSSlide22

Continuous Production

ACCEPTANCE SAMPLING PLANSSlide23

Variables

ACCEPTANCE SAMPLING PLANSSlide24

Table - Poisson Distribution