15 - 1

a form of inspection applied to lots or batches of items before or after a process to judge conformance to predetermined standards

Lesson 15

Acceptance Sampling

15 - 2

Acceptance Sampling is very useful when

. Large numbers of items must be processed in a short amount of time. The cost of “passing defectives” is low. Fatigue/boredom is caused by inspecting large numbers of items

Acceptance Sampling

. Destructive testing is required

15 - 3

Sampling Plans specify the lot size, sample size, number of samples and acceptance/rejection criteria. Sampling plans involve

. Single sampling

. Double sampling

. Multiple sampling

Random sample

Lot

Sampling Plans

15 - 4

Single Sampling Plan

A Single Sampling Plan is one where. A representative sample of n items is drawn from a lot size of N items.. Each item in the sample is examined and classified as good/defective. If the number of defective exceeds a specified rejection number (C - cut off point) the whole lot is rejected; otherwise the whole lot is accepted

Random sample (n items)

Lot (N items)

Random sample (n items)

Lot (N items)

15 - 5

A Double Sampling Plan allows the opportunity to take a second sample if the results of the original sample are inconclusive.

. Specifies the lot size, size of the initial sample, the accept/reject/inconclusive criteria for the initial sample (CL - lower level of defectives, CU - upper level of defectives). Specifies the size of the second sample and the acceptance rejection criteria based on the total number of defective observed in both the first and second sample (CT- total allowable defectives)

It works like the following example

Double Sampling Plan

15 - 6

First Random sample

Lot

CL CU

First sample inconclusive, take second sample

Reject LotAccept Lot

Compare number of defective found in the first random sample to CL and CU and make appropriate decision.

Double Sampling Plan

15 - 7

CT

Reject LotAccept Lot

Compare the total number of defective in both lots to CT and make the appropriate decision

Double Sampling Plan

Lot First Random sample

Second Random sample

15 - 8

A Multiple Sampling Plan is similar to the double sampling plan in that successive trials are made, each of which has acceptance, rejection and inconclusive options.

Which Plan you choose depends on . Cost and time . Number of samples needed and number of items in each sample

Multiple Sampling Plan

15 - 9

Acceptance Sampling

Advantages

EconomyLess handling damageFewer inspectorsUpgrading of the inspection jobApplicability to destructive testingEntire lot rejection (motivation forimprovement)

Purposes

Determine quality levelEnsure quality is within predetermined level

Disadvantages

Risks of accepting “bad” lots and rejecting “good” lotsAdded planning and documentationSample provides less information than 100-percent inspection

15 - 10

An Operating Characteristic Curve (OCC) is a probability curve for a sampling plan that shows the probabilities of accepting lots with various lot quality levels (% defectives).

Operating Characteristic Curve (OCC)

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

0 .05 .10 .15 .20

Prob

abilit

y of

acc

eptin

g lo

t

Lot quality (% defective)

Under this sampling plan, if the lot has 3% defective . the probability of accepting the lot is 90% . the probability of rejecting the lot is 10%

If the lot has 20% defective . it has a small probability (5%) of being accepted . the probability of rejecting the lot is 95%

15 - 11

Operating Characteristic Curve (OCC)

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

0 .05 .10 .15 .20

Prob

abilit

y of

acc

eptin

g lo

t

Lot quality (% defective)

Under this sampling plan what is the probability of accepting a lot that has 5% defectives?

Approximately 80%

This sampling plan may not be acceptable to customer. Therefore, this sampling plan may not be acceptable for meeting the customers level of quality.

15 - 12

Most customers understand that 100% inspection is impractical and are generally willing to accept that a certain level of defectives will be produced.

The Acceptable Quality Level (AQL) is the percentage level of defects at which a customer is willing to accept as lot as “good”.

The Lot Tolerance Percent Defective (LTPD)Lot Tolerance Percent Defective (LTPD) is the upper limit on the percentage of defectives that a customer is willing to accept.

Customers want lots with quality better than or equal to the AQLAQL but are willing to live with some lots with quality as poor as the LTPDLTPD, but prefer not to accept lots with quality levels worse than the LTPDLTPD.

Customer Acceptance Levels

15 - 13

Therefore the sampling plan must be designed to assure the customer that they will be receiving the required AQLAQL and LTPDLTPD.

The AQLAQL and LTPDLTPD are dependent on many things (reliability, liability, competitor quality levels, etc.) and will vary by industry and by customer. Typically industry standards are set because suppliers have more than one customer and customers have more than one supplier.

The Consumer’s RiskConsumer’s Risk is the probability that an unacceptable lot (e.g. above the LTPDLTPD) will be accepted.

The Producer’s RiskProducer’s Risk is the probability that a “good” lot will be rejected.

Customer Acceptance Levels

15 - 14

OCC, AQL & Producer’s Risk

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Prob

abilit

y of

acc

eptin

g lo

t

0

0.1

0 .05 .10 .15 .20 Lot quality (% defective)

AQL - percentage level of defects at which a customer is willing to accept

“Acceptable Lot”

Producer’s Risk = probability acceptable lot is rejected

15 - 15

OCC, LTPD & Consumer’s Risk

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Prob

abilit

y of

acc

eptin

g lo

t

0

0.1

0 .05 .10 .15 .20 Lot quality (% defective)

LTPD - upper limit on the percentage of defectives that a customer is willing to accept.

Consumer’s Risk = probability unacceptable is accepted

“Unacceptable Lot”

15 - 16

The result of acceptance sampling (assuming rejected lots are 100% inspected) is that the level of inspection automatically adjusts to the quality of the lots being inspected.

The Average Outgoing Quality (AOQ) is the average of rejected lots (100% inspection) and accepted lots ( a sample of items inspected).

The maximum outgoing quality level is referred to as the AOQL.

AOQ = P * p(N - n

N where

P = Probability of accepting a lot

p = Fraction defective

n = sample size

N = Lot size

ac

ac

)

Average Quality Of Inspected Lots

15 - 17

Example: Create an Operating Characteristic Curve for the sampling plan: Lot Size = N = 2000, sample size = n = 10, reject if number defectives > C = 1.

Answer the following questions.

OCC

15 - 18

15 - 19

Operating Characteristic Curves

What is the probability of accepting a lot which has 2.5% defective?

15 - 20

What is the Producer’s risk if the AQL is 1%? .0043

Mouse over the “Producer’s risk” cell to see the explanation.

Operating Characteristic Curves

15 - 21

What is the Consumer’s risk if the LTPD is 6%? .8824

Mouse over the “Consumer’s Risk” cell to see the explanation.

Operating Characteristic Curves

15 - 22

What is the AOQ curve?

What is the AOQL?

Operating Characteristic Curves

15 - 23

Homework

Read and understand all material in the chapter.

Discussion and Review Questions

Recreate and understand all classroom examples

Exercises on chapter web page