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Chapter 13

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Myth: “Acceptance sampling assures good quality.”

Truth: Acceptance sampling provides confidence that p (the population fraction defective) is stable over a long period of time and across many lots.

The fundamental goal of acceptance sampling is to reduce the amount of inspection needed to verify that lots of material have some predetermined level of quality.

Myths and Legends

Truth: Acceptance sampling allows for some

predetermined level of

non-conformances

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Modern production philosophies like small batch sizes and statistical process control by variables data are making acceptance by attributes increasingly less effective.

To achieve the high levels of quality that are being achieved in a free market through competition, it is getting increasingly difficult for acceptance sampling to meet its goal with reasonable sample sizes.

Not as popular today

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Part acceptance (old school)◦ Acceptable Quality Limits (AQL)◦ Incoming inspection

Process control (new school)◦ Control charts◦ Capability studies

Both ways have been used to decrease consumer risk of receiving non-conforming product from suppliers

Two schools of thoughts

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Very good at accepting very good lots and rejecting very bad lots – but what about in-between?

Sampling Dilemma

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In the past AQL’s of 1% were reasonable and process capability was accepted at Cpk=1

Now we need much lower AQL’s and Cpk much greater than 1

What happens to sampling?

How does this effect the zero defect mentality?

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Vendor certification◦ Companies need to prove

themselves worthy◦ Supplied data◦ Auditing

No receiving inspection Required SPC Cpk>1.5 usually 2 Ever hear of PPAP, APQP, FMEA,

AS9102? If you haven’t its coming.

Prove control and capability - then sample

What’s being done?

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The home company tells us they put about 13% RED M&Ms in their mix.

We have a lot (one bag) of delivered M&Ms. We are randomly going to sample a bag and we will only accept the lot if the sample has 13% or less red in it.

What is the probability of accepting a sampled lot?

Simple Example

999999999

How does this correspond to “Sampling Dilemma”?

What problems does this activity cause? How does it add cost?

What if we increase the sample size?

What can we learn from this?

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Type 1 (producer’s risk, alpha ) – The probability that a hypothesis that is actually true will be rejected◦ The chance that a good lot will be

rejected

Type 2 (consumer’s risk, beta ) – The probability that a hypothesis that is actually false will be accepted◦ The chance that a bad lot will be

accepted

Type I and Type II error

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What happens to:

producer’s risk

consumer’s risk

as you increase your sample size?

Why? What do we do?

Sample size compared to risk

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Commonly referred to as OC Curves Quantifies the producer’s and

consumer’s risk Identified by the sample size (n) and

the maximum acceptance number (c)

Constructed from the Poisson probability distribution

No perfect sampling plan exist, there will always be some risk

Operational Characteristic Curves

Ideal OC Curve

0

0.25

0.5

0.75

1

1% 2% 3%

Lot percent defective

Pa

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Characterized by◦ Only two independent outcomes◦ the average number of occurrences

per time period (pn=)◦ used for rare events when n is large

and p is small◦ Good to approximate the binomial

distribution Constructed by

◦ using a Poisson probability table Figure 13.2

◦ equation – the probability of exactly c defectives in a sample of n (pn=)

Poisson probability distribution

PDFPoisson !

)()(

c

pnecP

cpn

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1. Choose p values between 0 and .09

2. Multiply each p value by n and place it on the table

3. Make a percent column for p and mark it 100p

4. Using Figure 13.2, start at the pn value on the x-axis and go straight up to the c= line. Then move straight across to the y-axis. Read the probability of acceptance.

5. Record the Pa value on the table

How to construct an OC Curve

p pn 100p Pa0 0

0.01 10.02 20.03 30.04 40.05 50.06 60.07 70.08 80.09 9

151515151515151515

n=150c=3

Example

1.00.90.80.7

Pa 0.60.50.40.30.20.1

1 2 3 4 5 6 7 8 9100p

p pn 100p Pa0 0

0.01 10.02 20.03 30.04 40.05 50.06 60.07 70.08 80.09 9

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AQL Defined as

◦ The maximum percent defective that is allowed as a process average

◦ The level of quality of a submitted lot that has a 95% chance of being accepted

◦ 1-AQL is the producer’s risk Not the quality level that is being

produced or accepted Not always the quality goal In our exercise, it is .9%

How does sample size effect AQL?◦ See figure 13.7

Acceptable Quality Level

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IQL◦ The quality level that will be

accepted 50% of the time.◦ In our exercise, it is 2.5%◦ How does sample size effect IQL?

See figure 13.7

RQL◦ The level of quality that will be

accepted only 10% of the time◦ This is the consumer’s risk◦ In our exercise, it is 4.5%◦ How does sample size effect RQL?

See figure 13.7

Indifference / Rejectable Quality Level

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AOQL The maximum Average

Outgoing Quality Found on the Average Outgoing

Quality (AOQ) curve

Average Outgoing Quality Limit

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Shows the result of the incoming inspection and sorting of rejected lots

Outgoing quality is the quality level expected from the process of inspection

Assumptions◦ The lots size and incoming quality

level is relatively consistent◦ All the lots that pass go to

production◦ All rejected lots are 100%

inspected, non-conforming units are replaced with conforming units

Average Outgoing Quality Curve

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1. Create a table that includes;1. a column for incoming percent

defective (100p)2. percent accepted from the OC

curve(Pa),3. percentage rejected and fully sorted

(1-Pa)4. and defects outgoing (Pa*100p)

2. Fill in the table3. Graph the defects outgoing4. Identify the AOQL

How to construct an AOQ Curve

Incoming Defective(%)

Pa (%) Rejected (%)

Defects Outgoing

0123456789

100p 1-Pa Pa * 100p

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n=150c=3

ExampleIncoming

Defective(%)Pa (%) Rejected

(%)Defects

Outgoing

0123456789

1.31.21.11.00.90.80.7

AOQ 0.60.50.40.30.20.1

1 2 3 4 5 6 7 8 9Incoming Percent Defective

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Variable◦ Mil-Std-414◦ ANSI/ASQ-Z1.9-1993

Attribute◦ Mil-Std-105D◦ ANSI/ASQ-Z1.4-1993◦ Dodge-Romig Tables

Purpose◦ Establishes sampling plans and

procedures◦ Used as a reference to standardize

sampling◦ To drive conformity on the switching

procedures between the use a normal, tightened or reduced sampling plan

Inspection Plans

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Typically you are given a set of criteria to use by your customer

You will need to know the following:◦ Inspection level◦ Lot size◦ Single, double or multiple inspection◦ Normal, reduced or tightened◦ AQL

How to use

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1. Determine inspection level and lot size2. Find inspection plan code letter3. Determine if plan is single, double or

multiple inspection4. Determine if plan is normal, tightened or

reduced5. Find the correct plan chart6. Based on code letter, determine sample

size needed7. Inspect samples8. Find the appropriate AQL column9. Find the cell that connects the code letter

row to the AQL column10. Find acceptance and reject numbers

1. If your sample has non-conformances equal to or less than the Ac number, accept the lot

2. If your sample has non-conformances equal to or greater than the Re number, reject the lot

Procedure for using sample plans

Use Table 13.10-13.14

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Your customer requires you to use MIL-STD-105D, single sampling, normal inspection level II with an AQL of 1%.

The shipment that arrived had a lot quantity of 2000. You found the sample size and determined there are 3 non-conformances in the lot.

1. Do you accept or reject the lot?

2. What about a double inspection? Why do a double inspection?

Example

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As batch sizes get smaller, the effective number of parts requiring inspection gets bigger (approaches 100%)

You can see this in the sampling tables

As quality gets better, bigger and bigger samples are needed to detect a shift in the process average

Deming suggests a better (I think) answer:◦ Control the process with SPC.

If it’s capable and in control, don’t inspect any more than needed to keep it that way.

If it’s not capable and in control, 100% inspect.

The Deming Inspection Criterion