# How to establish a Sampling Plan from the Rework percentage?

#### sowmya

##### Involved - Posts
Experts,

I am sure, you should have discussed this in forum. but I could not able to take it.

Currrently we are shipping the products to our customer place and our customer test the units and ship it to end customer. Moving forward, our customer want us to do direct shipments to the end customer.

Current reject rate at customer end is 0.7% for product A and 0.3% for product B.

We have analyzed the rejects and put gate points based on pareto.

There is 100% visual inspection and functional testing at our end. over and above we are doing Outgoing audit at AQL percentage 0.01% normal inspection.
my question is to reduce the defect to 0.1% (1000PPM) at customer end, what would be the AQL I have to choose?

In simple words, I want to increase my sample size at OQA, so that customer is getting less than 1000PPM defect.

Thanks
Sowmya

#### Chennaiite

##### Never-say-die
Trusted Information Resource
I wouldn't prefer leaning on sample audit to reduce customer end ppm, even though statistics can prove it on paper. Why don't you go for the same controls what your customer have today for detecting 0.7% or 0.3%?

S

#### supreecha

Acceptance Sampling by Attributes

Measurement type: Go/no go
Lot quality in percent defective
Lot size: 5000
Use binomial distribution to calculate probability of acceptance

Acceptable Quality Level (AQL) 0.01
Producer's Risk (Alpha) 0.05

Rejectable Quality Level (RQL or LTPD) 10
Consumer's Risk (Beta) 0.1

Generated Plan(s)

Sample Size 22
Acceptance Number 0

Accept lot if defective items in 22 sampled <= 0; Otherwise reject.

Percent Probability Probability
Defective Accepting Rejecting AOQ ATI
0.01 0.998 0.002 0.010 32.9
10.00 0.098 0.902 0.980 4509.8

Average outgoing quality limit (AOQL) = 1.628 at 4.348 percent defective.

#### mdurivage

##### Quite Involved in Discussions
If there is rework involved, I would reccomend at least one a column shift left to demonstrate a more conservative approach because you will have increased the number of items inspected to make a decision of lot acceptability.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Experts,

my question is to reduce the defect to 0.1% (1000PPM) at customer end, what would be the AQL I have to choose?

In simple words, I want to increase my sample size at OQA, so that customer is getting less than 1000PPM defect.
Aside from Chennaiite's excellent point about determining the casual mechanisms of the defects and eliminating them - or creating 100% error proofing or defect detection methods - you really aren't looking for an AQL based sample size but an RQL (aka LTPD) or Rejectable Quality Level.

Remember that an AQL plan will ACCEPT the AQL defect rate 95% of the time. An RQL based plan will DETECT and REJECT the RQL defect rate.

When we select a sample size based on the AQL, the RQL is a 'residual' level depending on the accept number chosen. And in today's misguided world of accept on 0 plans teh RQL can be quite large.

You will find a spreadsheet that calculates the sample sizes needed based on either or both the RQL and AQL here.

fro example, if you really want to ship lots that are no more than .1% defective then you want a plan that has a .1% RQL.

IF you choose a c=0 plan then your sample size is 2996. This will give you a 95% chance of detecting and rejecting a lot that has .1% or more defects in it. The resulting AQL for this plan is about .0017% or about 17ppm

If you use an AQL of .1% and a c=0 plan your sample size is 51 and the resulting RQL is 5.7%.

(These plans are all based on 95% confidence and are irrespective of lot size. Lot size really doesn't matter until the lot becomes very small)

#### sowmya

##### Involved - Posts
You will find a spreadsheet that calculates the sample sizes needed based on either or both the RQL and AQL here.
Thanks Bev, can you pl. attach the spread sheet. I could not able to open.

I will go through this and come back for any clarifications.

Thanks again.
Sowmya

#### sowmya

##### Involved - Posts
I wouldn't prefer leaning on sample audit to reduce customer end ppm, even though statistics can prove it on paper. Why don't you go for the same controls what your customer have today for detecting 0.7% or 0.3%?
Thanks. We have put error proofing where ever possible. but some issues (like assembly damage, label peel off ) could not be error proofed 100%.

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