# How to calculate the Lot Reject Rate

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#### Helenliu

I go straight to the topic, Pls help to review and give some suggestion.Thanks a lot.

There are several steps for manufacturing the product, and there is sampling inspection for each lot each step, and calculate lot reject rate by this farmula: reject lot number in the month/ total inspection lot in the month. And if they find one reject unit in the lot, operator will rescreen the whole lot, but for the lot, we count it as reject.
For example:
Step 1: 2 (reject lots in the month)/ 100(total lot qty sampled in the month)=2.00%
Step 2: 3 (reject lots)/98=2.04%
.
.
.
.
Step 10: 1(reject lot)/101=0.9%

My question is how to calculate the total reject ratio of the whole process.

S

#### Surehawk

How can you have 101 lots in the last process when you only had 100 in the first (and rejected 2 of them)? Is the lot size different between the steps in the process?

If the lots were the same through the process it would just be to add together the failed lots and divide with the total number of lots manufactored in step 1.

Otherwise you will have to recalculate after the lots in each step. For example

Step 1. 100 parts per lot (set 100 as standard) 2 (rejected) X 1 (indexnumber) =1
Step 2. 2 (rejected) X 1 (since it is same lotsize) = 1
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.
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Step. 10 75 part per lot 1 (reject) X 0,75 (lower index since less in lots) = 0,75

And then add the rejected lots and parts of lots together and divide with total lots made in process 1.

Or else maybe I missunderstood the whole question and I am making a fool of myself.

#### Ajit Basrur

I go straight to the topic, Pls help to review and give some suggestion.Thanks a lot.

There are several steps for manufacturing the product, and there is sampling inspection for each lot each step, and calculate lot reject rate by this farmula: reject lot number in the month/ total inspection lot in the month. And if they find one reject unit in the lot, operator will rescreen the whole lot, but for the lot, we count it as reject.
For example:
Step 1: 2 (reject lots in the month)/ 100(total lot qty sampled in the month)=2.00%
Step 2: 3 (reject lots)/98=2.04%
.
.
.
.
Step 10: 1(reject lot)/101=0.9%

My question is how to calculate the total reject ratio of the whole process.
Refer an existing thread - Lot Reject Rate - The use of ppm vs. % (per cent)

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#### Bev D

##### Heretical Statistician
Super Moderator
Re: How to calculate the Lot Reject Rate ?

You may wan tot think about "rolled throughput yield". this is the 'opposite' of the lot reject rate you are asking for, but it has the same intent and the math is easy.

since manufacturing is usually a 'continuous' process (new plots introduced before previous lots are through the process) there will almost always be a different number of lots that make it through any given process step in any given reporting period. this calcaultion takes care of that.

simply take the YIELD (the number of lots that passed the step divided by the total numbe rof lots completed [passed + rejected] at the step) of each step and multiply the proportions for each step together.

step 1 - 30 lots passed, 15 rejected, yield = 30/45 = .67
step 2 - 35 lots passed, 12 rejected, yield = 35/47 = .74
step 3 - 28 lots passed, 10 rejected, yield = 28/38 = .74

and RTY = .67*.74*.74 = .37 or 37%

H

#### Helenliu

Re: How to calculate the Lot Reject Rate ?

Yes, it is rooling lot reject ratio. But it is only sampling inspection, maybe not lot based, but time base. let's make the lot as a unit.
If I samplied 5 lots in total 100 this month, I found one lot was reject. Then the LRR ratio=1/5*100% or =1/100*100%?

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