# How to decide the “U” to calcuate DPU and "opportunity" of DPMO

Dear Sirs,

We need help to clarify How to decide the “U” to calcuate DPU and “opportunity” of DPMO ?

“U” is inspection unit or use Production unit to calcuate DPU ?

and “opportunity” of DPMO - Can we use Inspection checking item to
calculate “opportunity” ?

We need to calculate the DPU, DPMO, Yield, Rolled Throughput Yield ( RTY ), Sampling size and Process Capability question.

We are an assembly factory for baby product, and be required to show our
In-Process and Finishing goods with the above Performance ratio.

Our each assembly convey line daily production about 1,000 units, and we have two Quality Control station A and B. per Assemply line - one is located in 1/3 of line for sub-assembly parts 100% inspection and another control station in the end of Assemlby line for Finishing goods sampling inspection.

We do have a checking list with 40 inspection items and using attribute data for checking each sampling unit, below is data that we collect and need to confirm the correct way to check the performance vs. DPU, DPMO, Throughput Yield, Rolled Throughput Yield ( RTY ) ratio.

Factory with Assembly line:
Daily Production units - 1,000 / day / line.
Per Line - has TWO (2) QC Station A and B.
QC Station A. - 100% Inspection for each sub-assembly part.
with 20 inspection items

QC Station B. - Random Sampling Inspection finishing units
( Inspect 100 units / per line / per day )
( PS. Checking each unit per 40 inspection items need to
take about 3.0 min. to 4.0 min. )

Example of data below:
Line 1. QC Station A. In-Process, Input 1,000 units, Output 950 units,
Defectsive 50 units, defects = 150

• DPU = 150 defects / 1000 units = 0.15
• DPMO = (150 defects / 1000 units * 20 inspection items ) * 1,000,000
= 7500
• Yield = 1-( 50/1,000 ) * 100 = 95.0%
• RTY = ???

Line 1. QC Station B. End of Line inspection,
Input 950 units, Output 940 units,
Sampling Inspection units = 100 units only
Defectsive 10 units, defects = 50

Question 1. - How to decide the “U” to calcuate DPU ?
“U” shall use Production unit = 1,000 units ?
or Inspection unit - 100 units ?

• DPU =
• DPMO =
• Yield =
• RTY = ???

Question 2. - How to determinr the Process Capability from attribute data ?
Question 3. - How many data need to collect of each assembly line to
calculate the Process Capability of attribute data?

Question 4. - Refer to our Facotry Production and assembly line status, What kind of Performance ratio - DPU, DPMO, Throughput Yield, Rolled Throughput Yield ( RTY ) ratio or Process Capability that is “BEST” data for us to watch the Quality Performance ? So, we are able to set up Performance Scordcard for each assembly line or each assembly factory ?

Question 5. What difference of “dpmu = defective per million unit “ vs. “DPMO = defects per million opportunity ” ? which one we shall use ?

Question 6. Is this correct ? Use DPU, DPMO to show performance of Finishing goods ?

use the Throughput Yield, Rolled Throughput Yield ( RTY ) for In-Process performance ?

Cp and Cpk are only the indexes commonly used in both studies attribute or not attribute to have an stimation of how good is my process mesured in ppms.

Why? Due to with this index it exixs a correlation with ppm, defects per million.

Cp, Cpk there is a table that gives you ppms

You have to select atribute variables and not atribute variables and them calculate for all of them the Cp, Cpk indexes, you need 100 parts divided in 20 shifts of 5 parts

Not atribute:

cp= (Tolerance Upper Limit - Tolerance Lowe limit ) / 6 Sigma.
Cpk= See literature.

and them ppm (Need histogram to test that the curve is a Gaus)

Attribute.

Althoug cp and cpk are for Gaus distribution it could be also used for atribute studies due to the sum of n experiments of Bernoulli are distribuited as a binomial, and the binomial under some circuntances could be trated as Gaus distribution.

But if you do not meet the criteria you can calculate in % of defect or directly in ppm,

burt if the criteria is met, the treatment is the same as variable.

Upper tolerance l- Lower Tolerance
Cp= --------
6 Sigma

Where

Lower Tolerance will be cero.

Upper Tolerance = Maximun number of defects we want to accept

Sigma = (Binaomial)= Square root(np*(1-np/n)

To summarize.

Attribute use Binomial, if coulf be treated as normal better.

Not attribute: use Gaus using Cp, Cpk and testing that the points are under Gaus distribution using the Wester electric rules that could be avoid using direcly the histogram.