We have posted about process yield, and the Impact of defect, now we would also like to discuss three more ways of measuring defects.

The first one is the parts per million or ppm. Before we had denoted p as the number of defective units over the total number of produced units.

## What is PPM?

Now, the term “ppm” is the number of defective units per million.

So the number of defective units in one million produced can also write as the fraction defective ‘p * 1’ million.

Now, you hear ppm typically used in scientific fields like chemistry, as a way of quantifying very small volumes, but you also hear it quite regularly in quality management.

So as an example, for a 99.379% yield at each step, what is the ppm? Well we have the yield at each step is going to be then 0.99739 which is equal to our ‘1 – p’, then p = 1 – 0.99739 = 0.00621. (**THIS IS A CORRECTION TO THE SLIDE**)

### Example 1

For a 99.379% yield at each

step what is the ppm?

1 – p = 0.99379

p = 1 – 0.99379 = 0.0621

ppm = 0.0621 × 1000000

**= 6210**

**Example 2**

For a 99.99966% yield at each step, what is the ppm?

1 -p = 0.9999966

p = 1 -0.9999966 = 0.0000034

ppm = 0.0000034×1000000

**= 3.4**

Now, we have our car example, if we have a car consisting of ten thousand parts and production processes, and if we have six thousand two hundred and ten parts per million defectives for each of those process steps or for each part, this then means our overall process yield as we said before is going to be (0.99379) ^10000.

**Example: **Assume a car consists of **10000 **parts and production processes.

6210 ppm -> 0.0062 fraction defective at each process step or part

**Process Yield = (0.99379)10000= 8.84**×**10-28= all vehicles faulty**

we took our fraction defective and we converted that then into the ‘1 – p’ and all of our vehicles will be faulty

**And if**

3.4 ppm -> 0.0000034fraction defective at each step process step or part

**Process Yield = (0.9999966)10000= 0.97 = 97% !**

we saw before 97% fault-free vehicles, good cars.

Source by TUM: Technische Universität München

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