How to decide the proper Beta Risk for our Process

How to decide the proper Beta Risk for our Process

Let’s start with a refresher…

Beta Risk in Measurement Systems is also known as Consumer’s Risk.

It is so called because Beta Risk is the proportion of Defectives Parts assessed by the measurement system as Ok Parts and therefore sent to the internal or external costumer. It is the proportion of defective parts not detected by our measurement system. In every Measurement System, there is always a Beta Risk greater than zero. But what is the proper one? It is always the typical 10% (sometimes 20%) mentioned in the technical literature?

The question is… Is Beta the actual Consumer’s Risk? Is Beta the proportion of NOK parts actually sent to the next step of the process or to the costumer?

Indeed it is not! Beta is not the proportion of NOK parts sent to the costumer out of the total. It is the proportion of NOK parts not detected by the Measurement System from the total NOK parts produced. So the consumer’s Risk depends on Beta, but also depends on the proportion of NOK parts produced by the process.

How to decide a proper Beta Risk

In the real world, Beta is always a Risk which implies a cost. A cost sometimes driven by

sample size, sometimes by technology reasons, …

The correct approach for Beta is taking in account not only Beta but also  along with the proportion of NOK parts produced by the process, as follows:

Proportion of NOK parts sent to the costumer = Beta x p

Where:

- Beta: Number of Nok parts assessed as OK / Total number of Nok parts

- p: proportion of Nok parts produced by the process

NOTE: Beta and p are estimated parameters, therefore it is very important  that a significant and representative sample size has to be taken to estimate those parameters.

From what has been said before we have to decide what is the Risk we are assuming of sending Nok parts to the costumer and then decide Beta and p that always mean cost.

Example

Imagine we are talking  about a characteristic that is classified as Significant Characteristic by our costumer, so a Ppk of 1,33 (Long Term capability) is the maximum Risk (minimum value of Ppk) our costumer is allowing us to have for that characteristic.

That means the proportion of Nok parts would be 34 parts per million. Expressed as a proportion, it would be: 0,000034

Imagine our process is performing with a proportion of 1 Defect out of 1000 parts, which is p=0,001.

If we work out Beta using the formula from above: Beta = 0,000034/0,001=0,034 -> 3,4%

So in this example we would need our measurement system to have a Beta Risk of 3,4%, which is better (lower) than the “typical” value of 10%.

That would be the case if the process is running and it is not possible to improve the proportion of defective parts the process is producing, which was p. At least if it would be not possible to improve immediately, so we would have to protect our costumer with a Measurement System performing at least with a Beta of 3,4%. Once the costumer is protected, we can analyze the problem, find out the root causes, and improve it with no pressure.

Once the process is improved, imagine an improvement of 90% of defects, then at the end we would have an improved process with p=0,0001 (1 defect out of 10000 parts). Then the Beta allowed would be: Beta=0,000034 / 0,0001 = 34%.

Once the process is improved, we would not need so much effort on the measurement system anymore.

FINAL CONCLUSION:

Beta Risk depends on the actual Risk our Costumer is allowing us to assume and how our process is performing (process capability).