# Six Sigma

## Calculator

Enter your Defects per One Million Opportunities (DPMO) to compute Sigma level.

## Explanation

Defects per Million Opportunities is the actual, observed number of defects, extrapolated to every 1,000,000 opportunities.

This is different from "defective parts per million" (defective PPM), because one "part" may have multiple "opportunities" to be defective.

As an example: let's say you manufacture 1cm ball bearings, and you measure for:

• Diameter must be correct within 0.01%
• Weight must be correct within 0.01%
• Roundness must be correct within 0.01%
• Hardness: must resist permanent deformity due to slow crushing by a specific testing machine

So each part has 4 opportunities to be defective.

If the alloy is too soft, then you may find bearings which fail both the roundness test and the hardness test.  The change in chemical composition may also cause failure of the weight test.

The opportunities should be criteria of value to the customer.

In Six Sigma the goal is to achieve DPMO below 3.4.

## Missed Opportunities

The above example dealt exclusively with some physical characteristics of the manufactured item.  Other types of defect opportunities might be overlooked, including:

• Cost overruns

Deadlines and costs are very appropriate "defect opportunities" for products that are not batched – custom cabinetry, for example.  For ball bearings, which are produced and shipped in batches, these "defect opportunities" are more correctly measured at the batch level.

## Gather Data

Having identified the opportunities for defects, the next task is to take a representative sample of units and measure them against the criteria.

In the above example, there are: 3 non-destructive physical tests; 1 test which may damage the ball bearings.  Let's say that 2,000 bearings are tested from various batches.

## Calculate

If we use the variables:

• D = number of Defects observed in the sample
• U = number of Units in the sample
• O = Opportunities per Unit

Then DPMO = 1,000,000 X D / ( U X O )

In our example, if there had been 7 defects (3 bearings for diameter and weight; 1 for roundness) out of 2,000 bearings, the calculation would be 1,000,000 X 7 / (2,000 X 4)  = 7,000,000/8,000 = 875.

## The Value of DPMO

Both "Defective PPM" and DPMO are indicators for the effectiveness of a process.

The use of DPMO helps in making the decision of "which process is most in need of improvement".  This is important because no organization has sufficient resources to improve everything immediately.

Here is an example.  You tested 2,000 ball bearings and rejected 4 (3 bearings for diameter and weight; 1 for roundness), for a total of 7 defects.  So DPMO is 875.
However, the Defective PPM is 1,000,000 X 4 / 2,000 = 2,000.  (4 bearings rejected out of 2,000).

Suppose you also manufacture a coiled spring that has 12 opportunities (length and diameter of the wire; length and diameter of the coil; weight; resistance to extension and compression along the axis at three operating temperatures; and roundness of the coil).  In testing 2000 coils, 8 coils were rejected; each failed different tests, but only one each.  Here, DPMO is 1,000,000 X 8 / (2,000 X 12) = 333; but the Defective PPM is 1,000,000 X 8 / 2,000 = 4,000.

Judging by Defective PPM, the coils have the bigger problem (4,000 versus 2,000).  However, judging by DPMO, the bearings are worse (875 versus 333).  There are "more problems" with the bearings than with the coils.

In the real world, gathering and analyzing the DPMO yields another benefit: knowing the type of defect may help isolate the cause.  To change the example above, suppose each defective coil failed the same test.  Then this might indicate it is valuable to determine what causes that failure.

So the process of determining DPMO has two major values:

• To determine which process should be improved, taking the product's complexity into account
• To begin isolating the cause(s) of defects

By Oskar Olofsson