Page 111 - DMGT206_PRODUCTION_AND_OPERATIONS_MANAGEMENT

Production and Operations Management

Notes A calculation is made using the following formula.
DPMO = (Number of defects × 1,000,000) / Number of opportunities for error per unit × Number
of units

As we have already studied, the control limit of acceptable error of any stream of numbers is
± 3 ‘s’ (‘s’ being the standard deviation). A product is considered acceptable if the variation is
± 3 s on the normal specification. This limits in specifications permit 66,738 defects per million.
In Six Sigma, on a long-term basis, no more than 3.4 defect parts per million or 3.4 defects per
million opportunities (DPMO) are permitted.
For a Six Sigma process with only one specification limit (upper or lower), there are six process
standard deviations between the mean of the process and the customer’s specification limit. This
is the origin of the name ‘Six Sigma’. For a process with two specification limits (upper and
lower), this translates to slightly more than six process standard deviations between the mean
and each specification limit such that the total defect rate corresponds to equivalent of six
process standard deviations. This relationship is shown graphically in Figure 5.4.

Figure 5.4: Six Sigma – A Statistical Representation

A process that is in Six Sigma control will produce no more than two defects out of every billion
units. Often, this is stated as four defects per million units which is true if the process is only
running somewhere within one sigma of the target specification.
The overall performance of a process, as the customer views it, might be 3.4 DPMO. However, a
process could indeed be capable of producing a near perfect output. As the process sigma value
increases from zero to six, the variation of the process around the mean value decreases. With a
high enough value of process sigma, the process approaches zero variation and is known as
‘zero defects’.
There are two aspects to Six Sigma programs: the people side and the methodology side. We will
take this up in order.

5.7.1 Six Sigma Roles and Responsibilities

Successful implementation of Six Sigma is based on using sound personnel practices as well as
technical methodologies. The roles and responsibilities of different people in a Six Sigma
organization are shown in Exhibit 5.1.

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