For a process running at the six sigma level of quality, which of the following represents the equivalent Defects per Million Opportunities (DPMO) value?

When evaluating the quality level at six sigma, it is important to recognize how this standard correlates with defects per million opportunities (DPMO). The six sigma level signifies a process that produces no more than 3.4 defects for every million opportunities, indicating a very high level of operational quality.

To understand why the DPMO for six sigma is 3.4, it's essential to grasp the underlying mathematical foundation. The six sigma methodology defines quality levels based on statistical probabilities. At six sigma, the number of standard deviations from the mean (which represents the target or ideal outcome) is six. This means that the process operates with very few deviations from the desired outcome, leading to an extremely low rate of defects. The calculation for DPMO can take into account potential defects and the opportunities for errors in the process, which is how the number comes to be approximately 3.4.

The other values provided do not align with the definition of six sigma quality. The value of 66,810 represents a high defect rate, while 10,000, though lower than the first option, still indicates significantly more defects than what is accepted at six sigma. The 6,000 value also does not reflect the stringent standard that six sigma