Understanding ASQ-CQA -Knowing The Ways
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Sigma levels<br />
<strong>The</strong> table below gives long-term DPMO values corresponding to various short-term<br />
sigma levels.<br />
<strong>The</strong>se figures assume that the process mean will shift by 1.5 sigma toward the side<br />
with the critical specification limit. In other words, they assume that after the initial<br />
study determining the short-term sigma level, the long-term C pk , C pk = min[ USL−ũ<br />
3σ 3σ<br />
or C pk = min[ USL−ũ<br />
, ũ−LSL<br />
] ? value will turn out to be 0.5 less than the short-term C<br />
6σ 6σ<br />
pk<br />
value.<br />
, ũ−LSL<br />
]<br />
So, now for example, the DPMO figure given for 1 sigma assumes that the long-term<br />
process mean will be 0.5 sigma beyond the specification limit<br />
• (Cpk = –0.17) [C pk = σ -0.5], rather than 1 sigma within it,<br />
3σ<br />
• (Cpk = 0.33) [C pk = σ ] as it was in the short-term study.<br />
3σ<br />
Sigma levels<br />
<strong>The</strong> table below gives long-term DPMO values corresponding to various short-term sigma levels.<br />
<strong>The</strong>se figures assume that the process mean will shift by 1.5 sigma toward the side with the critical<br />
specification limit. In other words, they assume that after the initial study determining the short-term sigma<br />
level, the long-term C pk, C pk= min[ USL−ũ , ũ−LSL ] or C<br />
3σ 3σ pk= min[ USL−ũ , ũ−LSL ] ? value will turn out to be 0.5 less<br />
6σ 6σ<br />
than the short-term C pk value.<br />
So, now for example, the DPMO figure given for 1 sigma assumes that the long-term process mean will be 0.5<br />
sigma beyond the specification limit<br />
• (Cpk = –0.17) [C σ pk= -0.5], rather than 1 sigma within it,<br />
3σ<br />
• (Cpk = 0.33) [C σ pk= ] as it was in the short-term study.<br />
3σ<br />
Note that the defect percentages indicate only defects exceeding the specification limit to which the process<br />
mean is nearest. Defects beyond the far specification limit are not included in the percentages. <strong>The</strong> formula<br />
used here to calculate the DPMO is thus:<br />
DPMO = 1000000 x (1-Φ(level-1.5))<br />
Note that the defect percentages indicate only defects exceeding the specification limit<br />
to which the process mean is nearest. Defects beyond the far specification limit are<br />
not included in the percentages. <strong>The</strong> formula used here to calculate the DPMO is thus:<br />
DPMO = 1000000 x (1-Φ(level-1.5))<br />
https://en.wikipedia.org/wiki/Six_Sigma<br />
Charlie Chong/ Fion Zhang