Understanding ASQ-CQA -Knowing The Ways

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