Page 263 - Lean six sigma demystified

Chapter 7 ReduCing VaRiation with Six Sigm a 241

Cr = 1/Cp, so a Cp of 1.33 is equal to a Cr of 0.75. Cr calculates the percent
(e.g., 75%) of the tolerance (USL–LSL) taken up by the data. Cr, ideally, should
be less than 0.75 (four sigma).
Z Target or ∆Z calculates how far the average varies from the target value
(the midpoint between USL and LSL). Ideally, the average should be no more
than 0.5 (half a standard deviation) from the target.
Cp and Cpk are more widely used, but some industries prefer Cr and
Z Target.
? still struggling

If you’re in manufacturing, most customers use Cp and Cpk to access your prod-
uct’s quality. using the Qi macros and data from your process combined with
customer specification limits, it’s easy to check Cp and Cpk.

Defects in Parts per Million

Because we’re using a small sample to analyze process capability, it might seem
difficult to calculate the estimated defects, but statistics makes it easy. Since we
know the standard deviation and the specification limits, through the magic of
statistics we can estimate how many parts out of a million will be outside the
specification limits. In Fig. 7-9, some of the data points are outside of the spec-
ification limits resulting in an actual defect rate in parts per million (PPM) of

30,000 and an estimate (based on standard deviation) of 26,710 (Cp = 0.74,
Cpk = 0.66). Figure 7-10 shows a centered distribution of wafer strength and
an estimated PPM of only 177 (Cp = 1.19, Cpk = 1.12).

Improvement Objectives

Once you have run a histogram to calculate Cp and Cpk, you can decide how
to improve. If the process is off-center, adjust your work so that it becomes
centered. If the capability is less than 1.33, adjust your process so that there is
less variation. In manufacturing, customers require Cp = Cpk greater than 1.33
(four sigma). If you are producing products for the Asian market, especially
Japan, they require Cp = Cpk greater than 1.66 (five sigma).