Page 227 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 207

When to Use

A key assumption is that the population has a normal distribution and is both
constant (it does not change over time) and homogeneous (a given sample is
representative of the sample as a whole).

Measure Stage

• To estimate process average (for baseline estimates) when insufficient
data exist to establish process control

Analyze Stage

• To compare the mean of samples from different process conditions

Methodology

Two methods may be used depending on whether you have historical evidence
of the population standard deviation.

Historical Standard Deviation Is Known

Calculate an average X of n sample units.
Calculate the confidence interval as

X − Z σ ( / n < µ < X + Z σ ( / n)
)
α /2 α /2
Based on the assumption that the samples are from a population with a

normal distribution, we use the normal distribution to determine the z values
based on a confidence level. For a 95% confidence level, α = 0.05, so for this
two-sided confidence interval (above and below the mean), the significance α
is split equally between the two sides of the interval. For α/2 = 0.025, we obtain
a value of z α/2 = 1.96 from Appendix 1.
For example, the average waiting time in a doctor’s office using a sample of
25 patients is 25.7 minutes. The population standard deviation is known to be
1.8 minutes. The confidence interval is calculated as

X + Z α /2 σ ( / n < µ < X + Z 1 −α /2 σ ( / n)
)
)( . / 25 < µ
+
(
25 .7 + − . 1 96 1 8 ) < < 25 7 1 96 1 8 / 25)
.
(
.
.
24 99 < µ < 26 41
.
.