Page 447 - Design for Six Sigma for Service (Six SIGMA Operational Methods)

Statistical Basics and Six Sigma Metrics 405

2
The commonly used statistical estimate for s in the normal distribution is
2
the sample variance s , where
n
s = 1 ∑ ( y − y) 2
2
−
n 1 i 1 i
=
2
for a sample of n observations y , y ,…, y from y ~ N(m, s ) and
1
2
n
y =∑ n y .
1
n i=1 i
The commonly used statistical estimates for p in a binomial distribution
ˆ
B(n, p) is the sample ratio : p
ˆ p = y
n
where y is the actual number of successes (S) in n trials.

However, statistical estimates are only approximations of the true pop-
ulation parameters. When the sample size is small, there will be sub-
stantial discrepancies between population parameters and statistical
estimates. As the sample size becomes larger, the discrepancies will get
smaller.

11.4 Quality Measures and Six Sigma Metrics

For any product or business process, there are always performance metrics
that we want to measure and improve. For example, in a loan approval
process, the cycle time (the time between the application and the loan
decision) is a performance metric. In Example 11.1, the oxide film thickness
is a performance metric and the ideal thickness is 560 Å. Most of the actual
process performance metrics are also random variables; clearly, the cycle
time of each loan application is a random variable, and the oxide film
thickness is also a random variable.

There are many quality measures that have been developed to measure the
process performance with the presence of randomness. Quality measures
compare the degree of randomness in the process performance and compare the
degree of randomness with the process performance specification. The most
commonly used process performance quality measure is the process capability
index. In Six Sigma practice, many other process performance–related metrics