1 Variance Test
-
There are times when the variance or 'spread' of a
process is of greater interest than its mean. For instance,
economists and investors use variance as a measure of
risk.
-
An operations application would be when quality
managers or engineers want to ensure their company’s
productis able to consistently meet specifications.
-
The focus on variance is especially important when you
are working to tight specifications which don't allow for
much scope for the process/product characteristic
-
Analyzes the difference between an observed process
standard deviation (or variance) and a specified
standard deviation or variance.
-
Pre-project
- Verify the variability of the process
is significantly different from
expectations, validating the need
for an improvementproject.
-
Mid-project
- Verify changes from the pre-project
standard, throughout the course of
making improvements.
-
End of
Project
- Verify the variability of the
controlled improved process is
different from the pre-project
variability. Of course, this assumes
that one of the goals of the project
was to reduce the variability of the
process.
-
A XYZ manufacturing company manufactures 3 nonmetallic cables (Type A, Type b, and Type C). Type A
cable is specified to be 16 mm in thick. A major
customer requires that the variance of the type A
cables to be not more than 4 mm2
. The quality testing
person randomly selects 20 type A cables and
measures with a precise instrument and noted the
values. At 95% confidence level determine whether the
type A cable variance is not more than 4mm2
.
-
Let us conduct one variance test to find out if
the variance is significant enough
-
Step 1.a: Conduct Normality test
Note 1: Tests of the variance are
very sensitive to the assumption
of normality.
Note 2: You can also evaluate the normality test by selecting
Minitab -> Stats -> Basic Statistics -> Normality Tests (or)
Minitab -> Graph -> Probability Plot
-
Step 1.b:Normality Check and Interpret
Interpret:
As P-value is greater than 0.05, we can conclude that the
data are normal and doesn’thave any outliers.
-
Step 2: Hypothesis
- Null Hypothesis Ho: Type A cable variance is 4mm2
- Can be rewritten as σ
2 = 4mm2
- Alternate Hypothesis Ha:
- Type A cable variance is less than 4mm2
- Can be rewritten as σ
2 < 4mm2
Note: 4mm2 was the original variance of the type A
cable and σ
2
is the current population variance of the
type A cable
-
Step 3: Conduct 1 Variance Test
-
Step 4: Interpretation
- Sample Variance = 0.920. At 95% confidence level (Chisquare), the maximum standard deviation is 1.315 i.e., the
maximum variance is 1.729.
- The upper bound variance 1.315 is less than target variance 4
& p-value (0.000) less than the alpha (0.05), so, we reject the
null hypothesis.
- P-value of 0.000 indicates that there is 0.00% chance that the
population variance will be 4mm2 or more
- Inference: Type A cable variance is less than 4mm2
.