- 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.
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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.
1 Variance Test
1 Variance Test Example
- 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
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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
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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 .