Six Sigma

Q1

A Six Sigma team is testing pilot test results to see if they have made a ststistically significant improvement.

They need to test this hypothesis statistically and determine the 95% Confidence Interval for the improvement.

Data from the baseline and pilot test are reported in the table below:

Defect

Defects Good Sample Rate

Baseline 6,290 613,710 620,000 0.01015

Pilot Test 466 48,534 49,000 0.00951

Q1.1 State the hypothesis.

Q1.2 Test the hypothesis and state the results in statistical and business statements.

Q1.3 State the 95% confidence interval for the baseline process defect rate in %.

Q1.4 State the 95% confidence interval for the improved process defect rate in %.

Q1.5 Compare the results from the Confidence Interval to the hypothesis test. Do they agree? Why or why not?

Q2.

Conduct a regression analysis for the following data.

Q2.1 Test the hypothesis that X is a good predictor of Y and explain why or why not.

Q2.2 Explain the various parameters of the linear equation.

Q2.3 Explain the strength of the model using the regression model and also using a correlation analysis.

Q2.4 Show the linear line on the scatter plot graph and the linear equation.

Q2.5 Determine the predicted value of Y given X is 93.1

Q 2.6 Plot the normal probability plot and the residual plot vs X. What do you infer from them?

X Y

78.4 -9

89.9 -18.2

54.2 -33.5

58.3 -25.6

98.3 -1.5

57.8 -9

63.7 4.1

66 -35.2

67.1 -20.3

97.3 -40.3

76.5 0.3

86.1

-16.1

62.7 -8.7

81.9 -5.5

88 -14.9

60.9 -19.8

60.7 0.9

70.1 -38.5

86.7 -5.8

94.4 -33.7

61.5 -38.4

72.4 -26.2

63.9 -3.1

97.4 -43.6

Q3
Q3.1 Explain how nuisance (noise) factors can affect data analysis and experiments in the Improve phase.
Q3.2 Explain how you would combat noise when it can be controlled.
Q3.3 Explain how you would combat noise when it can’t be controlled.
Q3.4 Explain how you would use residual analysis in an ANOVA experiment.