Dear Sir,
Following is the assignment came to me following a 6 Sigma assignment with small company. Being, out of touch with 6 Sigma and statistical Concept since 2 years (Currently I m in Software Quality Assurance), I request to you to help me by providing guidelines on how to approach on following real life situations.
Your answers will also be used to select/choose our six sigma guide/mentor/MBB for 6 sigma implementation.

Below are the set of questions on which I need your short replies. You are not suppose calculate and give complete analysis, but only display your approach to the problem solution step by step and analysis of output/Graphs as in Minitab.

Your earlier reply will be appreciated.

Thx and Regds
Aman

Situations

1. Conduct a Gage R & R study of the following data, where five parts are evaluated twice by two appraisers (A & B).
Appraiser A Appraiser B
Part 1 2 3 4 5 1 2 3 4 5
1 113 113 71 101 113 112 117 82 98 110
2 114 106 73 97 130 112 107 83 99 108
Utilize specification limits of 100 +/- 20.

2. Dice Exercise: Each person in a workshop rolls a die 25 times, records the number of times each number appears, and calculates an average value. The instructor collects from attendees the total number of times each number is rolled and plots the information. Average values from all attendees are collected and plotted in a histogram format. Note the shape of each curve.

3. From curve of the average rolls of the die (or averages of card draws), estimate the range of roll mean values that are expected for 25 rolls of the die 90% of the time. Describe how the distribution shape of mean values would change if there were 50 rolls of the die.

4. A part is not to exceed a failure rate of 3.4 failures in one million
1. Determine the sample size needed for a hypothesis test of the equality of this failure rate to a 3.4 ppm failure. Use risks of 0.05 and an uncertainty of +- 10% of the failure rate target
2. Determine the sample size if one failure were permitted with a 95% confidence statement (using a reduced sample size testing approach)
3. Determine the failure rate of the sample f two failures occurred during the testing (using a reduced sample size testing approach)
4. Comment on your results and implementation challenges
5. Solve the problem with failure rate 4.3 dpm

5. A manufactured wants to select only one supplier of a key part that is used in the manufacturing process. The cost for parts from supplier A is greater than that for supplier B. A random sample of 1000 parts was taken from each of the suppliers processes. The output from each sample was compared to the specifications. Suppliers A had 10 parts beyond the specification limits, while supplier B had 15.
1. Determine if there is a significance differences at a level of 0.1
2. Comment on the findings and make recommendations.

6. Fabric is woven on a large number of looms. It is suspected that variation can occur both within the samples from fabric from the same loom and between different looms. To investigate this, four looms were randomly selected and four strength determinations were made on the fabric that was produced. Conduct a variance of components analysis of the data.
Looms Observations
1 2 3 4
1 98 97 99 96
2 91 90 93 92
3 96 95 97 95
4 95 96 99 98

7. The breaking strength of a fiber is studied as a function of four machines and three operators using fiber from one batch. Using computer software, analyze the following data and draw conclusions. Comment on how these variables could be related to a transactional process.
Operator Machine
1 2 3 4
1 109 110 108 110
110 115 109 108
2 110 110 111 114
112 111 109 112
3 116 112 114 120
114 115 119 117

8. Conduct a multiple regression analysis of the four factors on cycle time. Comment on the results. Determine the expected value for Y given A = 93.1

A B C D Cycle Time
63.8 30.13 26.11 25.60 442.75
64.3 30.36 26.10 25.36 444.36
62.9 31.05 26.02 25.20 444.82
66.9 30.13 25.97 25.36 445.51
69.7 29.90 26.02 25.60 446.43
70.0 30.13 26.03 28.00 467.59
72.2 31.05 25.94 27.44 472.88
73.9 30.13 25.94 27.20 478.86
69.6 31.05 25.99 28.00 477.25
72.4 31.28 25.94 27.20 478.86
64.9 31.05 25.97 29.60 491.97
74.3 31.28 25.97 29.28 492.43
74.8 31.28 25.94 28.56 493.58

9. Create a two-factor interaction plot of the following data:
Temperature Pressure Response
100 250 275
100 300 285
120 250 270
120 300 325
a. Determine what parameter settings yield the highest response.
b. Determine what parameter settings would be the best if it were important to reduce the response variability that results from frequent temperature variations between the two extremes.

10. Create a 16 trial full factorial when the factors have two levels. Determine the contrast columns for all interactions and list them with the factorial design. Comment on the frequency of the +’s and –‘s in each columns