Computer upgrades have a nominal time of 80 minutes. Samples of five observation

Question

Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed.

Factors for three-sigma control limits for x¯x¯  and R charts

FACTORS FOR R CHARTS

a. Using factors from above table, determine upper and lower control limits for mean and range charts. (Round your intermediate calculations and final answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

b. Decide if the process is in control.

Yes

No

SAMPLE 1 2 3 4 5 6 79.2 80.5 79.6 78.9 80.5 79.7 78.8 78.7 79.6 79.4 79.6 80.6 80.0 81.0 80.4 79.7 80.4 80.5 78.4 80.4 80.3 79.4 80.8 80.0 81.0 80.1 80.8 80.6 78.8 81.1

Explanation / Answer

Mean = Average of all 5 observations
Range = Highest - lowest observation

Sample 1 mean = (79.2+78.8+80+78.4+81)/5= 79.48
Sample 1 range = 81 - 78.4 = 2.6

Sample 2 mean = (80.5+78.7+81+80.4+80.1)/5= 80.14
Sample 2 range= 81 - 78.7 = 2.3

Sample 3 mean = (79.6+79.6+80.4+80.3+80.8)/5= 80.14
Sample 3 range= 80.8 - 79.6 = 1.2

Sample 4 mean = (78.9+79.4+79.7+79.4+80.6)/5= 79.6
Sample 4 range= 80.6 - 78.9 = 1.7

Sample 5 mean = (80.5+79.6+80.4+80.8+78.8)/5= 80.02
Sample 5 range= 80.8 - 78.8 = 2

Sample 6 mean = (79.7+80.6+80.5+80+81.1)/5= 80.38
Sample 6 range= 81.1 - 79.7 = 1.4

X bar = (79.48+80.14+80.14+79.6+80.02+80.38)/6 =79.96
R bar = (2.6+2.3+1.2+1.7+2+1.4)/6 = 1.87

Range chart

UCL : D4 * R bar = 2.11 * 1.87 = 3.95
LCL: D3 * R bar = 0 * 1,87 = 0

Mean chart

UCL: Mean X + A2 * R bar = 79.96 + 0.5775*1.87 = 81.04
LCL: Mean X - A2 * R bar = 79.96 - 0.5775*1.87 = 78.88

Since no points fall outside the limits, the process is in control.

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