Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed. 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 Factors for three-sigma control limits for x⎯⎯x¯ and R charts FACTORS FOR R CHARTS Number of Observations in Subgroup, n Factor for x⎯⎯x¯ Chart, A2 Lower Control Limit, D3 Upper Control Limit, D4 2 1.88 0 3.27 3 1.02 0 2.57 4 0.73 0 2.28 5 0.58 0 2.11 6 0.48 0 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.72 13 0.25 0.31 1.69 14 0.24 0.33 1.67 15 0.22 0.35 1.65 16 0.21 0.36 1.64 17 0.20 0.38 1.62 18 0.19 0.39 1.61 19 0.19 0.40 1.60 20 0.18 0.41 1.59 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.) Mean Chart Range Chart UCL LCL b. Decide if the process is in control. multiple choice Yes No
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed.
| 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 |
Factors for three-sigma control limits for
and R charts
|
FACTORS FOR R CHARTS |
||||
| Number of Observations in Subgroup, n |
Factor for x⎯⎯x¯
Chart,A2 |
Lower Control Limit, D3 |
Upper Control Limit, D4 |
|
| 2 | 1.88 | 0 | 3.27 | |
| 3 | 1.02 | 0 | 2.57 | |
| 4 | 0.73 | 0 | 2.28 | |
| 5 | 0.58 | 0 | 2.11 | |
| 6 | 0.48 | 0 | 2.00 | |
| 7 | 0.42 | 0.08 | 1.92 | |
| 8 | 0.37 | 0.14 | 1.86 | |
| 9 | 0.34 | 0.18 | 1.82 | |
| 10 | 0.31 | 0.22 | 1.78 | |
| 11 | 0.29 | 0.26 | 1.74 | |
| 12 | 0.27 | 0.28 | 1.72 | |
| 13 | 0.25 | 0.31 | 1.69 | |
| 14 | 0.24 | 0.33 | 1.67 | |
| 15 | 0.22 | 0.35 | 1.65 | |
| 16 | 0.21 | 0.36 | 1.64 | |
| 17 | 0.20 | 0.38 | 1.62 | |
| 18 | 0.19 | 0.39 | 1.61 | |
| 19 | 0.19 | 0.40 | 1.60 | |
| 20 | 0.18 | 0.41 | 1.59 | |
a. Using factors from above table, determine upper and lower control limits for mean and
| Mean Chart | Range Chart | |
| UCL | ||
| LCL | ||
b. Decide if the process is in control.
multiple choice
-
Yes
-
No
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