Data Analysis-Take Home Final First Part1

# Data Analysis-Take Home Final First Part1 - Problem 8-21 a...

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Problem 8-21 a) The shape of the histogram looks to be bimodal, which usually occurs when there are two separate normal distributions included in the data. This could indicate that there are two drive-thru windows, each with its own service time distribution.

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b) Both charts appear to be in statistical control. The s value for the x-bar chart is 13 and 12 for the moving range chart, while the r value is 17 for both. The s and r values for each chart indicate that there must be more than 10 runs and fewer than 9 consecutive points for each run; both charts meet the critical value expectations. Also important, the X Bar chart shows all the data values are less than the 4 minute maximum service time that Wally’s strives to meet. c) The mean is indicated by the control chart x-bar for this process and is 1.998 minutes. For this process, the moving range of the control chart can be used to determine the standard deviation, which is 0.796 minutes. d) To estimate the percentage of time over the service time goal, a z-score is calculated using the Upper Tolerance Limit (UTL). The calculation is a follows: From Table II in Appendix B, a z-score of 2.52 indicates that an estimated 0.568 percent of drive-thru order will meet the 4-minute deadline that is desired. e) In order to achieve a 3.4 customer per million rate of service time below the UTL while maintain the same variance, the average serving time has to be decreased. Using
Table III from Appendix B, a z-score of 4.5 must be achieved in order to meet the desired rate. The following calculation shows how the desired average serving time is calculated that meets the 4-minute UTL: The average serving time must be reduced to 0.418 minutes to meet less than 3.4 customers per million that are served in excess of 4 minutes. f) The following equation calculates the necessary decrease in standard deviation required to allow no more than 3.4 customers per million to be served in over 4 minutes whiles maintaining the same average service time and UTL: With the new standard deviation, the new and original variances and be calculated. The variance must be decreased by 68.8 percent in order to meet the less than 3.4

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Data Analysis-Take Home Final First Part1 - Problem 8-21 a...

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