Dave Green, an analyst at Hyvee, shared his forecasts of the daily Tide sales for days 1 to 15 with you as given in the table below (actual sales for days 1 to 15 is already given to you in question 4 above). Using Dave’s forecasts given below answer the following questions:
Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Dave's Forecast | 20 | 27 | 14 | 14 | 8 | 11 | 18 | 15 | 8 | 24 | 12 | 26 | 24 | 27 |
24 |
Actual Sales | 17 | 21 | 17 | 11 | 11 | 16 | 15 | 18 | 17 | 21 | 20 | 23 | 22 | 24 | 26 |
a)
Day | Dave's forecast | Actual sales | Error(x) | (x-x̄)² | x̄ | UCL | LCL |
1 | 20 | 17 | -3 | 12.04 | 0.47 | 13.7 | -12.76 |
2 | 27 | 21 | -6 | 41.86 | 0.47 | 13.7 | -12.76 |
3 | 14 | 17 | 3 | 6.4 | 0.47 | 13.7 | -12.76 |
4 | 14 | 11 | -3 | 12.04 | 0.47 | 13.7 | -12.76 |
5 | 8 | 11 | 3 | 6.4 | 0.47 | 13.7 | -12.76 |
6 | 11 | 16 | 5 | 20.52 | 0.47 | 13.7 | -12.76 |
7 | 18 | 15 | -3 | 12.04 | 0.47 | 13.7 | -12.76 |
8 | 15 | 18 | 3 | 6.4 | 0.47 | 13.7 | -12.76 |
9 | 8 | 17 | 9 | 72.76 | 0.47 | 13.7 | -12.76 |
10 | 24 | 21 | -3 | 12.04 | 0.47 | 13.7 | -12.76 |
11 | 12 | 20 | 8 | 56.7 | 0.47 | 13.7 | -12.76 |
12 | 26 | 23 | -3 | 12.04 | 0.47 | 13.7 | -12.76 |
13 | 24 | 22 | -2 | 6.1 | 0.47 | 13.7 | -12.76 |
14 | 27 | 24 | -3 | 12.04 | 0.47 | 13.7 | -12.76 |
15 | 24 | 26 | 2 | 2.34 | 0.47 | 13.7 | -12.76 |
∑ Error = 7 | ∑(x-x̄)² = 291.72 |
Error = Actual sales - Forecasted sales
The first step is to calculate the standard deviation of the forecast errors.
Standard deviation of the forecast errors = 4.41
UCL = 0.47 + 3 x 4.41
UCL = 13.70
LCL = 0.47 - 3 x 4.41
LCL = -12.76
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b)
From the control chart above, we can observe that the forecast errors are within the upper control limit and lower control limit, hence the forecast errors are in control.
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