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Two independent methods of forecasting based on judgment and experience have been prepared each month for the past 10 months. The forecasts and actual sales are as follows:
| Month | Sales | Forecast 1 | Forecast 2 |
| 1 | 770 | 771 | 769 |
| 2 | 789 | 785 | 787 |
| 3 | 794 | 790 | 792 |
| 4 | 780 | 784 | 798 |
| 5 | 768 | 770 | 774 |
| 6 | 772 | 768 | 770 |
| 7 | 760 | 761 | 759 |
| 8 | 775 | 771 | 775 |
| 9 | 786 | 784 | 788 |
| 10 | 790 | 788 | 788 |
a. Compute a tracking signal for the 10th month for each forecast using the cumulative error for months 1 to 10. Use action limits of ± 4. Is there bias present? (Do not round your intermediate calculations. Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)
| Forecast | Tracking Signal | Bias |
| Method 1 | Present | |
| Method 2 | Present | |
b. Compute 2s control limits for each forecast. (Do not round your intermediate calculations. Round your answers to 2 decimal places.)
| Forecast | Control Limits |
| Method 1 | |
| Method 2 | |
Expert Answer
Answer
(a)
| Month | Sales | Forecast 1 | Absolute Error |
Error | Cumulative MAD | RSFE | TS =RSFE / MAD |
| 1 | 770 | 771 | 1 | -1 | 1.00 | -1.00 | -1.00 |
| 2 | 789 | 785 | 4 | 4 | 2.50 | 3.00 | 1.20 |
| 3 | 794 | 790 | 4 | 4 | 3.00 | 7.00 | 2.33 |
| 4 | 780 | 784 | 4 | -4 | 3.25 | 3.00 | 0.92 |
| 5 | 768 | 770 | 2 | -2 | 3.00 | 1.00 | 0.33 |
| 6 | 772 | 768 | 4 | 4 | 3.17 | 5.00 | 1.58 |
| 7 | 760 | 761 | 1 | -1 | 2.86 | 4.00 | 1.40 |
| 8 | 775 | 771 | 4 | 4 | 3.00 | 8.00 | 2.67 |
| 9 | 786 | 784 | 2 | 2 | 2.89 | 10.00 | 3.46 |
| 10 | 790 | 788 | 2 | 2 | 2.80 | 12.00 | 4.29 |
| Month | Sales | Forecast 2 | Absolute Error |
Error | Cumulative MAD | RSFE | TS =RSFE / MAD |
| 1 | 770 | 769 | 1 | 1 | 1.00 | 1.00 | 1.00 |
| 2 | 789 | 787 | 2 | 2 | 1.50 | 3.00 | 2.00 |
| 3 | 794 | 792 | 2 | 2 | 1.67 | 5.00 | 3.00 |
| 4 | 780 | 798 | 18 | -18 | 5.75 | -13.00 | -2.26 |
| 5 | 768 | 774 | 6 | -6 | 5.80 | -19.00 | -3.28 |
| 6 | 772 | 770 | 2 | 2 | 5.17 | -17.00 | -3.29 |
| 7 | 760 | 759 | 1 | 1 | 4.57 | -16.00 | -3.50 |
| 8 | 775 | 775 | 0 | 0 | 4.00 | -16.00 | -4.00 |
| 9 | 786 | 788 | 2 | -2 | 3.78 | -18.00 | -4.76 |
| 10 | 790 | 788 | 2 | 2 | 3.60 | -16.00 | -4.44 |
| Forecast | Tracking Signal | Bias |
| Method 1 | 4.29 | Present |
| Method 2 | -4.44 | Present |
(b)
2s Control Limits = 0 +/- 2*√MSE
| Month | Sales | Forecast 1 | Error | Error^2 |
| 1 | 770 | 771 | -1 | 1 |
| 2 | 789 | 785 | 4 | 16 |
| 3 | 794 | 790 | 4 | 16 |
| 4 | 780 | 784 | -4 | 16 |
| 5 | 768 | 770 | -2 | 4 |
| 6 | 772 | 768 | 4 | 16 |
| 7 | 760 | 761 | -1 | 1 |
| 8 | 775 | 771 | 4 | 16 |
| 9 | 786 | 784 | 2 | 4 |
| 10 | 790 | 788 | 2 | 4 |
| MSE = | 10.44 | |||
| Month | Sales | Forecast 2 | Error | Error^2 |
| 1 | 770 | 769 | 1 | 1 |
| 2 | 789 | 787 | 2 | 4 |
| 3 | 794 | 792 | 2 | 4 |
| 4 | 780 | 798 | -18 | 324 |
| 5 | 768 | 774 | -6 | 36 |
| 6 | 772 | 770 | 2 | 4 |
| 7 | 760 | 759 | 1 | 1 |
| 8 | 775 | 775 | 0 | 0 |
| 9 | 786 | 788 | -2 | 4 |
| 10 | 790 | 788 | 2 | 4 |
| MSE = | 42.44 |
| Forecast | Control Limits |
| Method 1 | (-6.46, 6.46) |
| Method 2 | (-13.03, 13.03) |
