Question

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

1. Build a control chart to monitor Dave’s forecast errors for days 1 to 15 (use 3 standard deviation control limits). Plot the forecast errors on the control chart you build.
2. Using the control chart you plot in part (a), discuss whether Dave’s forecast errors are in control or not.

Answer 1

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

-----------------------------------------------------------------------------------------------------------------------

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.