Question

Consider the following data. We want to monitor the forecasts.

Period	Demand	Forecasts
1	52	--
2	62	59
3	59	58
4	53	65
5	58	66

We want to calculate the UCL and the LCL for the appropriate control chart to monitor the magnitude of errors.
Answer the following related questions:
Below fill in the blanks (errors of periods 2 through 5).

Period	Errors
1
2
3
4
5

1. Calculate the overall MSE to determine if the errors of the forecasts are in control. Overall MSE?
2. UCL for the control chart?  
3. LCL for the control chart?  
4. Based on your control chart, are the forecasts in control? (Yes/No)

Answer 1

Period	Demand, Dt	Forecasts, Ft	Error = Dt - Ft
1	52	--
2	62	59	3
3	59	58	1
4	53	65	-12
5	58	66	-8

Period	Demand, Dt	Forecasts, Ft	Error = Dt - Ft	Error2
1	52	--
2	62	59	3	9
3	59	58	1	1
4	53	65	-12	144
5	58	66	-8	64
Totals			-16	256

MSE = 256 / (4 - 1) = 85.33

For the UCL and LCL, one needs to specify the confidence level or the sigma level. So, assume that we are concerned with a 95% confidence level with z =1.96

So,

UCL = 0 + 1.96 * √MSE = 18.11
LCL = 0 - 1.96 * √MSE = -18.11

Yes, the forecasts are in control as all the error estimates are wihin this [LCL, UCL] range.