Statistics for Environmental Engineers

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0    30    60    90    120    150


Observation


FIGURE 12.1 A Shewhart chart constructed using simulated duplicate observations (top panel) from a normal distribution with mean = 12 and standard deviation = 0.5. The mean level shifts up by 0.5 units from days 50-75, it is back to normal from days 76-92, it shifts down by 0.5 units from days 93-107, and is back to normal from day 108 onward.

TABLE 12.1


Calculations to Start the Control Charts for the Cusum, 5-Day Moving Average, and the Exponentially Weighted Moving Average (A = 0.5)


(1)


yi


(2)


У,12


(3)


Cusum


(4)


MA(5)


(5)


EWMA (A = 0.5)


11.89


0.11


0.11


12.00


12.19


0.19


0.08


12.10


12.02


0.02


0.10


12.06


11.90


0.10


0.00


11.98


12.47


0.47


0.47


12.09


12.22


12.64


0.64


1.11


12.24


12.43


11.86


-0.14


0.97


12.18


12.15


12.61


0.61


1.57


12.29


12.38


11.89


0.11


1.47


12.29


12.13


12.87


0.87


2.33


12.37


12.50


12.09


0.09


2.42


12.26


12.30


11.50


-0.50


1.93


12.19


11.90


11.84


-0.16

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