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XCHART Statement |
See CUSONES1 in the SAS/QC Sample Library |
An alternative to the V-mask cusum chart is the one-sided cusum chart with a decision interval, which is sometimes referred to as the "computational form of the cusum chart." This example illustrates how you can create a one-sided cusum chart for individual measurements.
A can of oil is selected every hour for fifteen hours. The cans are weighed, and their weights are saved in a SAS data set named CANS:*
data cans; length comment $16; label hour = 'Hour'; input hour weight comment $16. ; datalines; 1 8.024 2 7.971 3 8.125 4 8.123 5 8.068 6 8.177 Pump Adjusted 7 8.229 Pump Adjusted 8 8.072 9 8.066 10 8.089 11 8.058 12 8.147 13 8.141 14 8.047 15 8.125 ;
Suppose the problem is to detect a positive shift in the process mean of one standard deviation () from the target of 8.100 ounces. Furthermore, suppose that
Table 12.18 indicates that these ARLs can be achieved with the decision interval h=3 and the reference value k=0.5. The following statements use these parameters to create the chart and tabulate the cusum scheme:
title "One-Sided Cusum Analysis"; proc cusum data=cans; xchart weight*hour / mu0 = 8.100 /* target mean for process */ sigma0 = 0.050 /* known standard deviation */ delta = 1 /* shift to be detected */ h = 3 /* cusum parameter h */ k = 0.5 /* cusum parameter k */ scheme = onesided /* one-sided decision interval */ tableall /* table */ cinfill = ywh cframe = bigb cout = salmon cconnect = salmon climits = black coutfill = bilg; label weight = 'Cusum of Weight'; run;
The cusum plotted at HOUR=t is
The option TABLEALL requests the tables shown in Figure 12.6, Figure 12.7, and Figure 12.8. The table in Figure 12.6 summarizes the cusum scheme, and it confirms that an in-control ARL of 117.6 and an ARL of 6.4 at are achieved with the specified h and k.
The table in Figure 12.7 tabulates the information displayed in Figure 12.5.
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The table in Figure 12.8 presents the computational form of the cusum scheme described by Lucas (1976).
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Following the method of Lucas (1976), the process average at the out-of-control point (HOUR=7) can be estimated as
where S7 =3.12 is the upper sum at HOUR=7, and N7 =2 is the number of successive positive upper sums at HOUR=7.
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