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366 Statistical Process Control for Autocorrelated Processes
mean δ is measured in terms of the standard deviation of the observations. Each
simulation run is composed of 5000 iterations. The simulation program is coded in
3
FORTRAN 77. The AR(1) process is generated using the innovation algorithm while
sequences of i.i.d. normal random variables are generated using the IMSL FORTRAN
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Library . For comparison purposes, we fixed m = 200 and set the control limits of
λ LS, max and ¯ λ LS charts such that the corresponding in-control ARL is approximately
equal to the in-control ARL of an SCC with ±3σ limits. The comparison results are
shown in Table 23.2 and illustrated in Figure 23.8. These clearly show the superiority of
the control chart based on λ LS, max . This superiority is more pronounced when φ> 0.
These results are not unexpected because, as shown in the preceding section, the
λ LS, max chart possesses the desirable properties of the SCC and CUSUM on residuals.
It is interesting to note that compared to λ LS, max , ¯ λ LS performs better in detecting
small process shifts but is less sensitive in detecting large shifts particularly when φ is
large.

23.5 CONCLUSIONS

Most traditional control charting procedures are grounded on the assumption that the
process observations being monitored are independent and identically distributed.
With the advent of high-speed data collection schemes, the assumption of indepen-
dence is usually violated. That is, autocorrelation among measurements becomes
an inherent characteristic of a stable process. This autocorrelation causes significant
deterioration in control charting performance. To address this problem, several ap-
proaches for handling autocorrelated processes have been proposed. The most pop-
ular procedure utilizes either a Shewhart, CUSUM or EWMA chart of the residuals
of the appropriately fitted ARMA model. However, procedures of this type possess
poor sensitivity especially when dealing with positively autocorrelated processes. As
an alternative, we have explored the application of the statistics used in a time series
procedure for detecting outliers and level shifts in process monitoring.
The study focused on the detection of level shifts of autocorrelated processes with
particular emphasis on the important AR(1) model. The results presented showed that
a scheme for monitoring changes in level of autocorrelated processes can be based on
either λ LS, max or ¯ λ LS .The λ LS, max control chart possesses both the desirable properties
of the Shewhart and CUSUM charts. It therefore gives superior ARL performance
compared with the existing procedures for detecting level shifts of autocorrelated
processes. Compared to the SCC and λ LS, max charts, the ¯ λ LS chart is found to be more
sensitive in detecting small shifts but less sensitive in detecting large shifts.
One can easily extend the proposed control charting scheme to effectively detect the
presence of additive and innovational outliers. A refined identification of the type of
intervention affecting the process will allow users to effectively track the source of an
out-of-control situation which is an important step in eliminating the special causes of
variation. It is also important to note that the proposed procedure can also be applied
when dealing with a more general autoregressive integrated moving average model.
Autocorrelated process observations mainly arise under automated data collection
schemes. Such collection schemes are typically controlled by software which can be