Statistical process control procedures for correlated observations

Abstract

Measurements from industrial processes are often serially correlated. The impact of this correlation on the performance of the cumulative sum and exponentially weighted moving average charting techniques is investigated in this paper. It is shown that serious errors concerning the “state of statistical process control” may result if the correlation structure of the observations is not taken into account. The use of time series methods for coping with serially correlated observations is outlined. Paper basis weight measurements are used to illustrate the time series methodology.

The impact of Weibull data and autocorrelation on the performance of the Shewhart and exponentially weighted moving average control charts

“…Montgomery and Friedman (1989) found it to occur frequently in SPC data from computer-integrated manufacturing environments. Berthouex et al (1978); MacGregor et al (1990);and Harris et al (1991) found it in continuous processes and high technology industries. Woodall et al (1993) noted that positive autocorrelation is more common in manufacturing applications than negative autocorrelation.…”

“…Two parameters (shape and scale) provide the distribution with flexibility to model systems in which the number of events (e.g., failures) increases with time (e.g., product wear), decreases with time (e.g., infant mortality) or remains constant (e.g., failures due to external shocks to the system). Likewise, many real-world processes, ranging from machining to chemical to high technology, exhibit autocorrelated behavior as cited in research by Vasilopoulos et al (1978); Ermer et al (1979); Wardell et al (1992); Box et al (1976); Alwan and Bissell (1988); Montgomery and Friedman (1989); Berthouex et al (1978), MacGregor et al (1990) and Harris et al (1991).…”

Optimal Estimation and Sampling Allocation in Survey Sampling Under a General Correlated Superpopulation Model

“…It is however quite common in practiceand especially in continuous manufacture or production lines-that this assumption is violated, and this produces misleading and unreliable control charts (Alwan, 1992;Montgomery and Mastrangelo, 1991) with tighter control limits than the true ones. A lot of attention has been drawn lately to this area of research; see for example Alwan and Roberts (1988), Harris and Ross (1991), Mastrangelo and Montgomery (1995), Apley and Lee (2003) and Reynolds (1999, 2001), and all proposed approaches make use of the present autocorrelation to either modify the existing control limits, or to model the process, identify the autocorrelation, and use the independent errors instead of the measurements for constructing any statistical tool. The models that have been assumed are AR (1) (Autogregressive), MA(1) (Moving Average) and ARMA(1,1) (Autoregressive Moving Average) (Wardell et al, 1992) and efficiency in sampling and therefore construction of the control limits provided can be improved further if the specific type of correlation is taken into account.…”

The quality movement in hospital care

“…Alwan and Roberts (1988) proposed a general approach to monitor residuals of Univariate auto correlated time series where the systematic patterns are filtered out and the special changes are more exposed. Other studies include Montgomery and Friedman (1989), Harris and Ross (1991), Montgomery and Mastrangelo (1991), Maragah and Woodall (1992), Wardell, Moskowitz and Plante (1994), Lu and Reynolds (1999), West, Delana and Jarrett (2002) and West and Jarrett (2004), English and Sastri (1990), Pan and Jarrett (2004) suggested state space methodology for the control of auto correlated process. Further, additional technologies implemented by Testik (2005), Yang and Rahim (2005) and Yeh, Huang and Wu (2004) provide newer methods for enabling better MPC methods.…”