SPC of multiple stream processes: a chart for enhanced detection of shifts in one stream

Abstract

The efficiency of Boyd's group charts -the classical scheme for the statistical control of multiple-stream processes- is impaired by its underlying model of the process not considering that part of the variation in such processes is common to all streams. Mortell and Runger (1995) and Runger, Alt and Montgomery (1996) proposed alternative schemes which take this fact into account. We propose a third scheme: a modified group chart, based on the differences between the values of the quality characteristic in each particular stream and the average of the values of all streams. The average run lengths of this scheme and of the competing schemes in the case of shifts in the mean of one individual stream are obtained either analytically or by simulation and compared. The results show the superiority of the proposed scheme except for shifts smaller than one standard deviation, against which no one of the schemes is really efficient.

Statistical Control of Multiple-Stream Processes: A Literature Review

“…A third scheme that considers explicitly the two sources of variation described above is Epprecht et al (2011). For controlling the mean level, they proposed (exactly as Mortell andRunger 1995, andRunger et al 1996) using a chart on the average of all streams; and, for controlling the individual streams, they proposed a GCC on the differences between each stream and the average of all streams.…”

An EWMA control chart for the mean of individual streams in multiple stream processes

“…Nelson (1986) proposed a runs scheme to be used with group charts (with or without control limits): if a same stream yields the largest (or the smallest) reading more than r times in a row (where r is defined as a function of the number of streams of the process), this should be an indication that this particular stream has a higher (or lower) mean than the other ones. Some further works on the monitoring of MSPs are Mortell & Runger (1995), Runger et al (1996), Amin & Li, (2000), Lanning et al (2002), Liu et al (2008), Xiang & Tsung (2008), Meneces et al (2008) & Epprecht et al (2011a. For a comprehensive literature review of this topic, which describes these works with some detail & includes other references, see Epprecht (2015).…”

“…Other work based on the two-component model of MSP was Epprecht et al (2011a). They proposed a residuals GCC where, in contrast with the classic GCC for the mean, the points plotted at each sampling time t are the smallest and the largest estimates of the individual streams components in time t rather than the smallest and the largest averages among all streams.…”

“…However, as mentioned, Mortell & Runger (1995) and Runger et al (1996) had proposed and analyzed also EWMA versions of their charts, which were much faster in signalling shifts of small and moderate sizes ( 2 ≤ standard deviations) than their Shewhart-type counterparts. The fact that the residuals GCC proposed by Epprecht et al (2011a) outperformed the Shewhart-type versions of the charts of those authors raises the question whether an EWMA version of the residuals GCC might outperform the EWMA versions of those charts as well. This directly motivates the proposal and analysis of such an EWMA version of the residuals GCC, that is, an EWMA GCC on the smallest and the largest estimates of the individual streams components.…”

Overview of PCA-Based Statistical Process-Monitoring Methods for Time-Dependent, High-Dimensional Data

“…An MSP results in multiple streams of output for which, from the perspective of SPM, the quality variable and its specifications are identical across all streams. An MSP may also be defined as a continuous process where multiple measurements are made on a crosssection of the product (Epprecht et al, 2011). The NASA process has features of both of these definitions.…”