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Quality and Automated Process Gauging
Published in Stephan D. Murphy, In-Process Measurement and Control, 2020
The standard Cusum chart offers an alternative method for early detection of process drift from a target value, which, in this discussion, will always be assumed to be the basic dimension as it has already been emphasized that a controllable process should almost always be centered on the basic dimension. The term Cusum refers to the cumulative sum of the differences obtained by subtracting the target value from each observed value. If a process is stable and the observed values are symmetrically distributed about the target value, this cumulative sum should wander about the target value, being sometimes positive and sometimes negative but never departing far from the target value. Thus a discernible trend away from the target value would represent an out-of-adjustment signal. Figure 10.3 shows an example of a standard Cusum mask applied to a Cusum chart.
Continuous improvement
Published in John Oakland, Marton Marosszeky, Total Quality in the Construction Supply Chain, 2006
John Oakland, Marton Marosszeky
The cusum chart is a graph that takes a little longer to draw than the conventional control chart, but gives a lot more information. It is particularly useful for plotting the evolution of processes, because it presents data in a way that enables the eye to separate true changes from a background of random variation. Cusum charts can detect small changes in data very quickly, and may be used for the control of variables and attributes. In essence, a reference or ‘target value’ is subtracted from each successive sample observation, and the result accumulated. Values of this cumulative sum are plotted, and ‘trend lines’ may be drawn on the resulting graphs. If they are approximately horizontal, the value of the variable is about the same as the target value. A downward slope shows a value less than the target and an upward slope a value greater. The technique is very useful, for example, in comparing sales forecast with actual sales figures.
System and Software Testing Strategies
Published in Ron S. Kenett, Emanuel R. Baker, Process Improvement and CMMI® for Systems and Software, 2010
Ron S. Kenett, Emanuel R. Baker
If we want better performance in tracking defects, we can analyze the same data with a cumulative sum (CUSUM) sequential procedure designed to signal weaker changes in distribution. CUSUMs are more responsive to weak changes than the control charts presented above. Control charts are, however, more responsive to abrupt changes than CUSUM charts (see [26]). A CUSUM tracks cumulative differences relative to a target value from the data being monitored. In our case, the CUSUM tracks differences in the number of defects from a target value of “0.” The procedure can be seen as analogous to tracking the status of a bank account, which combines deposits with expenses over time. The cumulative sum is analyzed by positioning a “V-mask” on the last observation. The mask is determined by two parameters, h and k. The parameter h is the width of the mask at its right-hand side; the parameter k is the slope of the V-mask arms. The values of h and k determine the rate of false alarms and the time to detection once the software has reached acceptable quality levels. The build number falling outside the mask is identified as a point of change, where the system has reached an adequate quality level. Figure 6.8 presents such a chart with a V-mask positioned at build 28. The fact that the V-mask does not include observation 19 indicates that from build 19 onward, we experience a significant decrease in the number of defects. For more on CUSUM procedures, see [26]. The procedure was set up using version 15.2 of the Minitab™ software with a target value of “0” and specifications for the mask dimensions (h = 4.0 and k = 0.5) that ensure a false alarm rate of 1/370 and a reaction to change of about four observation times.
A supervised switching-mode observer of traffic state and parameters and application to adaptive ramp metering
Published in Transportmetrica A: Transport Science, 2022
Yue Zhou, Kaan Ozbay, Pushkin Kachroo, Edward Chung
It remains to design the supervisor to detect anomalies in . We apply the so-called cumulative sum (CUSUM) method (Montgomery 2007). CUSUM is a simple statistical technique to detect anomalies in sequential data. In this paper, we employ a specific CUSUM method called the standardized CUSUM (Montgomery 2007), which was first reported by Lucas and Crosier (1982). The principle of the standardized CUSUM is straightforward and can be generically represented as (Montgomery 2007; Barratt et al. 2007): where and are higher-side and lower-side CUSUMs (explained below), respectively; δ is a specified slackness constant; is the so-called standardized deviation of the monitored signal, i.e. where represents the monitored signal; and are priorly known stationary mean and standard deviation of the monitored signal, respectively. Note that, since the monitored signals in this study are residuals from an EKF which in stationary state are zero-mean white noises, thus is zero in this study. But in general the stationary mean of the monitored signals is not necessarily zero.
Real-time prediction of propulsion motor overheating using machine learning
Published in Journal of Marine Engineering & Technology, 2022
K. H. Hellton, M. Tveten, M. Stakkeland, S. Engebretsen, O. Haug, M. Aldrin
The assumed normality and independence of the residuals is, however, an oversimplification and results in a misspecified model. But due to the large amounts of available training data and the fact that the temperature faults of interest correspond to large changes in the mean, this simplistic model still yields good results in practice. Further, the threshold b is set based on the number of false alarms in the training data, irrespective of the model assumption of the CUSUM statistic. The model misspecification therefore does not result in loss of control of the false alarms, but rather speed of detection. Given that the relevant changes in the means are relatively large, any improvement in timeliness achieved by applying a more complex residual model appears to be small.
Pipe crack early warning for burst prevention by permanent acoustic noise level monitoring in smart water networks
Published in Urban Water Journal, 2020
Chi Zhang, Martin F. Lambert, Mark L. Stephens, Jinzhe Gong, Benjamin S. Cazzolato
Some statistical methods have been previously used to identify leak-related baseline change in continuous hydraulic measurements. The Western Electric Company (WEC) rule identifies a change when one or more consecutive measurements are beyond the sample mean by multiple standard deviations (Jung et al. 2015). Loureiro et al. (2016) defined the abnormal region based on sample median and median absolute deviation, which are more robust than sample mean and sample standard deviation. The cumulative sum method (CUSUM), is a statistical process control method, and is also widely used for change detection in flow or pressure measurements (Jung et al. 2015; Jung and Lansey 2014). CUSUM involves the calculation of a cumulative sum of deviations, and the cumulative sum exceeding a certain threshold value is a sign of change, or of the occurrence of a possible crack/leak in this case. Signal processing techniques have also been combined with the permanent monitoring system to achieve better management of water network. Allen et al. (2011) applied wavelet analysis to measured transient pressures. Pipe bursts are detected and localized by identifying wavefront of pressure drops induced by bursts.