Classical Cumulative Sum Research Articles

Improving the Performance of Combined Shewhart–Cumulative Sum Control Charts

For an improved monitoring of process parameters, it is generally desirable to have efficient designs of control charting structures. The addition of Shewhart control limits to the cumulative sum (CUSUM) control chart is a simple monitoring scheme sensitive to wide range of mean shifts. To improve the detection ability of the combined Shewhart–CUSUM control chart to off‐target processes, we developed the scheme using ranked set sampling instead of the traditional simple random sampling. We investigated the run length properties of the Shewhart–CUSUM with ranked set samples and compared their performance with certain established control charts. It is revealed that the proposed schemes offer better protection against different types of mean shifts than the existing counterparts including classical Shewhart, classical CUSUM, classical combined Shewhart–CUSUM, adaptive CUSUM, double CUSUM, three simultaneous CUSUM, combined Shewhart‐weighted CUSUM, runs rules‐based CUSUM and the mixed exponentially weighted moving average‐CUSUM. Applications on real data sets are also given to demonstrate the implementation simplicity of the proposed schemes Copyright © 2012 John Wiley & Sons, Ltd.

A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean

Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are commonly used for monitoring the process mean. In this paper, a new hybrid EWMA (HEWMA) control chart is proposed by mixing two EWMA control charts. An interesting feature of the proposed control chart is that the traditional Shewhart and EWMA control charts are its special cases. Average run lengths are used to evaluate the performances of each of the control charts. It is worth mentioning that the proposed HEWMA control chart detects smaller shifts substantially quicker than the classical CUSUM, classical EWMA and mixed EWMA–CUSUM control charts. Copyright © 2012 John Wiley & Sons, Ltd.

Mixed Exponentially Weighted Moving Average–Cumulative Sum Charts for Process Monitoring

The control chart is a very popular tool of statistical process control. It is used to determine the existence of special cause variation to remove it so that the process may be brought in statistical control. Shewhart‐type control charts are sensitive for large disturbances in the process, whereas cumulative sum (CUSUM)–type and exponentially weighted moving average (EWMA)–type control charts are intended to spot small and moderate disturbances. In this article, we proposed a mixed EWMA–CUSUM control chart for detecting a shift in the process mean and evaluated its average run lengths. Comparisons of the proposed control chart were made with some representative control charts including the classical CUSUM, classical EWMA, fast initial response CUSUM, fast initial response EWMA, adaptive CUSUM with EWMA‐based shift estimator, weighted CUSUM and runs rules–based CUSUM and EWMA. The comparisons revealed that mixing the two charts makes the proposed scheme even more sensitive to the small shifts in the process mean than the other schemes designed for detecting small shifts. Copyright © 2012 John Wiley & Sons, Ltd.

Progressive Mean Control Chart for Monitoring Process Location Parameter

Control charts are widely used for process monitoring. They show whether the variation is due to common causes or whether some of the variation is due to special causes. To detect large shifts in the process, Shewhart‐type control charts are preferred. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are generally used to detect small and moderate shifts. Shewhart‐type control charts (without additional tests) use only current information to detect special causes, whereas CUSUM and EWMA control charts also use past information. In this article, we proposed a control chart called progressive mean (PM) control chart, in which a PM is used as a plotting statistic. The proposed chart is designed such that it uses not only the current information but also the past information. Therefore, the proposed chart is a natural competitor for the classical CUSUM, the classical EWMA and some recent modifications of these two charts. The conclusion of this article is that the performance of the proposed PM chart is superior to the compared ones for small and moderate shifts, and its performance for large shifts is better (in terms of the average run length). Copyright © 2012 John Wiley & Sons, Ltd.

Active Fault Diagnosis Based on Stochastic Tests

Active Fault Diagnosis Based on Stochastic TestsThe focus of this paper is on stochastic change detection applied in connection with active fault diagnosis (AFD). An auxiliary input signal is applied in AFD. This signal injection in the system will in general allow us to obtain a fast change detection/isolation by considering the output or an error output from the system. The classical cumulative sum (CUSUM) test will be modified with respect to the AFD approach applied. The CUSUM method will be altered such that it will be able to detect a change in the signature from the auxiliary input signal in an (error) output signal. It will be shown how it is possible to apply both the gain and the phase change of the output signal in CUSUM tests. The method is demonstrated using an example.

A method for quantifying reflex responses from intra-muscular and surface electromyogram

Measuring human reflex responses from electromyogram (EMG) traces in an accurate, repeatable and reliable way with a high degree of specificity has traditionally been a difficult task. This paper describes a new method that can be used to quantify reflex responses from both surface and intra-muscular EMG. This technique extends the classical cumulative sum (CUSUM) calculations by defining precise points for the calculation of latencies, durations and strengths to facilitate automatic reflex detection and permit the strength of a reflex to be defined in absolute units. The effect of varying the pre-stimulus time, the number of trials averaged and the amount of filtering used on the identification and classification of reflex parameters are also investigated. Furthermore, the effect of noise on these values, and how to remove it, is discussed. The new method, which is an expansion of the CUSUM analysis, is compared and contrasted with the more common threshold-crossing method in two different muscles: masseter and first dorsal interosseous (FDI), in experiments utilizing both mechanical and electrical stimulation. There are a number of advantages to using the new method; not only does the modified CUSUM method detect reflexes earlier than threshold-crossing methods but also the strength and duration are less susceptible to averaging and filtering parameters while giving a better indication of the reflex size. The data suggests that a pre-stimulus analysis period of at least 100 ms be used to correctly identify the variability inherent in EMG traces. It is also concluded that for subtle reflexes, 50 stimuli should be the minimum number used when spike trigger averaging is employed as lower numbers are associated with much greater pre-stimulus variability. Zero-phase filtering the rectified averaged EMG traces is recommended as this makes it easier to identify significant changes in the electrical activity of the muscle in question. In addition, noise estimation and removal from averaged rectified EMG recordings yields results that are a more accurate representation of the synaptic activity of the motor units in question.

Weighted Cumulative Sum Technique

A class of weighted control schemes that generalizes the basic cumulative sum (CUSUM) technique is introduced. The schemes of the first type, in which the weights represent information concomitant with the data, prove to be especially useful when handling charts corresponding to samples of varying sizes. The schemes of the second type are based on giving greater weight to more recent information. Representatives of this class are shown to have better run length characteristics with respect to drift in the level of a controlled process than does the classical CUSUM, while maintaining good sensitivity with respect to shifts. Analogous to the classical CUSUM scheme, they admit a dual graphical representation; that is, the scheme can be applied by means of a one- or two-sided decision interval or via a V mask. A special case of this type of scheme, designated the geometric CUSUM, is considered in detail. It can be viewed as a CUSUM-type counterpart of the exponentially weighted moving average.