The RL2 chart versus the np chart for detecting upward shifts in fraction defective

The use of the np chart for monitoring fraction-defective is well-established, but there are a number of relatively simple alternatives based on run-lengths of conforming items. Here, the RL₂ chart, based on the moving sum of two successive conforming run-lengths, is investigated in order to provide SPC practitioners with clear-cut guidance on the comparative performance of these competing charts. Both sampling inspection and 100% inspection are considered here, and it is shown that the RL₂ chart can often be considerably more efficient than the np chart, but the comparative performance depends on the false-alarm rate used for the comparison. Graphs to aid parameter-choice for the RL₂ chart are also provided.     

Control charts for fraction nonconforming in a bivariate binomial process

Many multivariate quality control techniques are used for multivariate variable processes, but few work for multivariate attribute processes. To monitor multivariate attributes, controlling the false alarms (type I errors) and considering the correlation between attributes are two important issues. By taking into account these two issues, a new control chart is presented to monitor a bivariate binomial process. An example is illustrated for the proposed method. To evaluate the performance of the proposed method, a simulation study is conducted to compare the results with those using both the multivariate np chart and skewness reduction approaches. The results show that the correlation is taken into account in the designed chart and the overall false alarm is controlled at the nominal value. Moreover, the process shift can be quickly detected and the variable that is responsible for a signal can be determined.     

A new multivariate CUSUM chart using principal components with a revision of Crosier's chart

In this article, we introduce a new multivariate cumulative sum chart, where the target mean shift is assumed to be a weighted sum of principal directions of the population covariance matrix. This chart provides an attractive performance in terms of average run length (ARL) for large-dimensional data and it also compares favorably to existing multivariate charts including Crosier's benchmark chart with updated values of the upper control limit and the associated ARL function. In addition, Monte Carlo simulations are conducted to assess the accuracy of the well-known Siegmund's approximation of the average ARL function when observations are normal distributed. As a byproduct of the article, we provide updated values of upper control limits and the associated ARL function for Crosier's multivariate CUSUM chart.     

CUSUM chart for detecting range shifts when monotonicity of likelihood ratio is invalid

It is often encountered in the literature that the log-likelihood ratios (LLR) of some distributions (e.g. the student t distribution) are not monotonic. Existing charts for monitoring such processes may suffer from the fact that the average run length (ARL) curve is a discontinuous function of control limit. It implies that some pre-specified in-control (IC) ARLs of these charts may not be reached. To guarantee the false alarm rate of a control chart lower than the nominal level, a larger IC ARL is usually suggested in the literature. However, the large IC ARL may weaken the performance of a control chart when the process is out-of-control (OC), compared with a just right IC ARL. To overcome it, we adjust the LLR to be a monotonic one in this paper. Based on it, a multiple CUSUM chart is developed to detect range shifts in IC distribution. Theoretical result in this paper ensures the continuity of its ARL curve. Numerical results show our proposed chart performs well under the range shifts, especially under the large shifts. In the end, a real data example is utilized to illustrate our proposed chart.     

A single-featured EWMA-X control chart for detecting shifts in process mean and standard deviation

The combined EWMA-X chart is a commonly used tool for monitoring both large and small process shifts. However, this chart requires calculating and monitoring two statistics along with two sets of control limits. Thus, this study develops a single-featured EWMA-X (called SFEWMA-X) control chart which has the ability to simultaneously monitor both large and small process shifts using only one set of statistic and control limits. The proposed SFEWMA-X chart is further extended to monitoring the shifts in process standard deviation. A set of simulated data are used to demonstrate the proposed chart's superior performance in terms of average run length compared with that of the traditional charts. The experimental examples also show that the SFEWMA-X chart is neater and easier to visually interpret than the original EWMA-X chart.     

Evaluation of CUSUM Charts for Finite-Horizon Processes

This article analyses and evaluates the properties of a CUSUM chart designed for monitoring the process mean in short production runs. Several statistical measures of performance that are appropriate when the process operates for a finite-time horizon are proposed. The methodology developed in this article can be used to evaluate the performance of the CUSUM scheme for any given set of chart parameters from both an economic and a statistical point of view, and thus, allows comparisons with various other charts.     

A distribution-free multivariate CUSUM control chart using dynamic control limits

In modern quality control, it is becoming common to simultaneously monitor several quality characteristics of a process with rapid evolving data-acquisition technology. When the multivariate process distribution is unknown and only a set of in-control data is available, the bootstrap technique can be used to adjust the constant limit of the multivariate cumulative sum (MCUSUM) control chart. To further improve the performance of the control chart, we extend the constant control limit to a sequence of dynamic control limits which are determined by the conditional distribution of the charting statistics given the sprint length. Simulation results show that the novel control chart with dynamic control limits offers a better ARL performance, compared with the traditional MCUSUM control chart. Despite it, the proposed control chart is considerably computer-intensive. This leads to the development of a more flexible control chart which uses a continuous function of the sprint length as the control limit sequences. More importantly, the control chart is easy to implement and can reduce the computational time significantly. A white wine data illustrates that the novel control chart performs quite well in applications.     

A synthetic control chart for monitoring the small shifts in a process mean based on an attribute inspection

Abstract

In this paper, a synthetic control chart is proposed by integrating the salient features of the np_x chart and the CRL chart. The synthetic chart achieves higher detection effectiveness on both small and large mean shifts while retaining the operational simplicity of the attribute charts owing to only using attribute inspection. Both statistical and economic design of the synthetic chart are considered and numerical tests have indicated that the synthetic chart has a higher power for detecting mean shifts than the np_x chart, MON chart and CUSUM chart. In addition, sensitivity analyses are also performed under both the statistical and economic design model.     

An adaptive multivariate CUSUM control chart for signaling a range of location shifts

ABSTRACT

In this work, we proposed an adaptive multivariate cumulative sum (CUSUM) statistical process control chart for signaling a range of location shifts. This method was based on the multivariate CUSUM control chart proposed by Pignatiello and Runger (1990 Pignatiello, J.J., Runger, G.C. (1990). Comparisons of multivariate CUSUM charts. J. Qual. Technol. 22(3):173–186.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), but we adopted the adaptive approach similar to that discussed by Dai et al. (2011 Dai, Y., Luo, Y., Li, Z., Wang, Z. (2011). A new adaptive CUSUM control chart for detecting the multivariate process mean. Qual. Reliab. Eng. Int. 27(7):877–884.[Crossref], [Web of Science ®] , [Google Scholar]), which was based on a different CUSUM method introduced by Crosier (1988 Crosier, R.B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics 30(3):291–303.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The reference value in this proposed procedure was changed adaptively in each run, with the current mean shift estimated by exponentially weighted moving average (EWMA) statistic. By specifying the minimal magnitude of the mean shift, our proposed control chart achieved a good overall performance for detecting a range of shifts rather than a single value. We compared our adaptive multivariate CUSUM method with that of Dai et al. (2001 Dai, Y., Luo, Y., Li, Z., Wang, Z. (2011). A new adaptive CUSUM control chart for detecting the multivariate process mean. Qual. Reliab. Eng. Int. 27(7):877–884.[Crossref], [Web of Science ®] , [Google Scholar]) and the non adaptive versions of these two methods, by evaluating both the steady state and zero state average run length (ARL) values. The detection efficiency of our method showed improvements over the comparative methods when the location shift is unknown but falls within an expected range.     

Weighted adaptive multivariate CUSUM charts with variable sampling intervals

The adaptive multivariate CUSUM (AMCUSUM) chart has received considerable attention because of its superior sensitivity against a range of mean shift sizes than that of the conventional non-adaptive multivariate CUSUM (MCUSUM) chart. Recently, weighted AMCUSUM (WAMCUSUM) charts with a fixed sampling interval (FSI) have been proposed, called the WAMCUSUM-FSI charts, which provide more sensitivity than the AMCUSUM-FSI charts. In this paper, we extend this work and propose WAMCUSUM charts with variable sampling interval (VSI), named the WAMCUSUM-VSI charts, for efficiently monitoring the mean of a multivariate normally distributed process. The Monte Carlo simulation method is used to compute the average time to signal (ATS) and the adjusted ATS (AATS) profiles of the existing and proposed charts. It is found that the WAMCUSUM-VSI charts perform substantially and nearly uniformly better than the WAMCUSUM-FSI charts in terms of the ATS and AATS performance criterion. An example is given to explain the implementation of the WAMCUSUM charts with fixed and VSIs.     

CUSUM control schemes for Gaussian processes

A CUSUM control scheme for detecting a change point in a Gaussian process is derived. An upper and a lower bound for the distribution of the run length and for its moments is given. In a Monte Carlo study the average run length (ARL) of this chart is compared with the ARL of two other CUSUM procedures which are based on approximations to the sequential probability ratio, and, moreover, with EWMA schemes for autocorrelated data. Results on the optimal choice of the reference value are presented. Furthermore it is investigated how these charts behave if the model parameters are estimated.     

Optimal exponentially weighted moving average (EWMA) plans for detecting seasonal epidemics when faced with non-homogeneous negative binomial counts

Exponentially weighted moving average (EWMA) plans for non-homogeneous negative binomial counts are developed for detecting the onset of seasonal disease outbreaks in public health surveillance. These plans are robust to changes in the in-control mean and over-dispersion parameter of the negative binomial distribution, and therefore are referred to as adaptive plans. They differ from the traditional approach of using standardized forecast errors based on the normality assumption. Plans are investigated in terms of early signal properties for seasonal epidemics. The paper demonstrates that the proposed EWMA plan has efficient early detection properties that can be useful to epidemiologists for communicable and other disease control and is compared with the CUSUM plan.     

CUSUM control schemes for monitoring the covariance matrix of multivariate time series

Modified cumulative sum (CUSUM) control charts and CUSUM schemes for residuals are suggested to detect changes in the covariance matrix of multivariate time series. Several properties of these schemes are derived when the in-control process is a stationary Gaussian process. A Monte Carlo study reveals that the proposed approaches show similar or even better performance than the schemes based on the multivariate exponentially weighted moving average (MEWMA) recursion. We illustrate how the control procedures can be applied to monitor the covariance structure of developed stock market indices.     

A rational sequential probability ratio test control chart for monitoring process shifts in mean and variance

The sequential probability ratio test (SPRT) chart is a very effective tool for monitoring manufacturing processes. This paper proposes a rational SPRT chart to monitor both process mean and variance. This SPRT chart determines the sampling interval d based on the rational subgroup concept according to the process conditions and administrative considerations. Since the rational subgrouping is widely adopted in the design and implementation of control charts, the studies of the rational SPRT have a practical significance. The rational SPRT chart is designed optimally in order to minimize the index average extra quadratic loss for the best overall performance. A systematic performance study has also been conducted. From an overall viewpoint, the rational SPRT chart is more effective than the cumulative sum chart by more than 63%. Furthermore, this article provides a design table, which contains the optimal values of the parameters of the rational SPRT charts for different specifications. This will greatly facilitate the potential users to select an appropriate SPRT chart for their applications. The users can also justify the application of the rational SPRT chart according to the achievable enhancement in detection effectiveness.     

A Combination of CUSUM Charts for Monitoring a Zero-Inflated Poisson Process

The Zero-inflated Poisson distribution (ZIP) is used to model the defects in processes with a large number of zeros. We propose a control charting procedure using a combination of two cumulative sum (CUSUM) charts to detect increases in the parameters of ZIP process, one is a conforming run length (CRL) CUSUM chart and another is a zero truncated Poisson (ZTP) CUSUM chart. The control limits of the control charts are obtained using both Markov chain-based methods and simulations. Simulation experiments show that the proposed method outperforms an existing method. Finally, a real example is presented.     

A combined control scheme for monitoring the frequency and size of an attribute event

A traffic accident can be considered as an example of the attribute events, and the number of the injured in each accident is called the event size. Some control charts have been developed for monitoring either the time interval (T) between the occurrences of an event or the event size (C) in each occurrence. This article studies the statistical monitoring of the attribute events in which T and C are monitored simultaneously and C is an integer. Essentially, it integrates a T chart and a C chart, and is therefore referred to as a T&C scheme. Our studies show that the new chart is more effective than an individual T chart or C chart for detecting the out-of-control status of the event, in particular for detecting downward shifts (sparse occurrence and/or small size). Another desirable feature of the T&C scheme is that its detection effectiveness is more invariable against different types of shifts (i.e. T shift, C shift and joint shift in T&C) compared with an individual T or C chart. The improvement in performance is achieved due to the simultaneous monitoring of T and C. The T&C scheme can be applied in manufacturing systems and especially in non-manufacturing sectors (e.g. supply chain management, health care industry, disaster management and security control).     

A new synthetic control chart for monitoring process mean using auxiliary information

ABSTRACT

Quality control charts have been widely recognized as a potentially powerful statistical process monitoring tool in statistical process control because of their superior ability in detecting shifts in the process parameters. Recently, auxiliary-information-based control charts have been proposed and shown to have excellent speed in detecting process shifts than those based without it. In this paper, we design a new synthetic control chart that is based on a statistic that utilizes information from both the study and auxiliary variables. The proposed synthetic chart encompasses the classical synthetic chart. The construction, optimal design, run length profiles, and the performance evaluation of the new chart are discussed in detail. It turns out that the proposed synthetic chart performs uniformly better than the classical synthetic chart when detecting different kinds of shifts in the process mean under both zero-state and steady-state run length performances. Moreover, with reasonable assumptions, the proposed chart also surpasses the exponentially weighted moving average control chart. An application with a simulated data set is also presented to explain the implementation of the proposed control chart.     

The performance of multivariate CUSUM control charts with estimated parameters

In this paper, we study the effect of estimating the vector of means and the variance–covariance matrix on the performance of two of the most widely used multivariate cumulative sum (CUSUM) control charts, the MCUSUM chart proposed by Crosier [Multivariate generalizations of cumulative sum quality-control schemes, Technometrics 30 (1988), pp. 291–303] and the MC1 chart proposed by Pignatiello and Runger [Comparisons of multivariate CUSUM charts, J. Qual. Technol. 22 (1990), pp. 173–186]. Using simulation, we investigate and compare the in-control and out-of-control performances of the competing charts in terms of the average run length measure. The in-control and out-of-control performances of the competing charts deteriorate significantly if the estimated parameters are used with control limits intended for known parameters, especially when only a few Phase I samples are used to estimate the parameters. We recommend the use of the MC1 chart over that of the MCUSUM chart if the parameters are estimated from a small number of Phase I samples.     

Performance of the zone control chart

Average run lengths of the zone control chart are presented, The performance of this chart is compared with that of several Shewhart charts with and without runs rules, It is shown that the standard zone control chart has performance similar to some even simpler charts and a much higher false alarm rate than the Shewhart chart with all of the common runs rules. It is also shown that a slightly modified zone control chart outperforms the Shewhart chart with the common runs rules.