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Fast initial response (FIR) features are generally used to improve the sensitivity of memory-type control charts by shrinking time-varying control limits in the earlier stage of the monitoring regime. This paper incorporates FIR features to increase the sensitivity of the homogeneously weighted moving average (HWMA) monitoring schemes with and without measurement errors under constant as well as linearly increasing variance scenarios. The robustness and the performance of the HWMA monitoring schemes are investigated in terms of numerous run-length properties assuming that the underlying process parameters are known and unknown. It is found that the FIR features improves the performance of the HWMA monitoring scheme as compared to the standard no FIR feature HWMA scheme, and at the same time, it is observed that the simultaneous use of a recently proposed FIR feature and multiple measurements significantly reduces the negative effect of measurement errors. An illustrative example on the volume of milk in bottles is used to demonstrate a real-life application. The authors would like to thank the reviewers and the editorial team for taking their valuable time to evaluate our manuscript. Scopus

Random causes are vital part of every process in manufacturing and nonmanufacturing environments, and these do not affect the product features. Special causes, on the other hand, come because of some burden(s) in a process and requires special attention; otherwise, it ruins the products excellence. Special causes are categorized into small, moderate, and large shifts and are handled by statistical quality control charts. The Shewhart control chart is well known for large shifts, while the cumulative sum and exponentially weighted moving average are more effective in detecting small to moderate shifts. However, in practice, many processes require the simultaneous monitoring of both the small to the large shifts. In this study, we have designed an adaptive EWMA for dispersion parameter in connection with Huber and Tukey's bisquare functions. The performance measures used in this study include average run length, extra quadratic loss, relative average run length, and performance-comparison index. We have observed that the study proposals are good competitors to the other counter parts for an efficient monitoring of shifts of varying amounts. An illustrative example using real data is given to demonstrate the implementation of the study proposal.

In this paper, we propose 3 new control charts for monitoring the lower Weibull percentiles under complete data and Type-II censoring. In transforming the Weibull distribution to the smallest extreme value distribution, Pascaul et al (2017) presented an exponentially weighted moving average (EWMA) control chart, hereafter referred to as EWMA-SEV-Q, based on a pivotal quantity conditioned on ancillary statistics. We extended their concept to construct a cumulative sum (CUSUM) control chart denoted by CUSUM-SEV-Q. We provide more insights of the statistical properties of the monitoring statistic. Additionally, in transforming a Weibull distribution to a standard normal distribution, we propose EWMA and CUSUM control charts, denoted as EWMA-YP and CUSUM-YP, respectively, based on a pivotal quantity for monitoring the Weibull percentiles with complete data. With complete data, the EWMA-YP and CUSUM-YP control charts perform better than the EWMA-SEV-Q and CUSUM-SEV-Q control charts in terms of average run length. In Type-II censoring, the EWMA-SEV-Q chart is slightly better than the CUSUM-SEV-Q chart in terms of average run length. Two numerical examples are used to illustrate the applications of the proposed control charts.

Estimation of unknown process parameters with fixed-size samples are studied in the following. The standard textbook approach for phase I control chart implementation with a Shewhart control chart is evaluated for the case of normally distributed independent observations with random sampling. The x¯−s charts are simultaneously implemented by generating observations that have a given percentage of randomly scattered out-of-control observations. Simulating the phase I steps, where out-of-control samples are detected iteratively by determining trial control limits, identifying samples exceeding these limits, and revising the control limits, the standard practice is evaluated in terms of both detection performance and quality of parameter estimates. It is shown that standard phase I control chart implementations with 3-σ-limits may perform very poorly in identifying true out-of-control observations and providing a reference set of in-control observations for estimation in some practical settings. A chart design with 2-σ-limits is recommended for a successful phase I analysis.

Control charts play an important role in Phase I studies, which are conducted to establish process control and generate reference data for parameter estimation and calculation of prospective (Phase II) control limits. Researchers have tabulated the necessary charting constants for the normal theory–based Phase I Shewhart X¯ chart for the process mean to achieve a desired nominal false alarm probability given the number of Phase I subgroups, m, up to 15. However, in practice, when parameters are estimated, the currently recommended number of Phase I subgroups is much larger than covered by their tables. Recognizing the need and taking advantage of some recently available software and computing resources, an extension to these tables is provided for m = 3(1)10 , 15(5)30 , 50(25)300 and n = 3 , 5 , 7 , 10. In addition to the tables, an R program is provided to calculate the charting constant, on demand, for user-given values of nominal false alarm probability, m, and n. An appendix shows the details of how the program should be used.

This paper proposes a simple distribution-free control chart for monitoring shifts in location when the process distribution is continuous but unknown. In particular, we are concerned with big data applications where there are sufficient in-control data that can be used to specify certain quantiles of interest which, in turn, are used to assess whether the new, incoming data to be monitored are in control. The distribution-free chart is shown to lose very little power against the Shewhart charts designed for normally distributed data. The proposed charts offer a practical and robust alternative to the classical Shewhart charts which assume normality, particularly when monitoring quantiles and the data distribution is skewed. The effect of the size of the reference sample is examined on the assumption that the quantiles are known. Conclusions and recommendations are offered.

The exponentially weighted moving average (EWMA) control chart is a well-known statistical process monitoring tool because of its exceptional pace in catching infrequent variations in the process parameter(s). In this paper, we propose new EWMA charts using the auxiliary information for efficiently monitoring the process dispersion, named the auxiliary-information–based (AIB) EWMA (AIB-EWMA) charts. These AIB-EWMA charts are based on the regression estimators that require information on the quality characteristic under study as well as on any related auxiliary characteristic. Extensive Monte Carlo simulation are used to compute and study the run length profiles of the AIB-EWMA charts. The proposed charts are comprehensively compared with a recent powerful EWMA chart—which has been shown to be better than the existing EWMA charts—and an existing AIB-Shewhart chart. It turns out that the proposed charts perform uniformly better than the existing charts. An illustrative example is also given to explain the implementation and working of the AIB-EWMA charts.

Recent studies show that Shewhart median ( X˜) chart is simpler than the Shewhart X¯ chart and it is robust against outliers, but it is often rather inefficient in detecting small or moderate process shifts. The statistical sensitivity of a Shewhart control chart can be improved by using supplementary Run Rules. In this paper, we propose the Phase II median Run Rules type control charts. A Markov chain methodology is used to evaluate the statistical performance of these charts. Moreover, the performance of proposed charts is investigated in the presence of a measurement errors and modelled by a linear covariate error model. An extensive numerical analysis with several tables and figures to show the statistical performance of the investigated charts is provided for both cases of measurement errors and no measurement errors. An example illustrates the use of these charts.

Monitoring changes in the Weibull mean and variance simultaneously is of interest in quality control. The mean and variance of a Weibull process are determined by its shape and scale parameters. Most studies are focused on monitoring the Weibull scale parameter with fixed shape parameter or the Weibull shape parameter with fixed scale parameter. In this paper, we propose an exponentially weighted moving average chart based on the likelihood-ratio test and an inverse error function called ELR chart to monitor changes in the Weibull mean and variance simultaneously. The simulation approach is used to derive the average run length. We compare our proposed chart with other existing control charts for 3 cases, including scale parameter changes with fixed shape parameter, shape parameter changes with fixed scale parameter, and both parameters changes. The results show that the ELR chart outperforms the other control charts in terms of average run length in most cases. Two numerical examples are used to illustrate the applications of the proposed control chart.

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts are popular statistical tools to improve the performance of the Shewhart chart in detecting small process shifts. In this study, we propose the mixed generally weighted moving average (GWMA)-CUSUM chart and its reverse-order CUSUM-GWMA chart to enhance detection ability compared with existing counterparts. The simulation revealed that the mixed GWMA-CUSUM and mixed CUSUM-GWMA charts have the sensitivity to detect small process shifts and efficient structures compared with the mixed EWMA-CUSUM and mixed CUSUM-EWMA charts, respectively. Moreover, the mixed GWMA-CUSUM chart with a large design parameter has robust performance, regardless of the high tail t distribution or right skewness gamma distribution.

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries come from processes exhibiting nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. This paper thus proposes a standardized asymmetric exponentially weighted moving average (EWMA) variance chart with a double sampling scheme (SDS EWMA-AV chart) for monitoring process variability. We further explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using the proposed SDS EWMA-AV chart. The performance of the SDS EWMA-AV chart and that of the single sampling EWMA variance (SS EWMA-V) chart are then compared, with the former showing superior out-of-control detection performance versus the latter. We also compare the out-of-control variance detection performance of the proposed chart with those of nonparametric variance charts, the nonparametric Mood variance chart (NP-M chart) with runs rules, and the nonparametric likelihood ratio-based distribution-free EWMA (NLE) chart and the combination of traditional EWMA (CEW) and the SS EWMA-V control charts by considering cases in which the critical quality characteristic presents normal, double exponential, uniform, chi-square, and exponential distributions. Comparison results show that the proposed chart always outperforms the NP-M with runs rules, the NLE, CEW, and the SS EWMA-V control charts. We hence recommend employing the SDS EWMA-AV chart. Finally, a numerical example of a service system for a bank branch in Taiwan is used to illustrate the application of the proposed variability control chart.

The exponentially weighted moving average (EWMA) control chart is a memory-type process monitoring tool that is frequently used to monitor small and moderate disturbances in the process mean and/or process dispersion. In this study, we propose 2 new memory-type control charts for monitoring changes in the process dispersion, namely, the generally weighted moving average and the hybrid EWMA charts. We use Monte Carlo simulations to compute the run length profiles of the proposed control charts. The run length comparisons of the proposed and existing charts reveal that the generally weighted moving average and hybrid EWMA charts provide better protection than the existing EWMA chart when detecting small to moderate shifts in the process dispersion. An illustrative dataset is also used to show the superiority of the proposed charts over the existing chart.

The performance of the variable sampling interval- X¯(VSI- X¯) chart with estimated parameters has been investigated on the basis of the average time to signal (ATS) and standard deviation of time to signal (SDTS) in past research studies. Since the values of ATS and SDTS vary from practitioner to practitioner, the use of these 2 measures is not reliable. The use of different historical data sets in phase I results in varying parameter estimates, control limits, warning limits, ATS, and SDTS values. In this study, we use the standard deviation of average time to signal (SDATS) to evaluate and compare the performance of the VSI- X¯ chart with known parameters and estimated parameters. This study shows that variation reduction in ATS values requires a larger than previously recommended phase I data. Also, detection of up to moderate shifts in the process mean with the desired ATS value would be achievable with the number of samples recommended in the past, but the in-control performance of the chart would not be reliable. Furthermore, we evaluate the effect of using large and small desired values of ATS0 on the performance of in-control and out-of-control VSI- X¯ chart. We also study the effects of estimating the mean and standard deviation on the ATS values using numerical simulation. Finally, we present a method based on warning and control limits coefficients for the estimated parameters case to reduce the number of samples required in phase I.

In this article, we propose an exponentially weighted moving average (EWMA) control chart for monitoring the covariance matrix of a multivariate process based on the dissimilarity index of 2 matrices. The proposed control chart essentially monitors the covariance matrix by comparing the individual eigenvalues of the estimated EWMA covariance matrix with those of the estimated covariance matrix from the in-control (IC) phase I data. It is different from the conventional EWMA charts for monitoring the covariance matrix, which are either based on comparing the sum or product or both of the eigenvalues of the estimated EWMA covariance matrix with those of the IC covariance matrix. We compare the performance of the proposed chart with that of the best existing chart under the multivariate normal process. Furthermore, to prevent the control limit of the proposed EWMA chart developed using the limited IC phase I data from having extensively excessive false alarms, we use a bootstrap resampling method to adjust the control limit to guarantee that the proposed chart has the actual IC ARL(average run length) not less than the nominal level with a certain probability. Finally, we use an example to demonstrate the applicability and implementation of the proposed EWMA chart.

In modern industries, advanced imaging technology has been more and more invested to cope with the ever-increasing complexity of systems, to improve the visibility of information and enhance operational quality and integrity. As a result, large amounts of imaging data are readily available. This presents great challenges on the state-of-the-art practices in process monitoring and quality control. Conventional statistical process control (SPC) focuses on key characteristics of the product or process and is rather limited to handle complex structures of high-dimensional imaging data. New SPC methods and tools are urgently needed to extract useful information from in situ image profiles for process monitoring and quality control. In this study, we developed a novel dynamic network scheme to represent, model, and control time-varying image profiles. Potts model Hamiltonian approach is introduced to characterize community patterns and organizational behaviors in the dynamic network. Further, new statistics are extracted from network communities to characterize and quantify dynamic structures of image profiles. Finally, we design and develop a new control chart, namely, network-generalized likelihood ratio chart, to detect the change point of the underlying dynamics of complex processes. The proposed methodology is implemented and evaluated for real-world applications in ultraprecision machining and biomanufacturing processes. Experimental results show that the proposed approach effectively characterize and monitor the variations in complex structures of time-varying image data. The new dynamic network SPC method is shown to have strong potentials for general applications in a diverse set of domains with in situ imaging data.

The AEWMA control chart is an adaptive EWMA (exponentially weighted moving average) type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. To improve the detection performance of the FSI (fixed sampling interval) AEWMA control chart[7] in terms of the ATS(average time to signal), this paper proposes a new VSI (variable sampling interval) AEWMA control chart. A Markov chain approach is used to calculate the ATS values of the new VSI AEWMA control chart, and comparative results show that the proposed control chart performs better than the standard FSI AEWMA control chart and than other VSI control charts over a wide range of shifts.

A common assumption for most control charts is the fact that the process parameters are supposed to be known or accurately estimated from Phase I samples. But, in practice, this is not a realistic assumption and the process parameters are usually estimated from a very limited number of samples that, in addition, may contain some outliers. Recently, a median chart with estimated parameters has been proposed to overcome these issues and it has been investigated in terms of the unconditional Average Run Length (ARL). As this median chart with estimated parameters does not take the “Phase I between-practitioners” variability into account, in this paper, we suggest to revisit it using the Standard Deviation of the ARL as a measure of performance. The results show that this Standard Deviation of the ARL–based median chart actually requires a much larger amount of Phase I data than previously recommended to sufficiently reduce the variation in the chart performance. Due to the practical limitation of the number of the Phase I data, the bootstrap method is recommended as a good alternative approach to define new dedicated control chart parameters.

Control chart procedures for monitoring paired variables are sparse in the literature. After considering the average run length properties of the d¯ chart, which monitors the mean of the differences between paired variables, we propose a new chart based on Sd, the subgroup standard deviations of the differences. Our findings show that the d¯ chart is powerful for monitoring the changes in the means and the Sd chart is suitable for monitoring changes in the covariance structure. Furthermore, we show that the d¯ and Sd charts perform better than existing bivariate control charts for detecting shifts in mean and variance/covariance, respectively, when standards are known. The difference charts also performed well compared to common alternatives when the standards are unknown arising from a limited amount of Phase I data. An application of these difference charts in a finance context is illustrated using the returns of Apple Inc's stock and the S&P 500 index.

The traditional control charts produce frequent false alarm signals in the presence of autocorrelation. The implementation of the modified chart scheme is a way of handling the problem of autocorrelation in control charts. In modified charts, the standard control limits of the traditional charts are adjusted to offset the influence because of the autocorrelation. The exponentially weighted moving average– and cumulative sum–modified charts are 2 widely used charts for monitoring autocorrelated data. These charts have design parameters in their formulation, and the choice of these parameters play significant roles in the detection of out‐of‐control situations. In reality, the magnitude of the mean shift is uncertain, and this leads to a difficulty in the choice of design parameters by the practitioner. The use of optimal parameters can enhance process performance in such situations. In this paper, we determine optimal design parameters for the charts using an exhaustive search procedure. In the optimization process, we determine the parameters that produce the smallest extra quadratic loss (EQL) value for each autocorrelation coefficient. This criterion measures the anticipated loss attributed to poor quality in the process. The loss in quality is lowered by minimizing the EQL and the combination of parameters in the chart that yields the smallest EQL has a better detection ability over the entire shift range. For the purpose of this work, we concentrate on autocorrelation that can be specifically modelled with autoregressive models. This article provides the practitioner with optimal parameters that can be used to enhance the overall effectiveness of the charts over an entire shift range. Scopus

In real life applications, many process-monitoring problems in statistical process control are based on attribute data resulting from quality characteristics that cannot be measured on numerical or quantitative scales. For the monitoring of such data, a new attribute control chart has been proposed in this study, namely, the Poisson progressive Mean (PPM) control chart. The performance of the PPM chart is compared with the existing charts used for the monitoring of Poisson processes such as the Shewhart c-chart, Poisson Exponentially Weighted Moving Average chart, Poisson double Exponentially Weighted Moving Average chart and the Poisson Cumulative Sum charts. The average run length comparison indicated the superior performance of the PPM chart in terms of shift detection ability. This study will help quality practitioners to choose an efficient attribute control chart.

Classical statistical process control (SPC) by attributes is based on counts of nonconformities. However, process quality has greatly improved with respect to past decades, and the vast majority of samples taken from high-quality processes do not exhibit defective units. Therefore, control charts by variables are the standard monitoring scheme employed. However, it is still possible to design an effective SPC scheme by attributes for such processes if the sample units are classified into categories such as ‘large’, ‘normal’, or ‘small’ according to limits that are different from the specification limits. Units classified as ‘large’ or ‘small’ will most likely still be conforming (within the specifications), but such a classification allows monitoring the process with attributes charts. In the case of dimensional quality characteristics, gages can be built for this purpose, making inspection quick and easy and reducing the risk of errors. We propose such a control chart, optimize it, compare its performance with the traditional X¯ and S charts and with another chart in the literature that is also based in classifying observations of continuous variables through gaging, and present a brief sensitivity analysis of its performance. The new chart is shown to be competitive with the use of X¯–S charts, with the operational advantage of simpler, faster, and less costly inspection. Copyright © 2017 John Wiley & Sons, Ltd.

The k-chart, based on support vector data description, has received recent attention in the literature. We review four different methods for choosing the bandwidth parameter, s, when the k-chart is designed using the Gaussian kernel. We provide results of extensive Phase I and Phase II simulation studies varying the method of choosing the bandwidth parameter along with the size and distribution of sample data. In very limited cases, the k-chart performed as desired. In general, we are unable to recommend the k-chart for use in a Phase I or Phase II process monitoring study in its current form. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we consider the conditional performance of the equal-tailed and average run lengths (ARL)-unbiased two-sided S2 charts when the in-control variance of a normal process is estimated. We derive the exact probability distributions of the conditional ARL for the two S2 charts. Then we evaluate the performance of each S2 chart in terms of the percentiles, mean and standard deviation of the conditional in-control ARL distribution. Because the parameter estimation seriously affects the conditional performance of these S2 charts, we propose an exact method to design the equal-tailed and ARL-unbiased S2 charts with desired conditional in-control performance. The results indicate that the new ARL-unbiased S2 chart has far smaller standard deviation ARL values and the unconditional ARL values are more close to the desired value than the corresponding new equal-tailed S2 chart. Copyright © 2017 John Wiley & Sons, Ltd.

Supersaturated designs are designs in which the number of factors exceeds the run size; consequently, there are not enough degrees of freedom to estimate all the main effects. The goal here is to identify the dominant factors that constitute a small proportion of the overall set of factors, according to the assumption of effect sparsity. The analysis of such designs constitutes a challenging task and, even though many methods have been proposed in the literature assuming a normal response, only few works attempted to address the case of non-normal responses. In this paper, we propose a method for screening out the most important features in supersaturated designs assuming a Bernoulli distributed response. This new approach is based on an effective chart in Statistical Process Control, the cumulative sum control chart, combined with an information theoretic measure, and it is referred as the MIC algorithm. We judge the value of MIC through comparisons with three existing approaches suggested in the literature: the least absolute shrinkage and selection operator penalization method, and two feature selection algorithms, the Conditional Mutual Information Maximization and the minimal-redundancy-maximal-relevance. The simulation study reveals that the proposed method can be considered an advantageous method because of its extremely good performance in terms of statistical power. Copyright © 2017 John Wiley & Sons, Ltd.