A new nonparametric double exponentially weighted moving average control chart

There are many practical situations where the underlying distribution of the quality characteristic either deviates from normality or it is unknown. In such cases, practitioners often make use of the nonparametric control charts. In this paper, a new nonparametric double exponentially weighted moving average control chart on the basis of the signed-rank statistic is proposed for monitoring the process location. Monte Carlo simulations are carried out to obtain the run length characteristics of the proposed chart. The performance comparison of the proposed chart with the existing parametric and nonparametric control charts is made by using various performance metrics of the run length distribution. The comparison showed the superiority of the suggested chart over its existing parametric and nonparametric counterparts. An illustrative example for the practical implementation of the proposed chart is also provided by using the industrial data set.     

Bivariate semiparametric control charts for simultaneous monitoring of process mean and variance

In the present article, two semiparametric bivariate control charts are presented, which use order statistics and are effective in jointly monitoring of possible shifts in the process mean and/or variance. To achieve that both the median location (or more generally the location of a specific order statistic) and the number of specific observations of the test sample lying between the control limits are taken into account. The false alarm rate and the in-control average run length are not affected by the marginal distributions, while the effect of the dependence structure on them is negligible; therefore, they can be used as fully nonparametric charts. A performance-comparison study is carried out, and an illustrative example is provided using a real-world data set.     

Distribution‐free mixed cumulative sum‐exponentially weighted moving average control charts for detecting mean shifts

In this paper, we propose distribution‐free mixed cumulative sum‐exponentially weighted moving average (CUSUM‐EWMA) and exponentially weighted moving average‐cumulative sum (EWMA‐CUSUM) control charts based on the Wilcoxon rank‐sum test for detecting process mean shifts without any distributional assumption of the underlying quality process. The performances of the proposed charts are measured through the average run‐length, relative mean index, average extra quadratic loss, and average ratio of the average run‐length and performance comparison index. It is found that the proposed charts perform better than its counterparts considered in this paper under non‐normal distributions and outperform the classical mixed CUSUM‐EWMA and EWMA‐CUSUM charts in many cases under the normal distribution. The effect of the phase I sample size is also investigated on the phase II performance of the proposed charts. A numerical illustration is given to demonstrate the implementation and simplicity of the proposed charts.     

Detecting changes in location using distribution‐free control charts with big data

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.     

A survey on multivariate adaptive control charts: Recent developments and extensions

In the world of business, quality improvement is of high importance for the manufacturing industries. Statistical process control via control charts provides an online monitoring of the product's characteristic. The adaptive feature is being widely used in the design parameters of a control chart, which allows at least one of them to change during the process monitoring. Specifically, a control chart is considered adaptive if at least one of the chart's parameters (sample size, sampling interval, or control limit coefficient) is allowed to change in real time on the basis of the actual values of the sample statistics. In this paper, recent developments in the design of multivariate adaptive control schemes are presented and discussed.     

Design issues for adaptive control charts

Adaptive control charts allow the components of the quality‐monitoring scheme to vary in order to obtain improved performance over non‐adaptive control charts. Research has centered on components such as the sample size, time between samples, warning limits, and control limits and has recommended a variety of schemes, many of which are optimal in some sense. In practice, there are many other adaptive schemes that are near optimal, which will still yield considerable improvement over non‐adaptive control charts. In addition, the impact of parameter estimation on adaptive control chart performance must be taken into consideration. Based on the simulation results shown here, adaptive control charts should only be used for mature processes, where a sufficient amount of Phase I data have been obtained to ensure that the estimated control limits are accurate. When evaluating control chart performance, we consider initial state performance measures for simplicity and note that the conclusions obtained here apply to steady‐state performance measures. The evaluation of performance measures is easily handled by the Markov chain approach detailed in the Appendix. Copyright © 2008 John Wiley & Sons, Ltd.     

A class of new nonparametric circular-grid charts for signal classification

In this paper, some efficient monitoring and post-signal follow-up approaches are studied and compared for joint surveillance of location and scale of a process using the notions of circular-grid (CG) schemes. Precisely, three variants of CG Cucconi schemes are introduced and compared with three variants of percentile modified Lepage (PML) schemes. One of the PML schemes is equivalent to the traditional CG Lepage scheme, while another may be viewed as the Lepage type statistic using Gastwrith score, which is also a powerful tool for process surveillance. Overall, one of the proposed CG Cucconi schemes is most effective in identifying a class of signals, whether it is a location shift or scale shift or a shift in both parameters. It also indicates the direction of the shifts in either or both the parameters. Detecting a downward scale shift is the most challenging task in joint monitoring, and to this end, a new bias-corrected CG Lepage scheme is introduced. We compare the competing schemes in terms of correct signal classification probabilities. We illustrate the use of the proposed schemes in monitoring the trip-duration data in cab services. Some concluding remarks and future research problems are offered.     

Economic models and process quality control

Quality is an important business strategy in the economic and technological environment of today. To achieve high product quality, it is important to take explicit account of the cost of quality, and to use this cost as another management control. A new direction for achieving a cost-effective quality management system is to design statistical process controls so as to directly incorporate quality costs. This paper discusses the major approaches to the economic design of statistical process controls, and compares several different model formulations. The practical implication of these techniques is stressed. In particular, two economic models of the chart are presented: a full economic model requiring a user-specified process and nine cost parameters, and a semi-economic model using five user-specified parameters. Both of these could serve as approaches to reducing the total cost of process control. Because of its simplicity in application the semi-economic model should gain greater acceptance by practitioners for the design of process control techniques.     

A comparison study on effectiveness and robustness of control charts for monitoring process mean and variance

This article compares the effectiveness and robustness of nine typical control charts for monitoring both process mean and variance, including the most effective optimal and adaptive sequential probability ratio test (SPRT) charts. The nine charts are categorized into three types (the type, CUSUM type and SPRT type) and three versions (the basic version, optimal version and adaptive version). While the charting parameters of the basic charts are determined by common wisdoms, the parameters of the optimal and adaptive charts are designed optimally in order to minimize an index average extra quadratic loss for the best overall performance. Moreover, the probability distributions of the mean shift δ_µ and standard deviation shift δ_σ are studied explicitly as the influential factors in a factorial experiment. The main findings obtained in this study include: (1) From an overall viewpoint, the SPRT‐type chart is more effective than the CUSUM‐type chart and type chart by 15 and 73%, respectively; (2) in general, the adaptive chart outperforms the optimal chart and basic chart by 16 and 97%, respectively; (3) the optimal CUSUM chart is the most effective fixed sample size and sampling interval chart and the optimal SPRT chart is the best choice among the adaptive charts; and (4) the optimal sample sizes of both the charts and the CUSUM charts are always equal to one. Furthermore, this article provides several design tables which contain the optimal parameter values and performance indices of 54 charts under different specifications. Copyright © 2011 John Wiley & Sons, Ltd.     

The effect of measurement error on the performance of Mann-Whitney and Signed-Rank nonparametric control charts

Mann-Whitney and Signed-Rank control charts are two well-known nonparametric charts used for controlling the center of the process when the distribution of the process parameter is unknown or nonnormal. Considering the effect of measurement error on the performance of control charts, the mentioned effect with additive model is investigated on Mann-Whitney and Signed-Rank charts. Furthermore, a comparison is made between the two charts and a Shewhart-type $\overline{\mathrm{X}}$ chart (as a parametric one) in the presence of the error. To do so, a simulation program is used and average run length (ARL) of the charts are calculated under three distributions. The results for all three distributions show that the existence of measurement error weakens the performances of both nonparametric charts and larger values of the variance of the error will increase the effect. A numerical example is also discussed to show the effect on the performance of the charts. Multiple measurements is used as a way to decrease the effect of measurement error. Knowing the fact that it requires extra time and money, it can be used in real cases depending on the financial limitations of the user.     

Nonparametric signed‐rank control charts with variable sampling intervals

Variable sampling interval (VSI) charts have been proposed in the literature for normal theory (parametric) control charts and are known to provide performance enhancements. In the VSI setting, the time between monitored samples is allowed to vary depending on what is observed in the current sample. Nonparametric (distribution‐free) control charts have recently come to play an important role in statistical process control and monitoring. In this paper a nonparametric Shewhart‐type VSI control chart is considered for detecting changes in a specified location parameter. The proposed chart is based on the Wilcoxon signed‐rank statistic and is called the VSI signed‐rank chart. The VSI signed‐rank chart is compared with an existing fixed sampling interval signed‐rank chart, the parametric VSI ‐chart, and the nonparametric VSI sign chart. Results show that the VSI signed‐rank chart often performs favourably and should be used.     

Estimating the time of step change with Poisson CUSUM and EWMA control charts

Knowing when a process has changed would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process engineers. Much of the literature on change point models and techniques for statistical process control applications consider processes well modelled by the normal distribution. However, the Poisson distribution is commonly used in industrial quality control applications for modelling attribute-based process quality characteristics (e.g., counts of non-conformities). Some commonly used control charts for monitoring Poisson distributed data are the Poisson cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts. In this paper, we study the effect of changes in the design of the control chart on the performances of the change point estimators offered by these procedures. In particular, we compare root mean square error performances of the change point estimators offered by the Poisson CUSUM and EWMA control charts relative to that achieved by a maximum likelihood estimator for the process change point. Results indicate that the relative performance achieved by each change point estimator is a function of the corresponding control chart design. Relative mean index plots are provided to enable users of these control charts to choose a control chart design and change point estimator combination that will yield robust change point estimation performance across a range of potential change magnitudes.     

Monitoring the Weibull shape parameter by control charts for the sample range

In this paper, we propose control charts for monitoring changes in the Weibull shape parameter β. These charts are based on the range of a random sample from the smallest extreme value distribution. The control chart limits depend only on the sample size, the desired stable average run length (ARL), and the stable value of β. We derive control limits for both one‐ and two‐sided control charts. They are unbiased with respect to the ARL. We discuss sample size requirements if the stable value of βis estimated from past data. The proposed method is applied to data on the breaking strengths of carbon fibers. We recommend one‐sided charts for detecting specific changes in βbecause they are expected to signal out‐of‐control sooner than the two‐sided charts. Copyright © 2010 John Wiley & Sons, Ltd.     

Auxiliary-information-based efficient variability control charts for Phase I of SPC

The inclusion of correlated auxiliary variables into the monitoring scheme of quality characteristic of interest has gained notable attention in recent statistical process control (SPC) literature. Several authors have investigated the use of a correlated auxiliary variable for efficient monitoring of variability in Phase II of SPC. This phase is generally used to detect any shifts in the expected behavior of the process parameters which are often estimated from the historical in-control process in Phase I. However, no study has investigated the performance of auxiliary-based variability charts in Phase I of SPC. Here, we propose auxiliary-based dispersion control charts in Phase I of SPC. The auxiliary information is considered in the forms of regression, ratio, exponential, and power-ratio forms. The performance of the variability charts is evaluated and compared using probability to signal as a performance measure. An illustrative example is also provided to show the application of the charts. This study will provide practitioners with appropriate recommendations on the choice of dispersion charts for Phase I analysis.     

New CUSUM and Shewhart-CUSUM charts for monitoring the process mean

The CUmulative SUM (CUSUM) charts have sensitive nature against small and moderate shifts that occur in the process parameter(s). In this article, we propose the CUSUM and combined Shewhart-CUSUM charts for monitoring the process mean using the best linear unbiased estimator of the location parameter based on ordered double-ranked set sampling (RSS) scheme, where the CUSUM chart refers to the Crosier's CUSUM chart. The run-length characteristics of the proposed CUSUM charts are computed with the Monte Carlo simulations. The run-length profiles of the proposed CUSUM charts are compared with those of the CUSUM charts based on simple random sampling, RSS, and ordered RSS schemes. It is found that the proposed CUSUM charts uniformly outperform their existing counterparts when detecting all different kinds of shifts in the process mean. A real data set is also considered to explain the implementation of the proposed CUSUM charts.     

Shewhart control charts to detect mean and standard deviation shifts based on grouped data

A Shewhart control chart is proposed based on gauging theoretically continuous observations into multiple groups. This chart is designed to monitor the process mean and standard deviation for deviations from stability. By assuming an underlying normal distribution, we derive the optimal grouping criterion that maximizes the expected statistical information available in a sample. Control charts based on grouped observations are superior to standard control charts based on variables, such as X and R charts, when the quality characteristic is difficult or expensive to measure precisely, but economical to gauge.     

A wavelet‐based nonparametric CUSUM control chart for autocorrelated processes with applications to network surveillance

Statistical process control (SPC) has natural applications in data network surveillance. However, network data are commonly autocorrelated, which presents challenges to the basic SPC methods. Most existing SPC methods for correlated data assume parametric models to account for the correlation structure within the data. Those model assumptions can be difficult to justify in practice. In this paper, we propose a nonparametric cumulative sum (CUSUM) control chart for autocorrelated processes. In our proposed approach, we incorporate a wavelet decomposition and a nonparametric multivariate CUSUM control chart to obtain a robust procedure for autocorrelated processes without distribution assumptions. Extensive simulations show that the procedure appropriately controls the in‐control average run length and also has good sensitivity for detecting location shifts.     

Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location

Traditionally, a cost-efficient control chart for monitoring product quality characteristic is designed using prior knowledge regarding the process distribution. In practice, however, the functional form of the underlying process distribution is rarely known a priori. Therefore, the nonparametric (distribution-free) charts have gained more attention in the recent years. These nonparametric schemes are statistically designed either with a fixed in-control average run length or a fixed false alarm rate. Robust and cost-efficient designs of nonparametric control charts especially when the true process location parameter is unknown are not adequately addressed in literature. For this purpose, we develop an economically designed nonparametric control chart for monitoring unknown location parameter. This work is based on the Wilcoxon rank sum (hereafter WRS) statistic. Some exact and approximate procedures for evaluation of the optimal design parameters are extensively discussed. Simulation results show that overall performance of the exact procedure based on bootstrapping is highly encouraging and robust for various continuous distributions. An approximate and simplified procedure may be used in some situations. We offer some illustration and concluding remarks.     

Bayesian np control charts with adaptive sample size for finite production runs

The design of a control chart requires the specification of three decision variables, namely the sample size, n, the sampling interval, h, and the action limit under which the process must be stopped for potential repair. In this paper, the Bayesian attribute control chart, namely the np chart for short run production, using a variable sample size is discussed. In a simulated experiment, optimal solutions of the static np chart, the basic Bayesian np chart, and the Bayesian scheme with adaptive sample size are presented. Results of the empirical study show that varying the sample size leads to more cost savings compared with the other two approaches. In order to detect how the input parameters affect decision variables, a regression analysis is conducted. It is obtained that the benefits of using the basic Bayesian np chart and the Bayesian chart with adaptive sample size instead of the static scheme are affected by the length of the production run. Copyright © 2008 John Wiley & Sons, Ltd.     

Using economically designed Shewhart and adaptive ―X charts for monitoring the quality of tiles

This paper presents the economic design of ―X control charts for monitoring a critical stage of the main production process at a tile manufacturer in Greece. Two types of ―X charts were developed: a Shewhart‐type chart with fixed parameters and adaptive charts with variable sampling intervals and/or sample size. Our prime motivation was to improve the statistical control scheme employed for monitoring an important quality characteristic of the process with the objective of minimizing the relevant costs. At the same time we tested and confirmed the applicability of the theoretical models supporting the economic design of control charts with fixed and variable parameters in a practical situation. We also evaluated the economic benefits of moving from the broadly used static charts to the application of the more flexible and effective adaptive control charts. The main result of our study is that, by redesigning the currently employed Shewhart chart using economic criteria, the quality‐related cost is expected to decrease by approximately 50% without increasing the implementation complexity. Monitoring the process by means of an adaptive ―X chart with variable sampling intervals will increase the expected cost savings by about 10% compared with the economically designed Shewhart chart at the expense of some implementation difficulty. Copyright © 2006 John Wiley & Sons, Ltd.