Dual Nonparametric CUSUM Control Chart Based on Ranks

In this article, we provide a sequential rank-based dual nonparametric CUSUM (DNC) control chart for detecting arbitrary magnitude of shifts in the location parameter. It is a self-starting scheme and thus can be used to monitor processes at the start-up stages. Moreover, we do not require any prior knowledge of the underlying distribution. A simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also is efficient in detecting various magnitudes of shifts. An illustrative example is given to introduce the implementation of our proposed DNC control chart. It is easy to construct and fast to compute.     

Robust algorithms for economic designing of a nonparametric control chart for abrupt shift in location

The existing statistical process control procedures typically rely on the fundamental assumption of a parametric distribution of the quality characteristic. However, when there is a lack of knowledge about the underlying distribution (as full knowledge is not available in practice), the performance of these parametric charts is very likely to be heavily degraded. Motivated by this problem, a one-sided nonparametric monitoring procedure using the single sample sign statistic is proposed for detecting a shift in the location parameter of a continuous distribution. An economic model of the control chart is developed to optimize the sample size, sampling interval, and control limits. Three data-dependent estimation approaches for the unknown parameter are evaluated and discussed. Simulation results exhibit that our proposed procedure generally performs well under a great variety of continuous distributions and hence it is recommended as an alternative scheme especially when the knowledge of the underlying distribution is imperfect. Furthermore, beneficial recommendations of estimation approach selection are provided for practical implementation of the control chart.     

A generally weighted moving average exceedance chart

Distribution-free control charts gained momentum in recent years as they are more efficient in detecting a shift when there is a lack of information regarding the underlying process distribution. However, a distribution-free control chart for monitoring the process location often requires information on the in-control process median. This is somewhat challenging because, in practice, any information on the location parameter might not be known in advance and estimation of the parameter is therefore required. In view of this, a time-weighted control chart, labelled as the Generally Weighted Moving Average (GWMA) exceedance (EX) chart (in short GWMA-EX chart), is proposed for detection of a shift in the unknown process location; this chart is based on exceedance statistic when there is no information available on the process distribution. An extensive performance analysis shows that the proposed GWMA-EX control chart is, in many cases, better than its contenders.     

Nonparametric control chart based on change-point model

A change-point control chart for detecting shifts in the mean of a process is developed for the case where the nominal value of the mean is unknown but some historical samples are available. This control chart is a nonparametric chart based on the Mann–Whitney statistic for a change in mean and adapted for repeated sequential use. We do not require any knowledge of the underlying distribution such as the normal assumption. Particularly, this distribution robustness could be a significant advantage in start-up or short-run situations where we usually do not have knowledge of the underlying distribution. The simulated results show that our approach has a good performance across the range of possible shifts and it can be used during the start-up stages of the process.      

A bootstrap control chart for inverse Gaussian percentiles

The conventional Shewhart-type control chart is developed essentially on the central limit theorem. Thus, the Shewhart-type control chart performs particularly well when the observed process data come from a near-normal distribution. On the other hand, when the underlying distribution is unknown or non-normal, the sampling distribution of a parameter estimator may not be available theoretically. In this case, the Shewhart-type charts are not available. Thus, in this paper, we propose a parametric bootstrap control chart for monitoring percentiles when process measurements have an inverse Gaussian distribution. Through extensive Monte Carlo simulations, we investigate the behaviour and performance of the proposed bootstrap percentile charts. The average run lengths of the proposed percentage charts are investigated.     

Distribution-Free Exceedance CUSUM Control Charts for Location

Distribution-free (nonparametric) control charts can be useful to the quality practitioner when the underlying distribution is not known. A Phase II nonparametric cumulative sum (CUSUM) chart based on the exceedance statistics, called the exceedance CUSUM chart, is proposed here for detecting a shift in the unknown location parameter of a continuous distribution. The exceedance statistics can be more efficient than rank-based methods when the underlying distribution is heavy-tailed and/or right-skewed, which may be the case in some applications, particularly with certain lifetime data. Moreover, exceedance statistics can save testing time and resources as they can be applied as soon as a certain order statistic of the reference sample is available. Guidelines and recommendations are provided for the chart's design parameters along with an illustrative example. The in- and out-of-control performances of the chart are studied through extensive simulations on the basis of the average run-length (ARL), the standard deviation of run-length (SDRL), the median run-length (MDRL), and some percentiles of run-length. Further, a comparison with a number of existing control charts, including the parametric CUSUM chart and a recent nonparametric CUSUM chart based on the Wilcoxon rank-sum statistic, called the rank-sum CUSUM chart, is made. It is seen that the exceedance CUSUM chart performs well in many cases and thus can be a useful alternative chart in practice. A summary and some concluding remarks are given.     

A new double sampling control chart for monitoring process mean using auxiliary information

Statistical quality control charts have been widely accepted as a potentially powerful process monitoring tool because of their excellent speed in tracking shifts in the underlying process parameter(s). In recent studies, auxiliary-information-based (AIB) control charts have shown superior run length performances than those constructed without using it. In this paper, a new double sampling (DS) control chart is constructed whose plotting-statistics requires information on the study variable and on any correlated auxiliary variable for efficiently monitoring the process mean, namely AIB DS chart. The AIB DS chart also encompasses the classical DS chart. We discuss in detail the construction, optimal design, run length profiles, and the performance evaluations of the proposed chart. It turns out that the AIB DS chart performs uniformly better than the DS chart when detecting different kinds of shifts in the process mean. It is also more sensitive than the classical synthetic and AIB synthetic charts when detecting a particular shift in the process mean. Moreover, with some realistic beliefs, the proposed chart outperforms the exponentially weighted moving average chart. An illustrative example is also presented to explain the working and implementation of the proposed chart.     

A non parametric CUSUM control chart based on the Mann–Whitney statistic

We consider a novel univariate non parametric cumulative sum (CUSUM) control chart for detecting the small shifts in the mean of a process, where the nominal value of the mean is unknown but some historical data are available. This chart is established based on the Mann–Whitney statistic as well as the change-point model, where any assumption for the underlying distribution of the process is not required. The performance comparisons based on simulations show that the proposed control chart is slightly more effective than some other related non parametric control charts.     

A control chart for COM-Poisson distribution using a modified EWMA statistic

In this paper, a control chart has been developed for the Conway–Maxwell Poisson (COM-Poisson) distribution using the modified exponentially weighted moving average statistic. The proposed chart provides an efficient detection of smaller changes in the location parameter of the COM-Poisson distribution. The performance of the proposed control chart has been evaluated by the average and the standard deviation of the run length distribution for various parameters. Better detecting ability has also been compared with the existing control chart using EWMA statistic. Using simulation, we also showed the detecting ability over the traditional EWMA chart.     

A median loss control chart for monitoring quality loss under skewed distributions

The quality and loss of products are crucial factors separating competitive companies in global market. Firms widely employ a loss function to measure the loss caused by a deviation of the quality variable from the target value. Monitoring this deviation from the process target value is important from the view of Taguchi’s philosophy. In reality, there are many situations where the distribution of the quality variable may not be normal but skewed. This paper aims at developing a median loss (ML) control chart for monitoring quality loss under skewed distributions. Both the cases with fixed and variable sampling intervals are considered. Numerical results show that the ML chart with (optimal) variable sampling intervals performs better than the ML chart in detecting small to moderate shifts in the process loss centre or in the difference of mean and target and/or variance of a process variable. The ML chart and the ML chart with variable sampling intervals also illustrate the best performance in detection out-of-control process for a process quality variable with a left-skewed distribution. A numerical example illustrates the application of the proposed control chart.     

Economic design of non parametric sign control chart

An economic design of sign chart to control the median is proposed. Since the sign chart is distribution free, it can easily be applied to any process without prior knowledge of process quality distribution. The effect on loss cost observed for different shifts in location shows that the sign chart performs better for large shifts. The economic statistical performance study reveals that statistical performance of sign chart can be improved sufficiently for moderate shifts in the process. Sensitivity study shows that design is more sensitive for change in values of penalty loss cost and time required for search and repair of an assignable cause.     

Fast Initial Response Features for Poisson GWMA Control Charts

The Poisson GWMA (PGWMA) control chart is an extension model of Poisson EWMA chart. It is substantially sensitive to small process shifts for monitoring Poisson observations. Recently, some approaches have been proposed to modify EWMA charts with fast initial response (FIR) features. In this article, we employ these approaches in PGWMA charts and introduce a novel chart called Poisson double GWMA (PDGWMA) chart for comparison. Using simulation, various control schemes are designed and their average run lengths (ARLs) are computer and compared. It is shown that the PDGWMA chart is the first choice in detecting small shifts especially when the shifts are downward, and the PGWMA chart with adjusted time-varying control limits performs excellently in detecting great process shifts during the initial stage.     

The Generally Weighted Moving Average Variance Chart

This article extends the generally weighted moving average (GWMA) technique for detecting changes in process variance. The proposed chart is called the generally weighted moving average variance (GWMAV) chart. Simulation is employed to evaluate the average run length (ARL) characteristics of the GWMAV and EWMA control charts. An extensive comparison of these control charts reveals that the GWMAV chart is more sensitive than the EWMA control charts for detecting small shifts in the variance of a process when the shifts are below 1.35 standard deviations. Additionally, the GWMAV control chart performs little better when the variance shifts are between 1.35 and 1.5 standard deviation, and the 2 charts performs similar when the variance shifts are above 1.5 standard deviation. The design of the GWMAV chart is also discussed.     

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.     

CUSUM Control Charts for Multivariate Poisson Distribution

A cumulative sum control chart for multivariate Poisson distribution (MP-CUSUM) is proposed. The MP-CUSUM chart is constructed based on log-likelihood ratios with in-control parameters, Θ₀, and shifts to be detected quickly, Θ₁. The average run length (ARL) values are obtained using a Markov Chain-based method. Numerical experiments show that the MP-CUSUM chart is effective in detecting parameter shifts in terms of ARL. The MP-CUSUM chart with smaller Θ₁ is more sensitive than that with greater Θ₁ to smaller shifts, but more insensitive to greater shifts. A comparison shows that the proposed MP-CUSUM chart outperforms an existing MP chart.     

The Synthetic Mean Square Error Control Chart

A synthetic mean square error (MSE) control chart is presented in this study for monitoring the changes in the mean and standard deviation of a normally distributed process. The synthetic MSE control chart is a combination of the standard MSE control chart and the conforming run length (CRL) control chart. From the numerical comparisons, the synthetic MSE control chart is always more efficient than the standard MSE control chart in detecting shifts in the process mean and standard deviation. The synthetic MSE chart also performs better than the exponentially weighted moving average-semicircle (EWMA-SC) chart, except for some cases where the process mean shifts are small.     

Multivariate Synthetic |S| Control Chart with Variable Sampling Interval

A variable sampling interval (VSI) feature is introduced to the multivariate synthetic generalized sample variance |S| control chart. This multivariate synthetic control chart is a combination of the |S| sub-chart and the conforming run length sub-chart. The VSI feature enhances the performance of the multivariate synthetic control chart. The comparative results show that the VSI multivariate synthetic control chart performs better than other types of multivariate control charts for detecting shifts in the covariance matrix of a multivariate normally distributed process. An example is given to illustrate the operation of the VSI multivariate synthetic chart.     

A new approach for monitoring process variance

ABSTRACT

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having non-normal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used in such circumstances. In this paper, we propose a new variance chart based on a simple statistic to monitor process variance shifts. We explore the sampling properties of the new monitoring statistic and calculate the average run lengths (ARLs) of the proposed variance chart. Furthermore, an arcsine transformed exponentially weighted moving average (EWMA) chart is proposed because the ARLs of this modified chart are more intuitive and reasonable than those of the variance chart. We compare the out-of-control variance detection performance of the proposed variance chart with that of the non-parametric Mood variance (NP-M) chart with runs rules, developed by Zombade and Ghute [Nonparametric control chart for variability using runs rules. Experiment. 2014;24(4):1683–1691], and the nonparametric likelihood ratio-based distribution-free exponential weighted moving average (NLE) chart and the combination of traditional exponential weighted moving average (EWMA) mean and EWMA variance (CEW) control chart proposed by Zou and Tsung [Likelihood ratio-based distribution-free EWMA control charts. J Qual Technol. 2010;42(2):174–196] by considering cases in which the critical quality characteristic has a normal, a double exponential or a uniform distribution. Comparison results showed that the proposed chart performs better than the NP-M with runs rules, and the NLE and CEW control charts. A numerical example of service times with a right-skewed distribution from a service system of a bank branch in Taiwan is used to illustrate the application of the proposed variance chart and of the arcsine transformed EWMA chart and to compare them with three existing variance (or standard deviation) charts. The proposed charts show better detection performance than those three existing variance charts in monitoring and detecting shifts in the process variance.     

Likelihood ratio-based distribution-free sequential change-point detection

Most existing control charts are for monitoring location or scale parameters, rather than any change in process distribution such as shift in shape. Goodness-of-fit (GOF) test can detect any change in distribution. This paper develops a new distribution-free control chart by integrating a powerful two-sample nonparametric likelihood ratio GOF test into the effective change-point model. Our proposed chart is easy in computation, convenient to use, and very efficient in detecting any change in process distribution, including shifts in location, scale, and shape. It is also robust in detecting various magnitudes of shifts and especially powerful in monitoring any distributional change involving a decrease in scale.     

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.