Distribution-free Control Charts Research Articles

The Combined Shewhart-CUSUM Wilcoxon Signed-rank Control Charts for Process Location

Nonparametric one- and two-sided combined Shewhart-CUSUM (CSC) control charts for process location based on the Wilcoxon signed rank (WSR) statistic are proposed. The statistical performances of these charts are investigated through Monte Carlo simulations, when the underlying process distributions are normal, uniform and Laplace. It is observed that a CSC WSR chart can be designed so as to exhibit a trade-off statistical performance between the performances of the Shewhart WSR and CUSUM WSR charts for identifying a location shift of any size. Hence, it is a viable alternative to these two charts in a case where efficient detections of the small as well as large-sized location shifts are equally important. Computations of the control statistics of a one-sided CSC WSR chart are illustrated using simulated-data example.. KEYWORDS :Statistical process control, Average run length, Distribution-free control chart

Distribution-free control charts for monitoring scale in finite horizon productions

Distribution-free (also known as nonparametric) control charts have been shown to be useful for on-line monitoring of lot production within a finite horizon production (FHP) process. Despite the partial process knowledge at the beginning of production in a FHP process, a distribution-free control chart can be started without any restrictive assumption about the underlying distribution of the quality characteristic. In this work, three nonparametric Shewhart-type control charts are investigated to monitor the unknown scale parameter in FHP processes based on some well-known nonparametric tests for scale. To this end, the violation of the assumption of equal medians of the reference and the test population distributions is investigated and a fourth control chart based on the Moses test, which does not require this assumption, is considered. An extensive numerical analysis is performed to examine chart performance based on some metrics suitable in the FHP setting. A real industrial example is presented to show a practical implementation of the investigated charts. Conclusions and future research ideas are provided.

Efficient signed-rank based EWMA and HWMA repetitive control charts for monitoring process mean with and without auxiliary information

Control charts are powerful tools to observe the presentation of the manufacturing process. Mostly, when the data in industries come from the process may follow non-normal or unknown distributions. So, the distribution-free control charts are useful in practice when the possibility model of the process productivity is unknown. In such situations, the correct selection of the sampling mechanism is beneficial for process examination. This paper proposes a nonparametric exponentially weighted moving average signed-rank (EWMA-SR) and also proposed a homogeneously weighted moving average Signed-Rank (HWMA-SR) control charts for examining the small shift in process with the help of an auxiliary variable (in the form of a regression estimator) by using an efficient plan, namely, a repetitive sampling plan. The proposal’s presentation is evaluated and matched with its complements for different symmetric distributions by using some famous run length properties including average run length, median run length, and standard deviation of run length.

A distribution-free control chart for joint monitoring of location and scale in finite horizon productions

A distribution-free control chart for joint monitoring of location and scale in finite horizon productions

An exponentially weighted moving average control chart based on signed ranks for finite horizon processes

Distribution-free control charts are an efficient quality monitoring tool to inspect lots of parts manufactured within a finite production horizon. In this work, the performance of the Exponentially Weighted Moving Average chart based on the Wilcoxon signed rank statistic is investigated for on-line monitoring of finite production runs. The chart’s on-target performance is evaluated through a specific non-homogeneous Markov chain model under different process scenarios. A numerical analysis is conducted for determining its optimal design and a performance comparison with other available schemes is presented for different symmetric distributions of observations. Finally, an illustrative example is presented to show a practical implementation of the investigated chart.

A New Distribution-Free Control Chart for Monitoring Process Median Based on the Statistic of the Sign Test

Abstract Control charts are used to improve the quality of outputs in manufacturing, industrial, and service processes. The parametric control charts produce more false alarms and unacceptable out-of-control signals when the underlying distribution of the process is not normal. Nonparametric/distribution-free control charts are efficient alternatives to overcome the said situation. In this article, the performance of a distribution-free double exponentially weighted moving average (EWMA) chart has been investigated based on the sign test statistic under simple and ranked set sampling schemes. The run-length properties of the proposed charts have been evaluated and compared with nonparametric EWMA sign, parametric EWMA, and parametric double EWMA control charts, using different run-length measures. The comparison reveals the efficiency of the proposed chart over its alternatives in detecting small and medium shifts in the process location. A real-data application using the substrate manufacturing process has been provided to show the implementation of the proposed chart.

MONITORING PROCESS LOCATION AND DISPERSION SIMULTANEOUSLY USING A CONTROL REGION

Control charts are effective tools for detecting out-of-control conditions of process parameters in manufacturing and service industries. The development of distribution-free control charts is important in statistical process control when the process quality variable follows an unknown or a non-normal distribution. This research thus proposes to use a distribution-free technology to establish a new control region based on the exponentially weighted moving average median statistic and exponentially weighted moving average interquartile range statistic for simultaneously monitoring the process location and dispersion and further sets up a corresponding new control chart. We compute the out-of-control average run length to evaluate out-of-control detection performance of the proposed control region and also compare the proposed control region with some existing location and dispersion control charts. Results show that our proposed chart always exhibits superior detection performance when the shifts in process location and/or dispersion are small or moderate. The new control region is thus recommended. Keywords: control chart, distribution-free, dispersion and location, EWMA, kernel control region, kernel density estimation.

A distribution-free Shewhart-type Mann–Whitney control chart for monitoring finite horizon productions

Distribution-free control charts have been proposed in recent years to monitor processes with insufficient information about the distribution of observations. A promising field of application of these charts is the small production of finite batches of products, where the number of scheduled inspections is limited to a few tens. Following the machine reconfiguration after a process set-up, the quality practitioner cannot rely on past production runs to get knowledge about the distribution of the observations: this scenario can be referred to as the Case U (Unknown) condition in statistical process monitoring. Here, we investigate the issues related to the implementation of Mann–Whitney (MW) type control charts for monitoring the location in a finite horizon production (FHP) process. The practitioner-to-practitioner variability is considered while designing the control limits. The in-control and out-of-control chart performances are investigated over a wide set of scenarios and some graphical tools are proposed to help practitioners during the decision-making process. A comparison with the Shewhart Sign control chart for FHP processes is also presented. An illustrative example is provided to demonstrate the implementation of the proposed chart on a real industrial dataset.

A Nonparametric Repetitive Sampling DEWMA Control Chart Based on Linear Prediction

Distribution-free control charts can be useful in statistical process control (SPC) when only limited or no information about the distribution of the data of the process is available. In this paper, a linear prediction related double exponentially weighted moving average (DEWMA) sign control chart using a repetitive sampling scheme (RSNPDEBLP) has been considered for a binomially distributed process variable to improve the efficiency of detecting small drifts in its place of small changes. The proposed RSNPDEBLP control chart is assessed in average run length (ARL) for the various values of sample sizes. The efficiency of the proposed RSNPDEBLP control chart is compared with the existing EWMA and DEWMA sign control charts using single sampling and repetitive sampling schemes in terms of ARLs. When there are small changes in the process after the stabilization period, the proposed control chart is used to control small trends rather than small shifts.

A new nonparametric monitoring of data streams for changes in location and scale via Cucconi statistic

ABSTRACT Many distribution-free control charts have been proposed for jointly monitoring location and scale parameters of a continuous distribution when their in-control (IC) status are unknown in advance. Unfortunately, most existing methods require relatively large amount of historical observations to estimate the IC parameters or to activate the control chart, and batch observations to construct the charting statistic. When such assumptions are invalid, they may not be reliable for online monitoring. In this paper, we propose a novel distribution-free control chart for joint monitoring of location and scale parameters with extremely small IC sample size. The proposed control chart integrates the Cucconi test into the framework of change-point detection and exponentially weighted moving average strategy. It requires no prior knowledge of the underlying distribution, and is very robust in start-up situations. Comprehensive numerical results show that the proposed chart is superior to its competitors.

ROBUSTNESS OF GENERALLY WEIGHTED MOVING AVERAGE SIGNED – RANK CONTROL CHART FOR MONITORING A SHIFT OF SKEW PROCESSES

A distribution-free control charts play a virtual role in quality control chart because it is not necessary to know the assumption of specific distribution for any process. In this article, the robustness of a generally weighted moving average based on signed-rank (GWMA-SR) control charts are intensive studied for skew processes. In addition, the GWMA-SR control chart is compared the performance to detecting a shift in process mean based on GWMA with sign statistic (GWMA-SN) and exponentially weighted moving average with signed-rank statistic (EWMA-SR) control charts. The numerical results using Monte Carlo simulation found that the performance of GWMA-SR chart robust to skew process and perform as good as the benchmark charts. Furthermore, the GWMA-SR chart is superior to existing chart in many situations. Article DOI: https://dx.doi.org/10.20319/mijst.2018.43.125137 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

Conditional waiting time distributions of runs and patterns and their applications

In this paper, a simple and general method based on the finite Markov chain imbedding technique is proposed to determine the exact conditional distributions of runs and patterns in a sequence of Bernoulli trials given the total number of successes. The idea is that given the total number of successes, the Bernoulli trials are viewed as random permutations. Then, we extend the result to multistate trials. The conditional distributions studied here lead to runs and patterns-type distribution-free tests whose applications are widespread. Two applications are considered. First, a distribution-free test for randomness is applied to rainfall data at Oxford from 1858 to 1952. The second application is to develop runs and patterns-type distribution-free control charts which can be used as Phase I and/or Phase II control charts. Numerical results for two commonly used runs-type statistics, the longest run and scan statistics, are also given.

A generally weighted moving average exceedance chart

ABSTRACTDistribution-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 charts based on order statistics: Some advances

ABSTRACTIn this article, we introduce new nonparametric Shewhart-type control charts that take into account the location of two order statistics of the test sample as well as the number of observations in that sample that lie between the control limits. Exact formulae for the alarm rate, the run length distribution and the average run length (ARL) are all derived. A key advantage of the new charts is that, due to its nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the proposed charts for some typical FAR and ARL values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations, while they seem preferable from a robustness point of view in comparison with the distribution-free control chart of Balakrishnan et al. (2009).

A Cramér-von Mises test-based distribution-free control chart for joint monitoring of location and scale

This paper proposes a new distribution-free control chart by integrating the powerful nonparametric two-sample Cramér-von Mises test and the exponentially weighted moving average control scheme to on-line monitoring. The proposed control chart can be used to monitor the location and the scale parameters of a univariate continuous distribution, simultaneously. The control limits based on Monte-Carlo simulation are provided in a table. The sensitivity analysis of effect of the number of reference samples on the control chart is studied in detail. Comparison results based on Monte-Carlo simulation show that the proposed chart is quite robust to non-normally distributed data, and moreover, it shows satisfactory performance in detecting various process shifts in terms of the average run length and standard deviation of run length. The application of our proposed chart is illustrated by a real data example for automobile engine piston rings.

Distribution-free synthetic and runs-rules control charts combined with a Mann-Whitney chart

Control chart is one of the most important tools used in statistical process control and monitoring (SPCM) to detect changes in quality characteristics. This paper investigates the performance of the improved modified distribution-free synthetic and runs-rules charts combined with a Mann-Whitney (MW) chart, in terms of the average run length (ARL) and median run length (MRL) through intensive simulation. It is observed that the newly proposed improved modified synthetic and runs-rules MW charts present very attractive run-length properties and outperform the competing charts under non-normal underlying distributions. Numerical examples are given as illustration of the design and implementation of the proposed charts.

Design and implementation issues for a class of distribution-free Phase II EWMA exceedance control charts

Distribution-free (nonparametric) control charts can play an essential role in process monitoring when there is dearth of information about the underlying distribution. In this paper, we study various aspects related to an efficient design and execution of a class of nonparametric Phase II exponentially weighted moving average (denoted by NPEWMA) charts based on exceedance statistics. The choice of the Phase I (reference) sample order statistic used in the design of the control chart is investigated. We use the exact time-varying control limits and the median run-length as the metric in an in-depth performance study. Based on the performance of the chart, we outline implementation strategies and make recommendations for selecting this order statistic from a practical point of view and provide illustrations with a data-set. We conclude with a summary and some remarks.

Effects of Parameter Estimation on the Multivariate Distribution-free Phase II Sign EWMA Chart

Multivariate nonparametric control charts can be very useful in practice and have recently drawn a lot of interest in the literature. Phase II distribution-free (nonparametric) control charts are used when the parameters of the underlying unknown continuous distribution are unknown and can be estimated from a sufficiently large Phase I reference sample. While a number of recent studies have examined the in-control (IC) robustness question related to the size of the reference sample for both univariate and multivariate normal theory (parametric) charts, in this paper, we study the effect of parameter estimation on the performance of the multivariate nonparametric sign exponentially weighted moving average (MSEWMA) chart. The in-control average run-length (ICARL) robustness and the out-of-control shift detection performance are both examined. It is observed that the required amount of the Phase I data can be very (perhaps impractically) high if one wants to use the control limits given for the known parameter case and maintain a nominal ICARL, which can limit the implementation of these useful charts in practice. To remedy this situation, using simulations, we obtain the “corrected for estimation” control limits that achieve a desired nominal ICARL value when parameters are estimated for a given set of Phase I data. The out-of-control performance of the MSEWMA chart with the correct control limits is also studied. The use of the corrected control limits with specific amounts of available reference sample is recommended. Otherwise, the performance the MSEWMA chart may be seriously affected under parameter estimation. Copyright © 2016 John Wiley & Sons, Ltd.

Distribution-free Lepage Type Circular-grid Charts for Joint Monitoring of Location and Scale Parameters of a Process

In the last 5 years, research works on distribution-free (nonparametric) process monitoring have registered a phenomenal growth. A Google Scholar database search on early September 2015 reveals 246 articles on distribution-free control charts during 2000–2009 and 466 articles in the following years. These figures are about 1400 and 2860 respectively if the word ‘nonparametric’ is used in place of ‘distribution-free’. Distribution-free charts do not require any prior knowledge about the process parameters. Consequently, they are very effective in monitoring various non-normal and complex processes. Traditional process monitoring schemes use two separate charts, one for monitoring process location and the other for process scale. Recently, various schemes have been introduced to monitor the process location and process scale simultaneously using a single chart. Performance advantages of such charts have been clearly established. In this paper, we introduce a new graphical device, namely, circular-grid charts, for simultaneous monitoring of process location and process scale based on Lepage-type statistics. We also discuss general form of Lepage statistics and show that a new modified Lepage statistic is often better than the traditional of Lepage statistic. We offer a new and attractive post-signal follow-up analysis. A detailed numerical study based on Monte-Carlo simulations is performed, and some illustrations are provided. A clear guideline for practitioners is offered to facilitate the best selection of charts among various alternatives for simultaneous monitoring of location-scale. The practical application of the charts is illustrated. Copyright © 2016 John Wiley & Sons, Ltd.

A COMPARISON OF PHASE I CONTROL CHARTS

A carefully done Phase I analysis is a vital part of an overall statistical process control and monitoring regime. Distribution-free control charts can play a useful role in this analysis, as a parametric model assumption often cannot be adequately verified. The performance of two distribution-free charts for the location – the mean-rank and the median chart – are compared in this paper. For benchmarking reasons, the parametric -chart is included in the comparisons. It is seen that the distribution-free charts are in-control robust, whereas the -chart is not, and they both perform similarly to the -chart for normally distributed data. However, for non-normal data, they both outperform the -chart. The results provide evidence in favour of using distribution-free Phase I charts in practice. Concluding remarks and suggestions for future research are given.