Parametric Control Charts Research Articles

Multivariate process control chart based on sign and signed-rank tests for mixture distributions

The development and application of the traditional multivariate parametric control charts have been distribution-based procedures. This is because the process output is assumed to come from some specified probability distributions. However, in many quality/ process control applications, these distributional assumptions are either not satisfied or there is simply lack of enough information to verify the assumptions and this condition drops the performance of the charts. The purpose of this paper is to develop nonparametric control charts for mixture of multivariate normal and t-distributions with the view to evaluating the performance of the charts in simulation study. The results show that the charts are effective in monitoring process variability.

A non‐parametric double homogeneously weighted moving average control chart under sign statistic

AbstractIn practical situations, the underlying process distribution sometimes deviates from normality and their distribution is partially or completely unknown. In that instance, rather than staying with/depending on the conventional parametric control charts, we consider non‐parametric control charts due to their exceptional performance. In this paper, a new non‐parametric double homogeneously weighted moving average sign control chart is proposed with the least assumptions. This chart is based on a sign test statistic for catching the smaller deviations in the process location. Run‐length (RL) properties of the proposed chart are studied with the help of Monte Carlo simulations. Both in‐control and out‐of‐control RL properties show that the proposed chart is a better contender as compared to some existing charts from the literature. A real‐life application for practical consideration of the proposed chart is also provided.

Condition monitoring scheme via one-class support vector machine and multivariate control charts

A condition-based maintenance (CBM) has been widely employed to reduce maintenance cost by predicting the health status of many complex systems in prognostics and health management (PHM) framework. Recently, multivariate control charts used in statistical process control (SPC) have been actively introduced as monitoring technology. In this paper, we propose a condition monitoring scheme to monitor the health status of the system of interest. In our condition monitoring scheme, we first define reference data set using one-class support vector machine (OC-SVM) to construct the control limit of multivariate control charts in phase I. Then, parametric control chart or non-parametric control chart is selected according to the results from multivariate normality tests. The proposed condition monitoring scheme is applied to sensor data of two anemometers to evaluate the performance of fault detection power.

Methodology for the Application of Nonparametric Control Charts into Practice

Classical parametric statistical methods are based on several basic assumptions about data (normality, independence, constant mean and variance). Unfortunately, these assumptions are not always fulfilled in practice, whether due to problems arising during manufacturing or because these properties are not typical for some processes. Either way, when we apply parametric methods to such data, whether Shewhart’s or other types of parametric control charts, it is not guaranteed that they will provide the right results. For these cases, reliable nonparametric statistical methods were developed, which are not affected by breaking assumptions about the data. Nonparametric methods try to provide suitable procedures to replace commonly used parametric statistical methods. The aim of this paper is to introduce the reader to an alternative way of evaluating the statistical stability of the process, in cases where the basic assumptions about the data are not met. First, possible deviations from the data assumptions that must be met in order to use classical Shewhart control charts were defined. Subsequently, simulations were performed to determine which nonparametric control chart was better suited for which type of data assumption violation. First, simulations were performed for the in-control process. Then simulations for an out-of-control process were performed. This is for situations with an isolated and persistent deviation. Based on the performed simulations, flow charts were created. These flow charts give the reader an overview of the possibilities of using nonparametric control charts in various situations. Based on the performed simulations and subsequent verification of the methodology on real data, it was found that nonparametric control charts are a suitable alternative to the standard Shewhart control charts in cases where the basic assumptions about the data are not met.

On Designing Distribution-Free Homogeneously Weighted Moving Average Control Charts

Abstract There are many practical situations in which the underlying process distribution is either completely unknown or partially known but deviates from normality. In such cases, the performance of the traditional parametric control charts deteriorates, and nonparametric control charts are considered as a robust alternative for monitoring the process. In this article, two new nonparametric homogeneously weighted moving average (NPHWMA) control charts are proposed for monitoring the deviations in process location from the target value. The proposed charts assign a specific weight to the current sample information, and the remaining weight is equally distributed among the previous samples. The proposed NPHWMA charts are based on sign test and Wilcoxon signed-rank test for process monitoring under the skewed and symmetric distributions, respectively. The Monte Carlo simulations are used to study the run length properties and compare the performance of the proposed charts with some existing control charts. It is found that the proposed charts outperform their existing counterparts. Empirical illustrations are provided for practical implementation of the proposed charts.

Non parametric PROS quality control chart for monitoring the process mean

A non parametric Shewhart-type control chart based on a partially rank-ordered set (PROS) sampling design is considered in this study to monitor the process mean. Four non parametric estimators are proposed for the variance of PROS sample mean; also, the performances of these estimators are discussed theoretically and numerically. Then, three non parametric PROS control charts are proposed including the classic 3-sigma control chart, a non parametric bootstrap approach-based control chart, and a hybrid control chart based on a combination of classic 3-sigma and bootstrap control charts. The performance of the proposed PROS control charts is compared with the available chart in terms of controlling the false alarm rate. Results show the merits of both non parametric bootstrap and hybrid PROS control charts. Finally, control charts are illustrated with a real example.

A non-parametric CUSUM control chart for process distribution change detection and change type diagnosis

Non-parametric control charts have been good alternatives to parametric control charts when little information is known about the type of process distribution or the value of parameters. Most approaches proposed by the current literature monitor either location or scale change in batch mode and their performance is discounted when monitoring distribution change in both location and scale simultaneously in a sequential pattern. This paper proposed a log-likelihood-ratio-based non-parametric cumulative sum (CUSUM) control chart to monitor arbitrary distribution change and diagnose the detailed change type simultaneously. By integrating the superiority of log-likelihood ratio test to detect any change of distribution and CUSUM chart to detect a small change, the proposed approach can detect small potential changes in location, scale and shape; and provide detailed information about change type when control chart gives a signal. Comparison results with many other non-parametric approaches were provided by numerical simulation and the results of an application case demonstrate the effectiveness of the proposed approach.

A new nonparametric double exponentially weighted moving average control chart

AbstractThere 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.

Controle estatístico de processo paramétrico e não paramétrico em uma indústria de laticínios

O Brasil é um dos maiores produtores mundiais de leite bovino, sendo que grande parte é destinada para fabricação de queijos. Para que a indústria queijei ra se mantenha, o leite, sua principal matéria-prima, deve ser de qualidade. Sendo a qualidade do leite avaliada por diversas variáveis em fluxo contínuo, o controle estatístico de processo (CEP) pode ser uma ferramenta para monitorá-la. Neste trabalho foram utilizadas cartas de controle paramétricas e não paramétricas para verificar se o processo de recebimento de leite em uma queijaria da cidade de São Luís de Montes Belos, Goiás, estava sob controle estatístico. Foram verificadas normalidade e simetria dos dados, e como esperado, o CEP paramétrico se mostrou aparentemente mais poderoso. Os autores sugerem a utilização de CEP como ferramenta para assegurar a qualidade de laticínios, mas sempre verificando se as pressuposições de cada metodologia são atendidas. Em específico, se verificada normalidade, as cartas paramétricas são mais poderosas e por isso, são aconselhadas.

Nonparametric monitoring of multiple count data

Process monitoring of multiple count data has recently received considerable attention in the statistical process control literature. Most existing methods on this topic are based on parametric modeling of the observed process data. However, the assumed parametric models are often invalid in practice, leading to unreliable performance of the related control charts. In this article, we first show the consequence of using a parametric control chart in cases where the underlying parametric distribution is invalid. Then, we thoroughly investigate the performance of some parametric and nonparametric control charts in monitoring multiple count data. Our numerical results show that nonparametric methods can provide a more reliable and effective process monitoring in such cases. A real-data example about the crime log of the University of Florida Police Department is used for illustrating the implementation of the related control charts.

Design of a sign chart using a new EWMA statistic

In this article, a new non parametric control chart based on the modified or controlled exponentially weighted moving average (EWMA) statistic is developed to monitor the process deviation from the target value. The proposed control chart is evaluated for different values of design parameters using the average run length as a performance criterion under various sample sizes. The proposed chart is compared with the existing non parametric EWMA sign control chart. It is observed that the proposed chart is better than the existing EWMA sign control chart in terms of run length characteristics. An empirical example is provided for the practical implementation of the proposed chart.

Count data monitoring: Parametric or nonparametric?

AbstractCount data are common in practice, ranging from security protection, disease surveillance, to quality monitoring of a production process. To describe the distribution of a count data, we usually use a Poisson probability model or a similar parametric model (eg, a negative binomial model). In practice, however, such a parametric model may not be able to describe the distribution of a count data well in some cases, because the count data are often affected by some confounding factors and such a confounding impact is difficult to accommodate by the parametric model. In this paper, we study the count data monitoring problem and the consequence to use a parametric control chart in cases when the underlying parametric distribution model is invalid. On the basis of that study, we suggest using nonparametric charts to monitor count data when it is uncertain that the count data can be described well by a parametric distribution model.

Non parametric double generally weighted moving average sign charts based on process proportion

ABSTRACTNon parametric control charts have received increasing attention in the field of statistical process control. This paper presents a non parametric double generally weighted moving average (DGWMA) sign chart for monitoring small deviations when the quality characteristics of a process are unknown. The statistical performance of the non parametric DGWMA sign chart is evaluated and compared with those of other charts, including the exponentially weighted moving average (EWMA), generally weighted moving average (GWMA), and double EWMA (DEWMA) sign charts. Simulation studies indicate that the non parametric DGWMA sign chart with a large design and median adjustment parameters is always more sensitive than other charts in detecting small changes.

Nonparametric signed‐rank control charts with variable sampling intervals

AbstractVariable 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.

Phase I Distribution-Free Analysis of Multivariate Data

ABSTRACTIn this study, a new distribution-free Phase I control chart for retrospectively monitoring multivariate data is developed. The suggested approach, based on the multivariate signed ranks, can be applied to individual or subgrouped data for detection of location shifts with an arbitrary pattern (e.g., isolated, transitory, sustained, progressive, etc.). The procedure is complemented with a LASSO-based post-signal diagnostic method for identification of the shifted variables. A simulation study shows that the method compares favorably with parametric control charts when the process is normally distributed, and largely outperforms other multivariate nonparametric control charts when the process distribution is skewed or heavy-tailed. An R package can be found in the supplementary material.

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

ABSTRACTWe 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.

Investigating the Impact of Ranked Set Sampling in Nonparametric CUSUM Control Charts

Nonparametric control charts can be useful as an alternative in practice to the data expert when there is a lack of knowledge about the underlying distribution. In this study, a nonparametric cumulative sum (CUSUM) sign control chart for monitoring and detecting possible deviation from the process mean using ranked set sampling is proposed. Ranked set sampling is an effective method when the observations are inexpensive, and measurements are perhaps destructive. The average run length is used as performance measure for the proposed nonparametric CUSUM sign chart. Simulation study shows that the proposed version of the CUSUM sign chart using ranked set sampling generally outperforms than that version of the nonparametric CUSUM sign chart and the parametric CUSUM control chart using simple random sampling scheme. An illustrative example is also provided for practical consideration. Copyright © 2016 John Wiley & Sons, Ltd.

Use of ranked set sampling in nonparametric control charts

Control charts are widely used to identify changes in a production process. Nonparametric or distribution-free charts can be useful when there is a lack of underlying process distribution. A nonparametric exponentially weighted moving average (EWMA) control chart based on sign test using ranked set sampling (RSS) is proposed to monitor the possible small shifts in the process mean. The performance of the proposed chart is evaluated in terms of average run length, median run length, and standard deviation of the run length distribution. It has been observed that the proposed version of the EWMA sign chart, using RSS shows better detection ability than that version of the EWMA sign chart and the parametric EWMA control chart using simple random sampling scheme. An application with real data-set is also provided to explain the proposal for practical considerations.

A New Nonparametric Control Chart for Monitoring Variability

Statistical process control is widely used in industrial processes, service fields, among others. While parametric control charts are useful in certain processes, there is often a lack of enough knowledge about the process distribution. So, nonparametric control charts are needed in such situations. This paper develops a new nonparametric control chart based on the Ansari–Bradley nonparametric test and the effective change point model. Simulation results show that our proposed control chart is superior to other nonparametric control charts in monitoring process variability for most cases. Our proposed control chart is easy in computation, and powerful for monitoring process variability. Copyright © 2016 John Wiley & Sons, Ltd.

Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes

The nonparametric (distribution-free) control charts are robust alternatives to the conventional parametric control charts when the form of underlying process distribution is unknown or complicated. In this paper, we consider two new nonparametric control charts based on the Hogg–Fisher–Randle (HFR) statistic and the Savage rank statistic. These are popular statistics for testing location shifts, especially in right-skewed densities. Nevertheless, the control charts based on these statistics are not studied in quality control literature. In the current context, we study phase-II Shewhart-type charts based on the HFR and Savage statistics. We compare these charts with the Wilcoxon rank-sum chart in terms of false alarm rate, out-of-control average run-length and other run length properties. Implementation procedures and some illustrations of these charts are also provided. Numerical results based on Monte Carlo analysis show that the new charts are superior to the Wilcoxon rank-sum chart for a class of non-normal distributions in detecting location shift. New charts also provide better control over false alarm when reference sample size is small.