Nonparametric Control Research Articles

Nonparametric progressive sign chart for monitoring process location based on individual data

ABSTRACT Statistical process control (SPC) plays a vital role in the maintenances and improvements of quality outputs in manufacturing, industrial and service production processes. Control chart is an important SPC tool, used to detect noises and to improve process performance. When the underlying process distribution lacks the assumption of normality, nonparametric (NP) control charts become essential and particularly are useful because their in-control (IC) run length properties remain the same for every continuous distribution. This article develops the NP progressive mean sign (NPPM-SN) chart for monitoring the process target through 100% inspection by taking individual measurements from the process. The performance of the proposed NPPM-SN chart is examined under zero-state and steady-state scenarios. The IC and out-of-control run length properties of the proposed control chart are evaluated using Monte Carlo simulation. The proposed NPPM-SN chart is compared with traditional exponentially weighted moving average (EWMA), nonparametric EWMA sign (NPEWMA-SN) and traditional progressive mean (PM) control charts based on individual measurements using average run length and some other characteristics of the run-length distribution. The proposed NPPM-SN chart is found more robust (for all distributions) and efficient (for skewed distributions) as compared to its competitors. Along with a real-life example related to high voltage power supply, a simulated data example is also presented for the implementation of the proposed NPPM-SN chart.

A multivariate non-parametric control chart based on run test

Multivariate control charts have a wide range of applications in the field of quality management. This paper proposes a new multivariate non-parametric control chart based on run test. First, the shortest Hamiltonian path of the observations is determined by means of Kruskal algorithm. Then an EWMA control chart with sliding window based on the number of runs of the shortest Hamiltonian path is proposed. The selection of the design parameters and the determination of control limit are discussed in detail. The effect of different dimensions, shift magnitude, reference data size and the underlying distribution are investigated via Monte Carlo simulation. Compared with three recent non-parametric multivariate control charts, the newly proposed chart has superior performance when mean shift magnitude is large and the underlying distribution is non-normal. Also, the chart proposed is more suitable for monitoring in high-dimensional situations. A real case study is also presented to show the implementation procedures of the chart.

On Designing Non-Parametric EWMA Sign Chart under Ranked Set Sampling Scheme with Application to Industrial Process

Statistical process control (SPC) tools are used for the investigation and identification of unnatural variations in the manufacturing, industrial, and service processes. The control chart, the basic and the most famous tool of SPC, is used for process monitoring. Generally, control charts are constructed under normality assumption of the quality characteristic of interest, but in practice, it is quite hard to hold the normality assumption. In such situations, parametric charts tend to offer more frequent false alarms and invalid out-of-control performance. To rectify these problems, non-parametric control charts are used, as these have the same in-control run length properties for all the continuous distributions and are known as in-control robust. This study intends to develop a new non-parametric exponentially weighted moving average (NPEWMA) chart based on sign statistics under a ranked set sampling scheme that is hereafter named (NPREWMA-SN). The run-length profiles of the NPREWMA-SN chart are computed using the Monte Carlo simulation method. The proposed scheme is compared with NPEWMA-SN and classical EWMA-X¯ charts, using different run length measures. The comparison reveals the in-control robustness and superiority of the proposed scheme over its competitors in detecting all kinds of shifts in the process location. A practical application related to the substrate manufacturing process is included to show the demonstration of the proposed chart.

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.

An Intrinsic Geometrical Approach for Statistical Process Control of Surface and Manifold Data

We present a new method for statistical process control (SPC) of a discrete part manufacturing system based on intrinsic geometrical properties of the parts, estimated from three-dimensional sensor data. An intrinsic method has the computational advantage of avoiding the difficult part registration problem, necessary in previous SPC approaches of three-dimensional geometrical data, but inadequate if noncontact sensors are used. The approach estimates the spectrum of the Laplace–Beltrami (LB) operator of the scanned parts and uses a multivariate nonparametric control chart for online process control. Our proposal brings SPC closer to computer vision and computer graphics methods aimed to detect large differences in shape (but not in size). However, the SPC problem differs in that small changes in either shape or size of the parts need to be detected, keeping a controllable false alarm rate and without completely filtering noise. An online or “Phase II” method and a scheme for starting up in the absence of prior data (“Phase I”) are presented. Comparison with earlier approaches that require registration shows the LB spectrum method to be more sensitive to rapidly detect small changes in shape and size, including the practical case when the sequence of part datasets is in the form of large, unequal size meshes. A post-alarm diagnostic method to investigate the location of defects on the surface of a part is also presented. While we focus in this article on surface (triangulation) data, the methods can also be applied to point cloud and voxel metrology data.

Enhanced nonparametric control charts under simple and ranked set sampling schemes

Investigation and removal of unnatural variation in the processes of manufacturing, production and services require application of statistical process control. Control charts are the most famous and commonly used statistical process control tools to trace changes in the manufacturing and nonmanufacturing processes parameter(s). The nonparametric control charts become necessary when the distribution of underlying process is unknown or questionable. The nonparametric charts are robust alternative along with holding property of quick shift detection ability in process parameter(s). In this article, we have proposed nonparametric double exponentially weighted moving average chart based on Wilcoxon signed rank test under simple and ranked set sampling schemes for efficient monitoring of the process location. The proposed control charts are compared with classical exponentially weighted moving average, double exponentially weighted moving average, nonparametric exponentially weighted moving average sign, nonparametric exponentially weighted moving average signed rank, nonparametric cumulative sum signed rank charts using average run length and some other characteristics of run length distribution as performance measures. Comparison reveals that the proposed control charts performs better to detect all kinds of shifts in the process location than existing counterparts. A real-life application related to manufacturing process (the variable of interest is the diameter of piston ring) is also provided for the practical implementation of the proposed chart.

A New Nonparametric Composite Exponentially Weighted Moving Average Sign Control Chart

In this paper, a new nonparametric control chart based on two EWMA statistics is proposed for monitoring process deviation from the target value. The performance comparison of the proposed chart with the existing nonparametric EWMA sign control chart and a nonparametric CUSUM mean control chart are made by using out-of-control average run length. The simulation study showed the superiority of the suggested chart over the four other parametric and nonparametric charts. An empirical illustration is also provided for performance evaluation of the proposed chart. By comparing the proposed chart with the existing charts, it is concluded that the proposed chart is more sensitive in detecting a small shift in the process.

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.

Traffic congestion monitoring using an improved kNN strategy

A systematic approach for monitoring road traffic congestion is developed to improve safety and traffic management. To achieve this purpose, an improved observer merging the benefits of a piecewise switched linear traffic (PWSL) modeling approach and Kalman filter (KF) is introduced. The PWSL-KF observer is utilized as a virtual sensor to emulate the traffic evolution in free-flow mode. In the proposed approach, residuals from the PWSL-KF model are used as the input to k-nearest neighbors (kNN) schemes for congestion detection. Here, kNN-based Shewhart and exponential smoothing schemes are designed for discovering the traffic congestions. The proposed detectors merge the desirable properties of kNN to appropriately separating normal from abnormal features and the capability of the monitoring schemes to better identify traffic congestions. In addition, kernel density estimation has been utilized to set nonparametric control limits of the proposed detectors and compared them with their parametric counterparts. Tests on traffic measurements from the four-lane State Route 60 in California freeways show the effectiveness of the PWSL-KF-based kNN methods in supervising traffic congestions.

Nonparametric false discovery rate control for identifying simultaneous signals

It is frequently of interest to identify simultaneous signals, defined as features that exhibit statistical significance across each of several independent experiments. For example, genes that are consistently differentially expressed across experiments in different animal species can reveal evolutionarily conserved biological mechanisms. However, in some problems the test statistics corresponding to these features can have complicated or unknown null distributions. This paper proposes a novel nonparametric false discovery rate control procedure that can identify simultaneous signals even without knowing these null distributions. The method is shown, theoretically and in simulations, to asymptotically control the false discovery rate. It was also used to identify genes that were both differentially expressed and proximal to differentially accessible chromatin in the brains of mice exposed to a conspecific intruder. The proposed method is available in the R package github.com/sdzhao/ssa.

Learning Stable Nonparametric Dynamical Systems with Gaussian Process Regression

Modelling real world systems involving humans such as biological processes for disease treatment or human behavior for robotic rehabilitation is a challenging problem because labeled training data is sparse and expensive, while high prediction accuracy is required from models of these dynamical systems. Due to the high nonlinearity of problems in this area, data-driven approaches gain increasing attention for identifying nonparametric models. In order to increase the prediction performance of these models, abstract prior knowledge such as stability should be included in the learning approach. One of the key challenges is to ensure sufficient flexibility of the models, which is typically limited by the usage of parametric Lyapunov functions to guarantee stability. Therefore, we derive an approach to learn a nonparametric Lyapunov function based on Gaussian process regression from data. Furthermore, we learn a nonparametric Gaussian process state space model from the data and show that it is capable of reproducing observed data exactly. We prove that stabilization of the nominal model based on the nonparametric control Lyapunov function does not modify the behavior of the nominal model at training samples. The flexibility and efficiency of our approach is demonstrated on the benchmark problem of learning handwriting motions from a real world dataset, where our approach achieves almost exact reproduction of the training data.

Distribution-free monitoring schemes based on order statistics: a general approach

In this article, we establish a new class of distribution-free Shewhart-type monitoring schemes based on order statistics. The setup of the proposed family of nonparametric control charts is presented in detail. Specific monitoring schemes, already introduced in the literature, are confirmed to be members of the new class. In addition, a new nonparametric monitoring scheme that belongs to the class is established, while explicit formulae for its basic characteristics are reached. The numerical study carried out reveals that the proposed scheme achieves adversarial in-control and out-of-control performance.

Nonparametric adaptive CUSUM chart for detecting arbitrary distributional changes

Nonparametric control charts that can detect arbitrary distributional changes are highly desirable due to their flexibility to adapt to different distributional assumptions and changes. However, most of the nonparametric control charts in the literature either can only detect location changes, or involve intensive computation. In this article, we propose a new nonparametric adaptive CUSUM chart. The proposed control chart can detect arbitrary distributional changes and is computationally efficient. Its self-starting nature makes the proposed control chart applicable to situations where no sufficiently large reference data are available. The proposed control chart also has a built-in post-signal diagnostics function that can identify what kind of distributional changes have occurred after an alarm. Our simulation study and real data analysis show that the proposed control chart performs well across a broad range of settings, and compares favorably with existing nonparametric control charts.

An enhanced nonparametric EWMA sign control chart using sequential mechanism.

Control charts play a significant role to monitor the performance of a process. Nonparametric control charts are helpful when the probability model of the process output is not known. In such cases, the sampling mechanism becomes very important for picking a suitable sample for process monitoring. This study proposes a nonparametric arcsine exponentially weighted moving average sign chart by using an efficient scheme, namely, sequential sampling scheme. The proposal intends to enhance the detection ability of the arcsine exponentially weighted moving average sign chart, particularly for the detection of small shifts. The performance of the proposal is assessed, and compared with its counterparts, by using some popular run length properties including average, median and standard deviation run lengths. The proposed chart shows efficient shift detection ability as compared to the other charts, considered in this study. A real-life application based on the smartphone accelerometer data-set, for the implementation of the proposed scheme, is also presented.

Spatiotemporal analysis of Korean ginseng farm productivity

The past two decades has seen new methodological debates on the identification of production function. Olley and Pakes (J Polit Econ 101(6):1149–1164, 1996), Levinsohn and Petrin (Rev Econ Stud 70(2):317–340, 2003), and Ackerberg et al. (Econometrica 83(6):2411–2451, 2015) introduced nonparametric approaches to control for the unobserved productivity in the estimation of production function, which requires the availability of panel data. There has been an another body of the literature that argued that models that are typically estimated on the basis of panel data can also be identified with repeated cross-sections under certain conditions (Verbeek and Vella, 2005). The objective of this paper is two-fold. First, built on the insight of Verbeek and Vella (2005), this paper proposes a new approach to estimate the nonparametric control function based on repeated cross-sections. This is important because in many studies there is a lack of panel data where agents are followed over time, while repeated cross-sections may be available. Second, using cross-sections of Korean ginseng farms over 2006 to 2013, we apply our method to examine the evolution of farm-level productivity over time and across major production regions. Comparing our method with the pooled OLS regressions, the results show that the materials input coefficients are underestimated in the OLS regressions, which is consistent with the data where farms in the large ginseng production regions use relatively less materials than those in the other regions.

A Fast and Robust Nonparametric Monitoring Scheme for Free-Form Surface Scanning Data

The advance of new sensing technologies, such as the 3-D laser scanning, creates a data-rich environment for quality control in modern industries. The free-form surfaces of complex manufactured parts can be quickly scanned, producing thousands of data points. To monitor these large-scale surface scanning data, three major challenges have to be solved simultaneously: 1) simple parametric models are no longer sufficient to describe free-form surfaces; 2) the massive data points need fast computations; and 3) the presence of outliers calls for robust analytics. To fulfill this task, this paper proposes a novel monitoring scheme where the control chart is designed based on a new robust bilateral kernel smoothing method. A fast approximation algorithm is also developed for efficient online monitoring. This fast and robust nonparametric control chart shows significant superiority for surface monitoring in our numerical simulations. Finally, a real case study demonstrates the effectiveness of our proposed scheme in monitoring the stability of a 3-D printing process. Note to Practitioners —Recently, the widespread use of 3-D laser scanners in industries enables engineers to digitize any free-form surface into thousands of data points, which provides an unprecedented opportunity for quality control of complex manufactured products. This paper proposes a monitoring scheme which caters to arbitrary geometric features on a surface. Practitioners need no prior and specific surface mathematical models. A robust estimate of the surface can be quickly derived from the noisy scanning data by an approximation algorithm. Then, a statistic calculating the deviation of this surface from the target one is plotted in a control chart to monitor the stability of the manufacturing process. In practice, this monitoring scheme can be integrated with the 3-D laser scanner as a new production module for automatic quality control and decision making.

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.

Wilcoxon-type rank-sum control charts based on progressively censored reference data

In this article, we introduce a new distribution − free Shewhart − type control chart implementing a modified Wilcoxon-type rank sum statistic based on progressive Type-II censoring reference data. The proposed chart is also a tool for monitoring the incomplete data, because the censoring scheme applied allows the protection of experimental units at an early stage of the testing procedure. The setup of the new nonparametric control chart is presented in detail, while its operating characteristic function is studied. Explicit formulae for the evaluation of Alarm Rate and Average Run Length values for both in-control and out-of-control situations are established. A numerical study carried out depicts the performance and robustness of the proposed control chart. For illustration purposes, a practical example is also discussed.