Multiple Linear Profiles Research Articles

Profile monitoring using synthetic T2 control chart

In this paper, we propose synthetic T2 chart for monitoring different parameters including Slope, Intercept and Error variance for simple and multiple linear regression profiles in Phase II. The construction and optimal design of the proposed synthetic T2 chart are discussed in detail. The steady-state performance of the proposed chart is evaluated by the Average Run Length (ARL) and Standard Deviation of Run Length (SDRL) and is compared with the existing charts in the literature for monitoring simple and multiple linear profiles. It turns out that the proposed synthetic T2 chart performs uniformly better than the traditional T2 chart in detecting different kinds of shifts in the parameters of the simple and multiple linear profiles under steady-state run length performance. An example with a real data set is also presented to explain the implementation of the proposed chart.

Simultaneous monitoring of the mean vector and covariance matrix of multivariate multiple linear profiles with a new adaptive Shewhart-type control chart

There has been a growing interest in research regarding monitoring a process through a regression model (called a profile) rather than a simple quality characteristic. This paper proposes a new monitoring scheme to simultaneously monitor the multivariate multiple linear profiles’ parameters. This scheme is based on the Shewhart control chart concept and only has one single (max-type) control chart for monitoring regression coefficients and error’s variation, which uses a new statistic to improve the variability (error’s variance-covariance matrix) shift detection in multivariate profiles. To increase the sensitivity and capability of the proposed scheme, especially in detecting small to moderate shift sizes, we add a variable parameters (VP) adaptive scheme to the developed control chart as well, considering that no adaptive monitoring schemes have so far been developed for monitoring the multivariate multiple linear profiles and neither are there any VP adaptive features for all profile monitoring schemes. Next, we develop a Markov chain model to compute the time to signal and run length performance measures. After that, we perform extensive numerical analyses to first compare the proposed control chart with the best available control charts and then evaluate its performance under different shift scenarios as well as different dimensions. The results show that the new monitoring scheme performs well compared to the best available monitoring schemes, and more importantly, it is more applicable in real practice. Finally, an illustrative example is presented to show the implementation of the proposed scheme in practice.

A Robust Control Chart for Monitoring Autocorrelated Multiple Linear Profiles in Phase I

A Robust Control Chart for Monitoring Autocorrelated Multiple Linear Profiles in Phase I

Simultaneous monitoring of mean vector and covariance matrix of auto‐correlated multivariate multiple linear profiles

AbstractThe aim of this paper is to develop control charts for a simultaneous monitoring of the mean vector and covariance matrix of multivariate multiple linear regression profiles in phase II, when the independence assumption of the observations within each profile is violated, and there is multivariate autoregressive moving average (MARMA)(1,1) autocorrelation structure within each profile. A transformation method is applied to eliminate the autocorrelation, and six control charts for a simultaneous monitoring of the mean vector and covariance matrix of auto‐correlated multivariate multiple linear regression profiles are proposed. Then, through simulation runs, in terms of the average run length (ARL) criterion, it is shown that the proposed methods have better performance in comparison with the competing methods in detecting shifts in the parameters of regression profiles. Finally, the application of the proposed control charts is shown using real data in a machining process.

Monitoring Multiple Linear Profile based on EWMA Control Charts by using Ridge Regression Estimators: an application to Wind Tunnel data of NASA Langley Research Centre

Monitoring Multiple Linear Profile based on EWMA Control Charts by using Ridge Regression Estimators: an application to Wind Tunnel data of NASA Langley Research Centre

Online monitoring of autocorrelated multivariate linear profiles via multivariate mixed models

ABSTRACT Multivariate multiple profile monitoring has been studied extensively over the past few years. Most of these studies assumed that the observations are uncorrelated, which could be violated in practice. In this paper, multivariate linear mixed model is proposed to allow correlation among observations of the multivariate multiple linear profiles. In order to monitor random effects and process variability in phase II, three control charts are suggested. The results of performance comparisons with an existing method show the superiority of the proposed control chart. Finally, the applicability of the proposed method is illustrated using a real case.

Robust process capability indices for multiple linear profiles

AbstractIn some statistical process control applications, the quality of a process is described by a linear relationship between the response variable(s) and the independent variable(s), which is called a linear profile. Process capability is a significant issue in statistical process control. The ability of a process to meet customer specifications or standards is measured by the process capability indices (PCIs). There are several attempts for studying the process capability in linear profiles. In this research, two robust PCIs for multiple linear profiles are proposed. In the suggested robust PCIs, the process capability is estimated using the M‐estimator and the Fast‐τ‐estimator. Performances of the proposed robust PCIs in comparison with the classical PCIs in the absence and presence of contamination are evaluated. The results show that the robust PCIs proposed in this research perform as well as the classical PCIs in the absence of contamination and much better in the presence of contamination. The proposed PCIs, using Fast‐τ‐estimator, perform better in small shifts, and the proposed PCIs, using M‐estimator, perform better in large shifts. Introduction of robust indices for multivariate multiple linear profiles is an area for further research.

A novel robust control chart for monitoring multiple linear profiles in phase II

A profile is a relationship between the response variable(s) and the independent variable(s), which describes the quality of a process or product. The profile can be monitored by a process control chart, which is an important tool in the statistical process control. Using the robust estimators in monitoring profiles in the presence of contamination is so effective, and it improves the efficiency of a control chart in detecting any sustained shift in phase II. In this research, a novel robust control chart is proposed for monitoring multiple linear profiles using two robust estimate methods. In the proposed robust control chart, the parameters of a multiple linear profile are estimated using the M-estimator and the Fast-τ-estimator. Also, the efficiency of the proposed robust control chart is evaluated by means of ARL criterion and compared to the classic control chart in phase II. The results of simulation studies show that the proposed robust control chart performs as well as the classic control chart in the absence of contamination, while in the presence of contamination, it can detect the shifts quicker than the classical one. Moreover, the proposed robust control chart using Fast-τ-estimator and M-estimator performs better in low and high contamination, respectively.

Phase II monitoring of multivariate profiles with estimated parameters and optimal phase I subgroups

In this paper, we investigate the effect of parameter estimation from in-control Phase I samples on the in-control and out-of-control performance of the four Phase II control charts used for monitoring multivariate multiple linear profiles. These methods are evaluated in terms of out-of-control performance using corrected limits. The monitoring approaches investigated are then compared using the statistical properties of the ARL distribution. Furthermore, two optimization models are proposed for finding the optimum number of Phase I samples needed to achieve proper parameter estimations of desired accuracy and solved by using a novel hybrid simulation algorithm named HBSO.

A new Bayesian multivariate exponentially weighted moving average control chart for phase II monitoring of multivariate multiple linear profiles

AbstractRecently, statistical profile monitoring methods have become efficient tools for monitoring the quality of a product (or a production process) using control charts. The key idea is to describe the relationship between a response variable and a set of explanatory variables in the form of a statistical regression model, which called profile. Traditionally, those control charts are constructed with standard “frequentistic” regression models. Recently, it has been proposed to apply Bayesian regression models instead, and it has been empirically demonstrated that Bayesian regression models have the potential to perform significantly better. In this paper, we introduce a novel Bayesian multivariate exponentially weighted moving average control chart for monitoring multivariate multiple linear profiles in phase II. The key idea is to use the data from historical data sets to generate informative prior distributions for the regression models in phase II. The results of our empirical simulation studies show that the Bayesian multivariate multiple linear regression model is superior to its classical “frequentistic” counterpart in terms of the average run length. Our empirical findings are in agreement with findings reported in recently published articles. To shed more light onto the merit of the proposed Bayesian method, we carry out a sensitivity analysis, in which we investigate how the amount of phase I data influences the results. We also demonstrate the applicability and superiority of the proposed Bayesian method by a real‐world application.

Addressing the effect of parameter estimation on phase II monitoring of multivariate multiple linear profiles via a new cluster-based approach

Profile monitoring is applied when the quality of a product or a process can be determined by the relationship between a response variable and one or more independent variables. In most Phase II monitoring approaches, it is assumed that the process parameters are known. However, it is obvious that this assumption is not valid in many real-world applications. In fact, the process parameters should be estimated based on the in-control Phase I samples. In this study, the effect of parameter estimation on the performance of four Phase II control charts for monitoring multivariate multiple linear profiles is evaluated. In addition, since the accuracy of the parameter estimation has a significant impact on the performance of Phase II control charts, a new cluster-based approach is developed to address this effect. Moreover, we evaluate and compare the performance of the proposed approach with a previous approach in terms of two metrics, average of average run length and its standard deviation, which are used for considering practitioner-to-practitioner variability. In this approach, it is not necessary to know the distribution of the chart statistic. Therefore, in addition to ease of use, the proposed approach can be applied to other type of profiles. The superior performance of the proposed method compared to the competing one is shown in terms of all metrics. Based on the results obtained, our method yields less bias with small-variance Phase I estimates compared to the competing approach.

New control charts for simultaneous monitoring of the mean vector and covariance matrix of multivariate multiple linear profiles

ABSTRACTSimultaneous monitoring of the mean vector and covariance matrix in multivariate processes allows practitioners to avoid the inflated false alarm rate that results from using two independent control charts. In this paper, we extend exponentially weighted moving average semicircle and generally weighted moving average semicircle control charts to monitor the mean vector and covariance matrix of multivariate multiple linear regression profiles in Phase II simultaneously. These new control charts are compared with the existing control charts in the literature in terms of the average run length criterion. Finally, a case is considered to show the application of the proposed charts.

Supplier Selection for Multiple Linear Profiles with One-Sided Specifications

When the quality of a process is represented by a relationship between one response variable and one or more independent variables called a multiple linear profile with in statistical control, the process capability analysis is widely used to measure the capability of the process to manufactured item within the required tolerance. In this paper, we propose the difference test statistic to compare two processes for multiple linear profiles with one-sided specifications. The number of profiles required for a designated selection power and confidence level is also provided. The performance of the proposed method is assessed using simulation study. The results provide useful information to practitioners. A real data from the logistic service shows that our method performs well in the application. Copyright © 2014 John Wiley & Sons, Ltd.

Some Notes on Diagnostic Procedures in Simple and Multiple Linear Regression Profiles Monitoring

Sometimes a relationship between a response variable and one or more explanatory variables known as profile describes the quality of a process. In Phase I, after a control procedure signals the presence of an assignable cause(s), finding the out-of-control samples as well as attributing the shift to model parameters are main objectives. Some diagnostic methods proposed in Phase I analysis of simple and multiple linear profiles. In this article, we modify the procedure by Mahmoud (2008) to improve the method. Moreover, the diagnostic procedure by Mahmoud and Woodall (2004) is discussed. The improvement is illustrated using simulation and numerical examples.

Phase I Analysis of Multiple Linear Regression Profiles

This article considers the Phase I analysis of data when the quality of a process or product is characterized by a multiple linear regression model. This is usually referred to as the analysis of linear profiles in the statistical quality control literature. The literature includes several approaches for the analysis of simple linear regression profiles. Little work, however, has been done in the analysis of multiple linear regression profiles. This article proposes a new approach for the analysis of Phase I multiple linear regression profiles. Using this approach, regardless of the number of explanatory variables used to describe it, the profile response is monitored using only three parameters, an intercept, a slope, and a variance. Using simulation, the performance of the proposed method is compared to that of the existing methods for monitoring multiple linear profiles data in terms of the probability of a signal. The advantage of the proposed method over the existing methods is greatly improved detection of changes in the process parameters of linear profiles with high-dimensional space. The article also proposes useful diagnostic aids based on F-statistics to help in identifying the source of profile variation and the locations of out-of-control samples. Finally, the use of multiple linear profile methods is illustrated by a data set from a calibration application at National Aeronautics and Space Administration (NASA) Langley Research Center.