Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

A Time Truncated Moving Average Chart for the Weibull Distribution

A control chart of monitoring the number of failures is proposed with a moving average scheme, when the life of an item follows a Weibull distribution. A specified number of items are put on a time truncated life test and the number of failures is observed. The proposed control chart has been evaluated by the average run lengths (ARLs) under different parameter settings. The control constant and the test time multiplier are to be determined by considering the in-control ARL. It is observed that the proposed control chart is more efficient in detecting a shift in the process as compared with the existing time truncated control chart. ? 2013 IEEE.11Ysciescopu

Optimal statistical designs of multivariate EWMA and multivariate CUSUM charts based on average run length and median run leng

Carta kawalan multivariat ialah alat yang berkuasa dalam kawalan proses yang melibatkan kawalan serentak beberapa cirian kualiti yang berkorelasi. Carta-carta multivariat hasil tambah longgokan {MCUSUM) dan multivariat purata bergerak berpemberat eksponen (MEWMA) sentiasa dicadangkan dalam kawalan proses apabila pengesanan cepat anjakan tetap yang keciJ atau sederhana dalam vektor min adalah diingini. A multivariate control chart is a powerful tool in process control involving a simultaneous monitoring of several correlated quality characteristics. The multivariate cumulative sum (MCUSUM) and multivariate exponentially weighted moving average (MEWMA) charts are often recommended in process monitoring when a quick detection of small or moderate sustained shifts in the mean vector is desired

An optimization of on-line monitoring of simple linear and polynomial quality functions

This research aims to introduce a number of contributions for enhancing the statistical performance of some of Phase II linear and polynomial profile monitoring techniques. For linear profiles the idea of variable sampling size (VSS) and variable sampling interval (VSI) have been extended from multivariate control charts to the profile monitoring framework to enhance the power of the traditional T^2 chart in detecting shifts in linear quality models. Finding the optimal settings of the proposed schemes has been formulated as an optimization problem solved by using a Genetic Approach (GA). Here the average time to signal (ATS) and the average run length (ARL) are regarded as the objective functions, and ATS and ARL approximations, based on Markov Chain Principals, are extended and modified to capture the special structure of the profile monitoring. Furthermore,the performances of the proposed control schemes are compared with their fixed sampling counterparts for different shift levels in the parameters. The extensive comparison studies reveal the potentials of the proposed schemes in enhancing the performance of T^2 control chart when a process yields a simple linear profile. For polynomial profiles, where the linear regression model is not sufficient, the relationship between the parameters of the original and orthogonal polynomial quality profiles is considered and utilized to enhance the power of the orthogonal polynomial method (EWMA4). The problem of finding the optimal set of explanatory variable minimizing the average run length is described by a mathematical model and solved using the Genetic Approach. In the case that the shift in the second or the third parameter is the only shift of interest, the simulation results show a significant reduction in the mean of the run length distribution of the EWMA4 technique

On Data Depth and the Application of Nonparametric Multivariate Statistical Process Control Charts

The purpose of this article is to summarize recent research results for constructing nonparametric multivariate control charts with main focus on data depth based control charts. Data depth provides data reduction to large-variable problems in a completely nonparametric way. Several depth measures including Tukey depth are shown to be particularly effective for purposes of statistical process control in case that the data deviates normality assumption. For detecting slow or moderate shifts in the process target mean, the multivariate version of the EWMA is generally robust to non-normal data, so that nonparametric alternatives may be less often required

Variable Sample Size Control Charts for Monitoring the Multivariate Coefficient of Variation Based on Median Run Length and Expected Median Run Length

The monitoring of a well-functioning process system has always held significant importance. In recent times, there has been notable attention towards employing control charts to oversee both univariate and multivariate coefficients of variation (MCV). This shift is in response to the concern of erroneous outcomes that can arise when traditional control charts are applied under the condition of dependent mean and standard deviation, as highlighted by prior research. To address this, the remedy lies in adopting the coefficient of variation. Furthermore, this study underscores the application of MCV in scenarios where multiple quality attributes are simultaneously under surveillance within an industrial process. This aspect has demonstrated considerable enhancement in chart performance, especially when incorporating the variable sample size (VSS) feature into the MCV chart. Adaptive VSS, evaluated through metrics like median run length (MRL) and expected median run length (EMRL), is also integrated for MCV monitoring. In contrast to earlier studies that predominantly focused on average run length (ARL), this research acknowledges the potential inaccuracies in ARL measurement. In this study, two optimal designs for VSS MCV charts are formulated by minimizing two criteria: firstly, MRL; and secondly, EMRL, both accounting for deterministic and unknown shift sizes. Additionally, to assess the distribution's variability in run lengths, the study provides the 5th and 95th percentiles. The research delves into two VSS schemes: one with a defined small sample size (nS), and another with a predetermined large sample size (nL) for the initial subgroup (n(1)). The approach taken involves the development of a Markov chain method for designing and deriving performance measures of the proposed chart. These measures include MRL and EMRL. Moreover, a comparative analysis between the proposed chart's performance and the standard MCV chart (STD) is presented in terms of MRL and EMRL criteria. The outcomes illustrate the superiority of the proposed chart over the STD MCV chart for all shift sizes, whether they are upward or downward, and when n(1) equals nS or nL

Integrated Projection and Regression Models for Monitoring Multivariate Autocorrelated Cascade Processes

This dissertation presents a comprehensive methodology of dual monitoring for the multivariate autocorrelated cascade processes using principal component analysis and regression. Principle Components Analysis is used to alleviate the multicollinearity among input process variables and reduce the dimension of the variables. An integrated principal components selection rule is proposed to reduce the number of input variables. An autoregressive time series model is used and imposed on the time correlated output variable which depends on many multicorrelated process input variables. A generalized least squares principal component regression is used to describe the relationship between product and process variables under the autoregressive regression error model. The combined residual based EWMA control chart, applied to the product characteristics, and the MEWMA control charts applied to the multivariate autocorrelated cascade process characteristics, are proposed. The dual EWMA and MEWMA control chart has advantage and capability over the conventional residual type control chart applied to the residuals of the principal component regression by monitoring both product and the process characteristics simultaneously. The EWMA control chart is used to increase the detection performance, especially in the case of small mean shifts. The MEWMA is applied to the selected set of variables from the first principal component with the aim of increasing the sensitivity in detecting process failures. The dual implementation control chart for product and process characteristics enhances both the detection and the prediction performance of the monitoring system of the multivariate autocorrelated cascade processes. The proposed methodology is demonstrated through an example of the sugar-beet pulp drying process. A general guideline for controlling multivariate autocorrelated processes is also developed

On the constrained economic design of control charts: a literature review

The economic design is an appealing approach to settle the design parameters of a control chart. Unfortunately, the economic models to design control charts have been scarcely implemented by quality practitioners due to the simplifying assumptions when representing the multifaceted complexity and constraints present within manufacturing and transactional environments. Although there has been an increasing scepticism about the economic models usefulness in practice, some recent studies proposed in literature face the problem of the control charts economic design from a new point of view: the objective is to achieve a well balanced trade-off between the operational and the statistical aspects. Under this perspective, the economic design problem can be intended in a broader sense as the constrained design of a SPC inspection procedure. This paper presents a discussion of some recent trends in the economic design stream of research and outlines the importance of considering the constraints related to SPC resources availability and modelling the occurrence of random shifts