A simple approach for monitoring business service time variation.

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries comes from processes having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. In this paper, we propose a new asymmetric EWMA variance chart (EWMA-AV chart) and an asymmetric EWMA mean chart (EWMA-AM chart) based on two simple statistics to monitor process variance and mean shifts simultaneously. Further, we explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using both the EWMA-AV chart and the EWMA-AM chart. The performance of the EWMA-AV and EWMA-AM charts and that of some existing variance and mean charts are compared. A numerical example involving nonnormal service times from the service system of a bank branch in Taiwan is used to illustrate the applications of the EWMA-AV and EWMA-AM charts and to compare them with the existing variance (or standard deviation) and mean charts. The proposed EWMA-AV chart and EWMA-AM charts show superior detection performance compared to the existing variance and mean charts. The EWMA-AV chart and EWMA-AM chart are thus recommended

Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

A Binary Control Chart to Detect Small Jumps

The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most recent observations. Our aim is to construct a control chart for detecting a shift of an unknown size, allowing for an unknown distribution of the error terms. Simulation studies indicate that the proposed chart is su- perior in terms of out-of-control average run length, when one is interest in the detection of very small shifts. We provide a (functional) central limit theorem under a change-point model with local alternatives which explains that unexpected and interesting behavior. Since real observations are often not independent, the question arises whether these re- sults still hold true for the dependent case. Indeed, our asymptotic results work under the fairly general condition that the observations form a martingale difference array. This enlarges the applicability of our results considerably, firstly, to a large class time series models, and, secondly, to locally dependent image data, as we demonstrate by an example

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

An Improved Wavelet‐Based Multivariable Fault Detection Scheme

Data observed from environmental and engineering processes are usually noisy and correlated in time, which makes the fault detection more difficult as the presence of noise degrades fault detection quality. Multiscale representation of data using wavelets is a powerful feature extraction tool that is well suited to denoising and decorrelating time series data. In this chapter, we combine the advantages of multiscale partial least squares (MSPLSs) modeling with those of the univariate EWMA (exponentially weighted moving average) monitoring chart, which results in an improved fault detection system, especially for detecting small faults in highly correlated, multivariate data. Toward this end, we applied EWMA chart to the output residuals obtained from MSPLS model. It is shown through simulated distillation column data the significant improvement in fault detection can be obtained by using the proposed methods as compared to the use of the conventional partial least square (PLS)‐based Q and EWMA methods and MSPLS‐based Q method

Towards Enhanced Diagnosis of Diseases using Statistical Analysis of Genomic Copy Number Data

Genomic copy number data are a rich source of information about the biological systems they are collected from. They can be used for the diagnoses of various diseases by identifying the locations and extent of aberrations in DNA sequences. However, copy number data are often contaminated with measurement noise which drastically affects the quality and usefulness of the data. The objective of this project is to apply some of the statistical filtering and fault detection techniques to improve the accuracy of diagnosis of diseases by enhancing the accuracy of determining the locations of such aberrations. Some of these techniques include multiscale wavelet-based filtering and hypothesis testing based fault detection. The filtering techniques include Mean Filtering (MF), Exponentially Weighted Moving Average (EWMA), Standard Multiscale Filtering (SMF) and Boundary Corrected Translation Invariant filtering (BCTI). The fault detection techniques include the Shewhart chart, EWMA and Generalized Likelihood Ratio (GLR). The performance of these techniques is illustrated using Monte Carlo simulations and through their application on real copy number data. Based on the Monte Carlo simulations, the non-linear filtering techniques performed better than the linear techniques, with BCTI performing with the least error . At an SNR of 1, BCTI technique had an average mean squared error of 2.34% whereas mean filtering technique had the highest error of 5.24%. As for the fault detection techniques, GLR had the lowest missed detection rate of 1.88% at a fixed false alarm rate of around 4%. At around the same false alarm rate, the Shewhart chart had the highest missed detection of 67.4%. Furthermore, these techniques were applied on real genomic copy number data sets. These included data from breast cancer cell lines (MPE600) and colorectal cancer cell lines (SW837)

Monitoring of the BTA Deep Hole Drilling Process Using Residual Control Charts

Deep hole drilling methods are used for producing holes with a high lengthto- diameter ratio, good surface finish and straightness. The process is subject to dynamic disturbances usually classified as either chatter vibration or spiralling. In this work, we propose to monitor the BTA drilling process using control charts to detect chatter as early as possible and to secure production with high quality. These control charts use the residuals obtained from a model which describes the variation in the amplitude of the relevant frequencies of the process. The results showed that chatter is detected and some alarm signals are related to changing physical conditions of the process. --