The Effect of Median Based Estimators on CUSUM Chart

Cumulative Sum (CUSUM) chart has been used extensively to monitor mean shifts.It is highly sought after by practitioners and researchers in many areas of quality control due to its sensitivity in detecting small to moderate shifts. Normality assumption governs its ability to monitor the process mean. When the assumption is violated, CUSUM chart typically loses its practical use. As normality is hard to achieve in practice, the usual CUSUM chart is often substituted with robust charts.This is to provide more accurate results under slight deviation from normality. Thus, in this paper, we investigate the impact of using robust location estimators, namely, median and Hodges-Lehmann on CUSUM performance. By pairing the location estimators with a robust scale estimator known as median absolute deviation about the median (MADn), a duo median based CUSUM chart is attained.The performances of both charts are studied under normality and contaminated normal distribution and evaluated using the average run length (ARL). While demonstrating an average power to detect the out-of-control situations, the in-control performances of both charts remain unaffected in the presence of outliers. This could very well be advantageous when the proposed charts are tested on a real data set in the future. A case in point is when the statistical tool is used to monitor changes in clinical variables for the health care outcomes.By minimising the false positives, a sound judgement can be made for any clinical decision

Parametric, Nonparametric, and Semiparametric Linear Regression in Classical and Bayesian Statistical Quality Control

Statistical process control (SPC) is used in many fields to understand and monitor desired processes, such as manufacturing, public health, and network traffic. SPC is categorized into two phases; in Phase I historical data is used to inform parameter estimates for a statistical model and Phase II implements this statistical model to monitor a live ongoing process. Within both phases, profile monitoring is a method to understand the functional relationship between response and explanatory variables by estimating and tracking its parameters. In profile monitoring, control charts are often used as graphical tools to visually observe process behaviors. We construct a practitioner’s guide to provide a stepby- step application for parametric, nonparametric, and semiparametric methods in profile monitoring, creating an in-depth guideline for novice practitioners. We then consider the commonly used cumulative sum (CUSUM), multivariate CUSUM (mCUSUM), exponentially weighted moving average (EWMA), multivariate EWMA (mEWMA) charts under a Bayesian framework for monitoring respiratory disease related hospitalizations and global suicide rates with parametric, nonparametric, and semiparametric linear models

25 Years of IIF Time Series Forecasting: A Selective Review

We review the past 25 years of time series research that has been published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982-1985; International Journal of Forecasting 1985-2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on possible future research directions in this field.Accuracy measures; ARCH model; ARIMA model; Combining; Count data; Densities; Exponential smoothing; Kalman Filter; Long memory; Multivariate; Neural nets; Nonlinearity; Prediction intervals; Regime switching models; Robustness; Seasonality; State space; Structural models; Transfer function; Univariate; VAR.

The impact of data anomaly on EWMA phase II performance

In applying control chart with estimated parameters for monitoring changes in a process, Phase I samples are typically assumed to be free of outliers or any other data anomaly. Naturally, the sample mean and the sample standard deviations are used as estimators, yielding efficient estimates for the chart. Nonetheless, when Phase I may be contaminated, this regular practice is no longer suitable as classical estimators are susceptible to the effect of outliers which in turn may affect control chart performance. This study shows that the effect is not trivial via. the application of EWMA control chart. Moreover, this study focuses on the effect using alternative and robust Phase I estimators on the EWMA when the chart is used to monitor changes in the process mean. In this study, an automatic trimmed mean estimator is used to provide estimate for the process mean. Meanwhile, for the standard deviation of the process, this study employs three different estimators including the corresponding robust scale estimator used in the trimming process of the location measure. Simulated data were used to test the performance of the EWMA control charts. The finding based on mean and percentiles of the run-length distribution shows quicker detection of out-of-control status when robust statistics were used to compute parameter estimates in Phase I of the EWMA chart upon contamination in the data set

A semi-empirical Bayesian chart to monitor Weibull percentiles

This paper develops a Bayesian control chart for the percentiles of the Weibull distribution, when both its in-control and out-of-control parameters are unknown. The Bayesian approach enhances parameter estimates for small sample sizes that occur when monitoring rare events as in high-reliability applications or genetic mutations. The chart monitors the parameters of the Weibull distribution directly, instead of transforming the data as most Weibull-based charts do in order to comply with their normality assumption. The chart uses the whole accumulated knowledge resulting from the likelihood of the current sample combined with the information given by both the initial prior knowledge and all the past samples. The chart is adapting since its control limits change (e.g. narrow) during the Phase I. An example is presented and good Average Run Length properties are demonstrated. In addition, the paper gives insights into the nature of monitoring Weibull processes by highlighting the relationship between distribution and process parameters.Comment: 21 pages, 3 figures, 5 table

The Effect of Median Based Estimators on CUSUM Chart

Cumulative Sum (CUSUM) chart has been used extensively to monitor mean shifts. It is highly sought after by practitioners and researchers in many areas of quality control due to its sensitivity in detecting small to moderate shifts. Normality assumption governs its ability to monitor the process mean. When the assumption is violated, CUSUM chart typically loses its practical use. As normality is hard to achieve in practice, the usual CUSUM chart is often substituted with robust charts. This is to provide more accurate results under slight deviation from normality. Thus, in this paper, we investigate the impact of using robust location estimators, namely, median and Hodges-Lehmann on CUSUM performance. By pairing the location estimators with a robust scale estimator known as median absolute deviation about the median (MADn), a duo median based CUSUM chart is attained. The performances of both charts are studied under normality and contaminated normal distribution and evaluated using the average run length (ARL). While demonstrating an average power to detect the outof-control situations, the in-control performances of both charts remain unaffected in the presence of outliers. This could very well be advantageous when the proposed charts are tested on a real data set in the future. A case in point is when the statistical tool is used to monitor changes in clinical variables for the health care outcomes. By minimising the false positives, a sound judgement can be made for any clinical decision

The performance of robust multivariate Ewma control charts

Multivariate Exponential Weighted Moving Average (MEWMA) control chart is a popular statistical tool for monitoring multivariate process over time. However, this chart is sensitive to the presence of outliers arising from the use of classical mean vector and covariance matrix in estimating the MEWMA statistic. These classical estimators are known to be sensitive to the outliers. To address this problem, robust MEWMA control charts based on modified one-step M-estimator (MOM) and Winsorized modified one-step M-estimator (WM) are proposed. Their performance is then compared with the standard MEWMA control chart in various situations. The findings revealed that the proposed robust MEWMA control charts are more effective in controlling false alarm rates especially for large sample sizes and high percentage of outlier

Robustification of CUSUM control structure for monitoring location shift of skewed distributions based on modified one-step M-estimator

Including three existing charts, a new approach employing a modified one-step M-estimator (MOM) with Cumulative Sum (CUSUM) control structure were evaluated and compared for their Phase II performances based on the average run length (ARL) under various skewed distributions. The primary focus was on the robustness of the CUSUM charts in two separate cases: (i) when the process parameters are known and (ii) when the process mean is unknown and estimated from an in-control Phase I sample. The simulation and real data analysis showed the proposed technique is comparable or sometimes better than the existing charts