Analyzing Baseline Phase Data

This chapter discusses the analysis of the baseline phase. The baseline serves as the comparison for information collected during subsequent phases. It allows the researcher or practitioner to determine if the target behaviors are changing in a desirable or undesirable direction. Two different types of baselines are presented, concurrent and reconstructed. In a concurrent baseline, data are collected simultaneously, while other assessment activities are being conducted. A reconstructed baseline is an attempt to approximate naturally occurring behavior based on memories or case records. Issues related to comparing phases are discussed and illustrated, including stability of the baseline, trending data, and autocorrelation (or serial dependency). Guidance is provided on how each of these can be assessed and addressed, including the transformation of highly autocorrelated data. Examples are provided throughout to illustrate each concept.

Forecasting and Controlling Key Performance Indicators in Call Centers

This paper proposes a methodology for modeling and controlling the performance of call centers. Most call centers use CRM (Customer Relationship Management) systems to record data of all contacts between agents and clients. These data may be autocorrelated. To model autocorrelated processes effectively, the proposed methodology integrates in a logical way ARIMA (Autoregressive Integrated Moving Average) modeling and SPC (Statistical Process Control) tools. ARIMA is used to model the process and identify the model that best fits the time series. The fitted model is used to compute residuals, predict future values for the quality variable(s) being monitored and determine the prediction errors. To achieve these goals, the Box-Jenkins methodology is employed. These outputs are then used to apply SPC, in this case the Shewhart control charts for autocorrelated data. First, the computed residuals are used to build the control charts in Phase I of SPC, verify the process stability and estimate the process parameters. Then, these parameters are used to establish the control limits of the charts used in Phase II of SPC to monitor and control the prediction errors. The proposed methodology is tested in a case study of a large call center in Portugal. The results of the case study suggest that ARIMA modeling and SPC, when properly integrated, provide a set of effective tools for monitoring call center performance when autocorrelated data are available. This paper has important implications for both theory and practice.

Application of Statistical Monitoring Using Autocorrelated Data and With the Influence of Multicollinearity in a Steel Process

The purpose of this article is to demonstrate a practical application of control charts in an industrial process that has data auto-correlated with each other. Although the control charts created by Walter A. Shewhart are very effective in monitoring processes, there are very important statistical assumptions for Shewhart's control charts to be applied correctly. Choosing the correct Control Chart is essential for managers to be able to make coherent decisions within companies. With this study, it was possible to demonstrate that the original data collected in the process, which at first appeared to have many special causes of variation, was actually a stable process (no anomalies present). However, this finding required the use of autoregressive models, multivariate statistics, autocorrelation and normality tests, multicollinearity analysis and the use of the EWMA control chart. It was concluded that it is of fundamental importance to choose the appropriate control chart for monitoring industrial processes, to ensure that changes in processes do not incorporate non-existent variations and do not cause an increase in the number of defective products.

MAD Control Chart for Autoregressive Models with Skew-Normal Distribution

The major problem in analyzing control charts is to work with autocorrelated data. This problem can be solved by fitting a suitable model to the data and using the control chart for the residuals. The problem becomes very important, when the distribution of observation is nonnormal, in addition to being autocorrelated. Much recent research has focused on the development of appropriate statistical process control techniques for the autocorrelated data or nonnormal distribution, but few studies have considered monitoring the process mean of both nonnormal and autocorrelated data. In this paper, a simulation study is conducted to compare the performances of the control chart based on the median absolute deviation method (MAD) with those of existing control charts for the skew normal distribution. Simulation results indicate considerable improvement over existing control charts for nonnormal data can be achieved when the control charts with control limits based on the MAD method are used to monitor the process mean of nonnormal autocorrelated data.