Murat Caner Testik

Review: A review of data mining applications for quality improvement in manufacturing industry

Many quality improvement (QI) programs including six sigma, design for six sigma, and kaizen require collection and analysis of data to solve quality problems. Due to advances in data collection systems and analysis tools, data mining (DM) has widely been applied for QI in manufacturing. Although a few review papers have recently been published to discuss DM applications in manufacturing, these only cover a small portion of the applications for specific QI problems (quality tasks). In this study, an extensive review covering the literature from 1997 to 2007 and several analyses on selected quality tasks are provided on DM applications in the manufacturing industry. The quality tasks considered are; product/process quality description, predicting quality, classification of quality, and parameter optimisation. The review provides a comprehensive analysis of the literature from various points of view: data handling practices, DM applications for each quality task and for each manufacturing industry, patterns in the use of DM methods, application results, and software used in the applications are analysed. Several summary tables and figures are also provided along with the discussion of the analyses and results. Finally, conclusions and future research directions are presented.

Conditional and marginal performance of the Poisson CUSUM control chart with parameter estimation

Cumulative Sum (CUSUM) type control charts are widely used in industry because of their effectiveness for process control. The Poisson CUSUM is a powerful and easy-to-implement control chart, which is appropriate for monitoring the counts of nonconformities in a unit from a repetitive production process. In the literature, control chart performances are generally evaluated under the assumption of known in-control process parameters. However, in-control process parameters are rarely known in practice and often parameter estimates from a reference sample are used instead. As a consequence of the additional variability introduced by parameter estimation, operational performance of a control chart might differ from the expected performance when the parameters are known. In this paper, effect of estimated process mean on the conditional and marginal performance of the Poisson CUSUM chart are quantified. The Markov Chain approach is used for calculating the aspects of the run length distribution. The effect of estimation on the in-control average run length performance is shown to be significant. Sample-size recommendations are provided.

Properties of the exponential EWMA chart with parameter estimation

Count rates may reach very low levels in production processes with low defect levels. In such settings, conventional control charts for counts may become ineffective since the occurrence of many samples with zero defects would cause control statistic to be consistently zero. Consequently, the exponentially weighted moving average (EWMA) control chart to monitor the time between successive events (TBE) or counts has been introduced as an effective approach for monitoring processes with low defect levels. When the counts occur according to a Poisson distribution, the TBE observations are distributed as exponential. Although the assumption of exponential distribution is a reasonable choice as a model of TBE observations, its parameter, i.e. the mean (also the standard deviation), is rarely known in practice and its estimate is used in place of the unknown parameter when constructing the exponential EWMA chart. In this article, we investigate the effects of parameter estimation on the performance measures (average run length, standard deviation, and percentiles of the run length distribution) of the exponential EWMA control chart. A comprehensive analysis of the conditional performance measures of the chart shows that the effect of estimation can be serious, especially if small samples are used. An investigation of the marginal performance measures, which are calculated by averaging the conditional performance measures over the distribution of the parameter estimator, allows us to provide explicit sample size recommendations in constructing these charts to reach a satisfactory performance in both the in-control and the out-of-control situation. Copyright

Multivariate one-sided control charts

Process knowledge can be exploited to improve the performance of control charts and it is not unusual to know that a specific variable shifts above or below its mean under an assignable cause. In such a case, a one-sided control chart is common. The available statistical theory for the one-sided tests is used to provide a reasonable compromise for a numerical procedure to design and implement multivariate solutions. Although simulation is used in the analysis, it is not a direct estimate of performance through simulation. Instead, weights are estimated and these are used to easily set a desired on-target average run length. Furthermore, an interesting quadratic programming solution is incorporated into the analysis. Then the statistical results are extended to a partial one-sided case where only some (not all) variables are known to shift in one direction and the numerical procedure is extended to design and implement the charts. A modern method can blend theory and algorithms into a practical solution. We conclude that modern computer software permits an efficient solution to this problem with meaningful performance advantages over traditional multivariate control charts.

The Poisson INAR(1) CUSUM chart under overdispersion and estimation error

The Poisson INAR(1) CUSUM chart has been proposed to monitor integer-valued autoregressive processes of order 1 with Poisson marginals. The effectiveness of this chart has been shown under the assumptions of Poisson marginals and known in-control process parameters, but these assumptions may not be very well satisfied in practical applications. This article investigates the practical issues concerning applications of the Poisson INAR(1) CUSUM chart, considering average run lengths obtained through a bivariate Markov chain approach. First, the effects of deviations from the assumed Poisson model are investigated when there is overdispersion. Design recommendations for achieving robustness are provided along with an extension, the Winsorized Poisson INAR(1) CUSUM chart. Next, analyzing the conditional average run length performance under some hypothetical cases of parameter estimation, it is shown that estimation errors may severely affect the chart’s performance. The marginal average run length performance is used to derive sample size recommendations. An example for monitoring the number of beds occupied at a hospital emergency department is used to illustrate the proposed approach.

The Effect of Estimated Parameters on Poisson EWMA Control Charts

Abstract Performance of control charts is generally evaluated with the assumption that the process parameters are known. In many control chart applications, however, the process parameters are rarely known and their estimates from an in-control reference sample are used instead. In such cases, the moments of the run length distribution depend on the values of the estimated parameters. The Poisson exponentially weighted moving average (EWMA) is an effective control chart in situations where the number of nonconformities per unit from a repetitive production process is monitored. The objective of this paper is to study the effect of estimating the mean on the performance of the Poisson EWMA control chart. We make use of the Markov Chain approach. Sample-size recommendations and some concluding comments are provided.

A Two‐Sided Cumulative Sum Chart for First‐Order Integer‐Valued Autoregressive Processes of Poisson Counts

Count data processes are often encountered in manufacturing and service industries. To describe the autocorrelation structure of such processes, a Poisson integer-valued autoregressive model of order 1, namely, Poisson INAR(1) model, might be used. In this study, we propose a two-sided cumulative sum control chart for monitoring Poisson INAR(1) processes with the aim of detecting changes in the process mean in both positive and negative directions. A trivariate Markov chain approach is developed for exact evaluation of the ARL performance of the chart in addition to a computationally efficient approximation based on bivariate Markov chains. The design of the chart for an ARL-unbiased performance and the analyses of the out-of-control performances are discussed. Copyright

Relationships among control charts used with feedback control

Feedback control is common in modern manufacturing processes and there is a need to combine statistical process control in such systems. Typical types of assignable causes are described and fault signatures are calculated. A fault signature can be attenuated by the controller and an implicit confounding among faults of different types is discussed. Furthermore, the relationships between various control statistics are developed. Control charts have been proposed previously for deviations from target and for control adjustments. We describe why one or the other can be effective in some cases, but that neither directly incorporates the magnitude (or signature) of an assignable cause. Various disturbance models and control schemes, both optimal and non-optimal, are included in a mathematically simple model that obtains results through properties of linear filters. We provide analytical results for a widely-used model of feedback control. Copyright

Experimental Designs for Constrained Regions

The familiar factorial, fractional factorial, and response surface designs are designs for regularly-shaped regions of interest, typically cuboidal regions and spherical regions. An irregularly shaped region of experimentation arises in situations where there are constraints on the factor level combinations that can be run or restrictions on portions of the region of exploration. Computer-generated designs based on some optimality criterion are a logical alternative for these problems. We give a brief tutorial on design optimality criteria and show how one of these, the D-optimality criteria, can lead to very reasonable designs for constrained regions of interest. We show through a simulation study that D-optimal designs perform very well with respect to the capability of selecting the correct model and accurately estimating the design factor levels that result in the optimal response.

Discovering Blood Donor Arrival Patterns Using Data Mining: A Method to Investigate Service Quality at Blood Centers

Blood centers without fixed appointments for collecting blood often experience nonconstant donor arrival rates, which vary due to time-of-day, day-of-week, etc. When a constant workforce size is employed in such blood centers, there is either idle personnel, or donor satisfaction is compromised due to long waiting times, or both conditions alternate over time. Consequently, a method to obtain adaptive workforce requirements might be valuable. This study utilized the Two-Step Cluster method and the Classification and Regression Trees method in succession to identify both daily and hourly donor arrival patterns at Hacettepe University Hospitals’ Blood Center. A serial queuing network model of the donation process was then employed for each of the identified donor arrival patterns. By considering and accomodating variations in the donor arrival patterns, required workforce sizes and their decomposition among process steps were predicted to achieve predetermined target values of expected waiting times and to balance workforce utilizations in the blood donation processes. Although a blood center is considered for the proposed methodology, the approach is general and applications in various operations of healthcare organizations are possible.