A robust \overline {\hbox{X}} control chart based on M-estimators in presence of outliers

Specifying the control limits is an important step in designing a control chart. The control limits are determined by the estimates of mean and/or standard deviation of the process. In the $ \overline {\hbox{X}} $ control chart, when outliers exist in the data, using the classical estimators to estimate parameters may cause the limits to become wider or to shift in the same direction. Robust estimators which are not affected by outliers are used in this research to determine the control limits for $ \overline {\hbox{X}} $ control chart. The mean and the dispersion estimators which are currently applied to define control limits are evaluated, and their performances in control charting are compared with the proposed method by vast simulation and real data examples. Based on the results, it is revealed that when M-estimators with bisquare ρ functions is used to estimate the mean and the dispersion of the process, the control chart has the best performance among the other robust and classical control charts.     

Multiple-objective design of an \overline{{\user2{X}}} control chart with multiple assignable causes

Control charts are widely implemented in firms to establish and maintain statistical control of a process which leads to the improved quality and productivity. Therefore, designs of control charts have gained particular attention from the outset. Design of control charts requires that the engineer selects a sample size, a sampling frequency, and the control limits for the chart. In this paper, a possible combination of design parameters is considered as a decision-making unit which is identified by three attributes: hourly expected cost, detection power of the chart, and in-control average run length. Subsequently, optimal design of control charts is formulated as a multiple-objective decision-making problem. Moreover, the cost function is extended from single to multiple assignable causes because there exist multiple assignable causes in real practice. An algorithm using data envelopment analysis is applied to solve the multiple-objective decision-making (MODM) model. Some numerical and experimental analyses are provided to illustrate the algorithm procedure. Sensitivity analysis is carried out to investigate the robustness of the model, and comparisons with other related published papers are made. It is shown that the proposed MODM model can overcome some drawbacks attached to the previous models and approaches.     

Generally weighted moving average control chart for monitoring process variability

Most applications of the EWMA control chart for monitoring processes depend on detecting shifts in the process mean. The problem of detecting an increase in process variability, which can also strongly affect the quality of products, is perhaps more important. When a process moves from the pilot phase to the production phase, the mean may not shift but the variation will probably increase because new sources of variation are introduced, including new people and materials. A simulation is performed to evaluate the ARL to false alarm and to monitor the change in the process variability of the EWMA control chart and the GWMA control chart. An extensive comparison reveals that the GWMA control chart is more sensitive than the EWMA control chart in monitoring the variance of a process. The results of this study can be applied to monitor the process variability in automated industries.     

Optimal design of \overline {\text{X}} -control chart with Pareto in-control times

Economic control chart models usually assume that the time to occurrence of an assignable cause follows an exponential or Weibull distribution. This paper extends that to the Pareto distribution in order to investigate, in general, the effect on the economic control chart parameters like sample size, time between two successive samples, and the cost per unit time of the distributional assumption. The Pareto distribution arises as a limiting distribution of the waiting time for the number of new observations needed to obtain a value exceeding the greatest among “n” observations. It was found that the economic design of $ \overline {\text{X}} $ chart is greatly influenced by the distributional assumption. Using the cost model, the sensitivity analysis of the statistical economic design of the $ \overline {\text{X}} $ chart with respect to the parameters and costs is studied.     

Improved feature-based test statistic for assessing suitability of the preliminary samples for constructing control limits of \bar{X} chart

In spite of using a large number of subgroups (m) of small samples (n), the estimated control limits of $ \bar{X} $ chart in phase I can be erroneous unless the preliminary samples are drawn from a stable process. As a result, the performance of the chart in phase II can be significantly affected. The pattern in the $ \bar{X} $ chart, exhibited by the plots of the subgroup averages of the preliminary samples, will be different depending on stability and instability of the process while the preliminary samples were collected. Based on this concept, a new feature-based test statistic (FTS) is proposed for evaluating suitability of the preliminary samples for the designing of the $ \bar{X} $ chart. The FTS, for given m, approximately follows $ N[1,{\text{ SD(}}m{)]} $ , where SD(m) is a function of m. The goodness of the approximation and effectiveness of the test are evaluated using simulated data. The results show that both are satisfactory for m?>?=48. The proposed statistic is also quite effective in detecting unstable process condition resulting in a cyclic pattern. The computation of FTS involves some complexities. However, now-a-days computers are widely available and so computation difficulty may not be a problem.     

An Economic design for a variable-sampling-interval {\bar{x}} control chart for a continuous-flow process

Most of the studies in economic design of control charts focus on a fixed-sampling interval (FSI), however, it has been discovered that variable-sampling-interval (VSI) control charts are substantially quicker in detecting shifts in the process than FSI control charts due to a higher frequency in the sampling rate when a sample statistic shows some indication of a process change. In this paper, an economic design for a VSI $\bar{x}$ control chart is proposed for a continuous-flow production process. The results of a numerical example adopted from an actual case indicate that the economic design of VSI control charts is consistently lower in loss-cost than that of the FSI scheme.     

Statistical design of variable sample size and sampling interval $\bar{X}$\bar{X}control charts with run rules

In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sampling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size combined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parameter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and moderate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem.     

Distributed multiparametric model predictive control design for a quadruple tank process

Distributed control for plant wide control has received attention lately. In this paper, multiparametric quadratic programming based controllers have been developed for a benchmark quadruple tank problem. A centralized control strategy is developed by partitioning its six dimensional vector space based on constraint satisfaction, stability and optimality. Control design is simplified using its decentralized version after a relative gain array analysis of the benchmark. A cooperative game theory based distributed model predictive controller and decentralized proportional integral (PI) controller are also designed for the same system. A decoupling based cooperative distributed multiparametric model predictive controller (mpMPC) is proposed. The controllers are subjected to reference tracking and disturbance rejection and the performance measures are compared. Also, the robustness of cooperative mpMPC to parameter uncertainties is discussed. Distributed design approach is a natural fit for the vector space partitioning based mpMPC design. Simulations results are analyzed and the performance of the five controllers is discussed.