The economic design of cumulative sum charts used to maintain current control of non-normal process means

This paper proposes a method for the economic design of cusum charts to maintain the current control of the non-normal process means. The economic design involves the determination of the design parameters that minimize a relevant cost function. An expression for the expected loss-cost function for the process is defined. An algorithm for near-optimal determination of the design parameters is presented. A computer program is designed for the application of the algorithm, and deriving the values of the design parameters and loss-cost function of an economic design of cusum chart to control non-normal process means. Also a numerical example is provided. Finally, a simplified scheme, which would be appliable at the workshop level is presented.     

A simple approach for robust economic design of control charts

Robust economic control chart designs incorporating robustness with regard to the uncertainty in the cost and process parameters, reported in the literature, fall into two broad categories. One category of robust economic designs considers the uncertainty in the estimates of the cost and process parameters and makes the design suitable to operate well in any scenario arising out of the uncertainty. Other category of robust economic design considers different possible discrete scenarios for a single process and makes the control chart robust to all possible scenarios. The approach suggested for the robust designs for each category is different and somewhat complicated. The present paper proposes a design approach by introducing a simple statistic for the robust economic design problem of a ‘process with multiple scenarios’. SGA has been used in the optimization. The suggested statistic handles the information regarding the relative frequency of occurrence of each scenario of the process for the robust designs.     

The economic design of control charts with repair cost depending on detection delay

This study extends Duncan's [1] model to two different manufacturing process models in which the processes continue and discontinue in operations during the search for the assignable cause. A more realistic assumption considered in this paper is that the cost of repair and the net hourly out-of-control income are functions of detection delay. In the continuous model, detection delay is defined as the elapsed time from the time when the shift of the process occurs until it is identified by control charts and the assignable cause is eliminated. The discontinuous model defines detection delay as the time interval from the occurrence of the process shift to the completion of testing a set of samples and interpreting the results. An efficient procedure is developed to determine the optimal designs without using any approximation approach. Thus, the proposed procedure can obtain the truly optimal designs rather than those approximate designs determined by Duncan [1] and other subsequent researchers. This paper illustrates several numerical examples and makes some relevant comparisons. The results indicate that this optimal solution procedure is more accurate than that of Panagos et al. [2]. Also, detection delay is sensitive to the economic design of control charts.     

Interaction between process design and process control: economic analysis of process dynamics

A method is presented to assess the impact of disturbances on plant economic performance. The method is suitable for use during process design, and can be used to help evaluate alternative process structures or alternative control schemes for a given process. Non-linear steady-state optimization is performed to determine the best operating point in the absence of disturbances. Frequency response analysis of a linearized plant dynamic model is used to estimate the effects of plant disturbances on this ideal performance under a variety of control strategies. The method is illustrated on a case study involving minerals flotation circuit design.     

New EWMA control charts for monitoring process dispersion

There exist two EWMA-type dispersion charts for monitoring dispersion increases in the literature. One resets the EWMA statistic to zero whenever it is below zero. The other one truncates negative normalized observations to zero in the EWMA statistic. This paper proposes two one-sided EWMA charts for detecting dispersion increases and decreases, respectively, and one two-sided EWMA chart for monitoring dispersion increases or decreases simultaneously. Simulation studies show that the proposed upper-sided EWMA chart performs better than the two existing counterparts for detecting increases in dispersion, and that the proposed lower-sided EWMA chart significantly outperforms the two lower-sided EWMA charts developed similar to their two existing upper-sided EWMA charts for detecting decreases in dispersion. Moreover, the proposed two-sided EWMA chart provides much better sensitivity than the two two-sided EWMA charts generalized from the two existing upper-sided EWMA charts for detecting overall changes in dispersion.     

A neural network approach to characterize pattern parameters in process control charts

Abnormal patterns on manufacturing process control charts can reveal potential quality problems due to assignable causes at an early stage, helping to prevent defects and improve quality performance. In recent years, neural networks have been applied to the pattern recognition task for control charts. The emphasis has been on pattern detection and identification rather than more detailed pattern parameter information, such as shift magnitude, trend slope, etc., which is vital for effective assignable cause analysis. Moreover, the identification of concurrent patterns (where two or more patterns exist together) which are commonly encountered in practical manufacturing processes has not been reported. This paper proposes a neural network-based approach to recognize typical abnormal patterns and in addition to accurately identify key parameters of the specific patterns involved. Both single and concurrent patterns can be characterized using this approach. A sequential pattern analysis (SPA) design was adopted to tackle complexity and prevent interference between pattern categories. The performance of the model has been evaluated using a simulation approach, and numerical and graphical results are presented which demonstrate that the approach performs effectively in control chart pattern recognition and accurately identifies the key parameters of the recognized pattern(s) in both single and concurrent pattern circumstances.     

A new auxiliary information based cumulative sum median control chart for location monitoring

Control charts are commonly used tools in statistical process control for the detection of shifts in process parameters. Shewhart-type charts are efficient for large shift values, whereas cumulative sum (CUSUM) charts are effective in detecting medium and small shifts. Control chart use commonly assumes that data are free of outliers and parameters are known or correctly estimated based on an in-control process. In practice, these assumptions are not often true because some processes occasionally have outliers. Monitoring the location parameter is usually based on mean charts, which are seriously affected by violations of these assumptions. In this paper we propose several CUSUM median control charts based on auxiliary variables, and offer comparisons with their corresponding mean control charts. To monitor the location parameter, we examined the performance of mean and median control charts in the presence and absence of outliers. Both symmetric and non-symmetric processes were studied to examine the properties of the proposed control charts to monitor the location parameter using CUSUM control charts. We used different run length measures to study in-control and out-of-control performances of CUSUM charts. Results revealed that our proposed control charts perform much better than the traditional charts in the presence of outliers. A real application of our study was provided using data on concrete compressive strength as it relates to the quality of cement manufacturing.

     

An alternative approach to fuzzy control charts: Direct fuzzy approach

The major contribution of fuzzy set theory lies in its capability of representing vague data. Fuzzy logic offers a systematic base to deal with situations, which are ambiguous or not well defined. In the literature, there exist few papers on fuzzy control charts, which use defuzziffication methods in the early steps of their algorithms. The use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis. Linguistic data in those works are transformed into numeric values before control limits are calculated. Thus both control limits as well as sample values become numeric. In this paper, some contributions to fuzzy control charts based on fuzzy transformation methods are made by the use of α-cut to provide the ability of determining the tightness of the inspection: the higher the value of α the tighter inspection. A new alternative approach “Direct Fuzzy Approach (DFA)” is also developed in this paper. In contrast to the existing fuzzy control charts, the proposed approach is quite different in the sense it does not require the use of the defuzziffication. This prevents the loss of information included by the samples. It directly compares the linguistic data in fuzzy space without making any transformation. We use some numeric examples to illustrate the performance of the method and interpret its results.     

A new monitoring design for uni-variate statistical quality control charts

In this research, an iterative approach is employed to analyze and classify the states of uni-variate quality control systems. To do this, a measure (called the belief that process is in-control) is first defined and then an equation is developed to update the belief recursively by taking new observations on the quality characteristic under consideration. Finally, the upper and the lower control limits on the belief are derived such that when the updated belief falls outside the control limits an out-of-control alarm is received. In order to understand the proposed methodology and to evaluate its performance, some numerical examples are provided by means of simulation. In these examples, the in and out-of-control average run lengths (ARL) of the proposed method are compared to the corresponding ARL’s of the optimal EWMA, Shewhart EWMA, GEWMA, GLR, and CUSUM[11] methods within different scenarios of the process mean shifts. The simulation results show that the proposed methodology performs better than other charts for all of the examined shift scenarios. In addition, for an autocorrelated AR(1) process, the performance of the proposed control chart compared to the other existing residual-based control charts turns out to be promising.     

Development of fuzzy process control charts and fuzzy unnatural pattern analyses

Many problems in scientific investigation generate nonprecise data incorporating nonstatistical uncertainty. A nonprecise observation of a quantitative variable can be described by a special type of membership function defined on the set of all real numbers called a fuzzy number or a fuzzy interval. A methodology for constructing control charts is proposed when the quality characteristics are vague, uncertain, incomplete or linguistically defined. Fuzzy set theory is an inevitable tool for fuzzy control charts as well as other applications subjected to uncertainty in any form. The vagueness can be handled by transforming incomplete or nonprecise quantities to their representative scalar values such as fuzzy mode, fuzzy midrange, fuzzy median, or fuzzy average. Then crisp methods may be applied to those representative values for control chart decisions as “in control” or “out of control”. Transforming the vague data by using one of the transformation methods may result in biased decisions since the information given by the vague data is lost by the transformation. Such data needs to be investigated as fuzzy sets without transformation, and the decisions based on the vague data should not be concluded with an exact decision. A “direct fuzzy approach (DFA)” to fuzzy control charts for attributes under vague data is proposed without using any transformation method. Then, the unnatural patterns for the proposed fuzzy control charts are defined using the probabilities of fuzzy events.     

An approach to robust control design

A robust stability test is formulated and the methodology of its use in the robust control system design is presented. The paper makes a contribution to the existing approaches to solution of this class of problems.     

An optimal control approach to robust control design

We propose an optimal control approach to robust control design. Our goal is to design a state feedback to stabilize a system under uncertainty. We translate this robust control problem into an optimal control problem of minimizing a cost. Because the uncertainty bound is reflected in the cost, the solution to the optimal control problem is a solution to the robust control problem. Our approach can deal with both linear and non-linear systems. Furthermore it can handle both matched and unmatched uncertainties. It can also handle uncertainty in the control input matrix.     

A neural network applied to estimate process capability of non-normal processes

It is always crucial to estimate process capability index (PCI) when the quality characteristic does not follow normal distribution, however skewed distributions come about in many processes. The classical method to estimate process capability is not applicable for non-normal processes. In the existing methods for non-normal processes, probability density function (pdf) of the process or an estimate of it is required. Estimating pdf of the process is a hard work and resulted PCI by estimated pdf may be far from real value of it. In this paper an artificial neural network is proposed to estimate PCI for right skewed distributions without appeal to pdf of the process. The proposed neural network estimates PCI using skewness, kurtosis and upper specification limit as input variables. Performance of proposed method is validated by simulation study for different non-normal distributions. Finally, a case study using the actual data from a manufacturing process is presented.     

Detection of chatter vibration in a drilling process using multivariate control charts

Time series analysis and multivariate control charts are used to devise a real-time monitoring strategy in a drilling process. The process is used to produce holes with high length-to-diameter ratio, good surface finish and straightness. It is subject to dynamic disturbances that are classified as either chatter vibration or spiralling. A new nonparametric control chart for multivariate processes is proposed. It is used to detect chatter vibration which is dominated by single frequencies. The results showed that the proposed monitoring strategy can detect chatter vibration and that some alarm signals are related to changing physical conditions of the process.     

An approach to multivariable combustion control design

In this paper, an approach to multivariable combustion control design within the Individual Channel Design (ICD) framework for analysis and control design is presented. ICD is a framework which involves an interplay between customer specification, uncertain plant characteristics, and the multivariable feed-back design itself. Established multivariable methods and process engineering knowledge can be incorporated or evaluated within the ICD framework. The combustion control has been designed and evaluated with a computer simulation of both a linearized model and a nonlinear model of the closed-loop system. The ICD multivariable framework shows in a highly transparent manner, by way of simple graphical frequency response indicators, what the main possibilities and difficulties posed by a combustion process for multivariable control are, and how much trade-off between control specifications is possible. Solutions are also presented for problems such as: integrity of closed-loop control, balance of input-output channels, simple and transparent controller structure, and robustness.     

Regulator configuration design by means of model predictive control

This paper presents new concepts and methods for regulator configuration design for stable and unstable multivariable systems. Nowadays the self-definitions of dynamic relative gain rarely consider the interaction influences of closed-loop controllers, and the interaction measurement can be also showed from the effects from controlled variables to manipulated variables through closed-loop controllers. Model Predictive Control (MPC) is an important multivariable centralized control strategy; by means of SFPC (State Feedback Predictive Control) and MGPC (Multivariable Generalized Predictive Control), two closed-loop interaction analysis methods are first put forward. Based on the control rate optimized, two inverse normalized gain arrays are obtained from SFPC and MGPC which show the dynamic effects of controlled variables on manipulated variables. With the inverse normalized gain arrays, the regulator configuration design of unstable systems can be carried out due to the effect of multivariable centralized control. Finally the advantages and effectiveness of proposed interaction analysis approaches are highlighted via several examples.     

An approach towards the design of intelligent man-machine interfaces used in process control

This paper is related to improvements carried out n the field of human-machine communication in complex industrial processes, using the concept of the ‘intelligent’ interface. Following a review of literature on this subject, an ‘intelligent’ interface design based on ergonomical concepts is described. Finally, we present our approach to the design of an ‘intelligent’ interface. The Decisional Module of Imagery (D.M.I.) as it is called, is based on two models: a task model and a user model. The D.M.I.'s structure and its integration in an experimental platform are described in the last part of this paper.     

Systematic top-down economic plantwide control of the cumene process

Plantwide control system design for economic operation over a wide through range (design throughput to maximum throughput) encompassing multiple active constraint regions, is studied for the cumene process. A unique feature of the process is that it recycles the heavy side-product to extinction. A novel top-down control system synthesis approach, where the control objectives for maximum throughput operation are first obtained using steady state optimization followed by control loop pairings with highest priority to economic objectives, is applied. The control structure thus obtained is unconventional with tight active constraint control requiring ‘long’ level loops that maintain the reflux drum and bottom sump levels of a column using the two process fresh feeds. This structure for maximum throughput operation is adapted for economic operation at lower throughputs. Rigorous dynamic simulations show that the structure provides acceptable process regulation for large disturbances despite the long level loops over the entire throughput range. More importantly, no back-off from the active hard equipment capacity constraints also ensure that the loss in throughput from the maximum achievable is negligible. This work is amongst the first reports illustrating the application of the top-down plantwide control system design approach for superior economic performance with robust process stabilization.     

一种经济型数控系统的设计

本文介绍了一种基于NC和PLC控制的薄板卷筒点焊成型机系统,详细阐述了硬件和软件的设计。