A variable parameter Shewhart control scheme for joint monitoring of process mean and variance

This paper presents a new Statistical Process Control model for the economic optimization of a variable-parameter control chart monitoring a process operation where two assignable causes may occur, one affecting the mean and the other the variance of the process. Therefore, it is possible for the process to operate in statistical control, when none of the two assignable causes has occurred, or under the effect of one or both the assignable causes. By making the assumption that the occurrence rate of each assignable cause is exponential, a Markov chain approach is utilized to determine the probabilities that the process operates at any of the above possible states. The model uses an economic (or an economic/statistical) optimization criterion for the time to the next sampling instance, the size of the next sample, as well as the control limits of the inspection. That is, all design parameters of the control scheme are selected so as to minimize the total expected quality-related costs. The superiority of the proposed model is estimated by comparing its expected quality control cost vs. the outcome of the Fp (Fixed-parameter) Shewhart control chart, the Variable Sample Size (VSS) control chart, the Variable Sampling Interval (VSI) and the Variable Sample Size and Sampling Interval (VSSI) control chart, for a benchmark of examples. The numerical investigation indicates that the economic improvement of the proposed model may be significant.     

An adaptive Bayesian scheme for joint monitoring of process mean and variance

This paper presents a new model for the economic optimization of a process operation where two assignable causes may occur, one affecting the mean and the other the variance. The process may thus operate in statistical control, under the effect of either one of the assignable causes or under the effect of both assignable causes. The model employed uses the Bayes theorem to determine the probabilities of operating under the effect of each assignable cause. Based on these probabilities, and following an economic optimization criterion, decisions are made on the necessary actions (stop the process for investigation or not) as well as on the time of the next sampling instance and the size of the next sample. The superiority of the proposed model is estimated by comparing its economic outcome against the outcome of simpler approaches such as Fp (Fixed-parameter) and adaptive Vp (Variable-parameter) Shewhart charts for a number of cases. The numerical investigation indicates that the economic improvement of the new model may be significant.     

A generalized Conforming Run Length control chart for monitoring the mean of a variable

The attribute Conforming Run Length (CRL) control chart has attracted increasing research interests in Statistical Process Control (SPC). It decides the process status based on the interval or distance between two nonconforming units. This article proposes a Generalized CRL chart (namely GCRL chart) for monitoring the mean of a measurable quality characteristic x under 100% inspection. To run a GCRL chart, each unit will be classified as a passing or nonpassing unit depending on whether the sample value of x falls within or beyond a pair of lower and upper inspection limits LIL and UIL. When a nonpassing unit is detected, the GCRL chart checks the distance between the current and last nonpassing units in order to determine the process status (in control or out of control). The inspection limits LIL and UIL are determined by an optimization design. The GCRL chart not only solves a dead-corner problem suffered by the conventional CRL chart, but also considerably outperforms the latter for detecting mean shifts. The most interesting finding is that the attribute GCRL chart excels the variable X chart to a significant degree in SPC for variables. It suggests that the simple attribute chart may replace the variable chart in some SPC applications. The design of the GCRL chart has to be carried out by a computer program, but the design can be completed almost in no time in a personal computer.     

Extended maximum generally weighted moving average control chart for monitoring process mean and variability

In this paper, we propose an extended control chart, called the maximum generally weighted moving average (MaxGWMA) control chart, to simultaneously detect both increases and decreases in the mean and/or variability of a process. Simulations are performed to evaluate the average run length, standard deviation of the run length, and diagnostic abilities of the MaxGWMA and maximum exponentially weighted moving average (MaxEWMA) charts. An extensive comparison reveals that the MaxGWMA control chart is more sensitive than the MaxEWMA control chart.     

A multivariate control chart for simultaneously monitoring process mean and variability

Recently, monitoring the process mean and variability simultaneously for multivariate processes by using a single control chart has drawn some attention. However, due to the complexity of multivariate distributions, existing methods in univariate processes cannot be readily extended to multivariate processes. In this paper, we propose a new single control chart which integrates the exponentially weighted moving average (EWMA) procedure with the generalized likelihood ratio (GLR) test for jointly monitoring both the multivariate process mean and variability. Due to the powerful properties of the GLR test and the EWMA procedure, the new chart provides quite robust and satisfactory performance in various cases, including detection of the decrease in variability and individual observation at the sampling point, which are very important cases in many practical applications but may not be well handled by existing approaches in the literature. The application of our proposed method is illustrated by a real data example in ambulatory monitoring.     

一种离散时间系统变结构控制的新方法

研究离散时间系统变结构控制问题,提出一种新的离散变结构趋近律.利用该趋近律设计的离散变结构控制器,不仅能大幅度削弱抖振,使系统运动最终趋干原点不存在稳态振荡,而且可使系统的准滑动模态保持步步穿越切换面的基本属性,有效地改善了控制品质,提高了系统的鲁棒性.仿真结果验证了该方法的有效性与合理性.     

On SISO and MIMO variable structure control of non linear distributed parameter systems: application to fixed bed reactors

This paper deals with the design of variable structure control of distributed parameter systems. The control problem is discussed in relation to a model consisting of a set of non-linear, time varying partial differential equations of hyperbolic type. A formulation of a Single Input–Single Output (SISO) variable structure controller based on the distributed parameter model (late lumping control) is given. An extension to the Multiple Input–Multiple Output (MIMO) case is derived when the control variables are coupled and located on boundary conditions. A theoretical proof of DPS convergence in sliding mode is given. A fixed bed bioreactor in which drinkable water is treated, was used as a simulated example to prove the effectiveness of the control design. The bioreactor must control the harmful component concentrations in such a way that the quality of water fulfils international standards.     

A two-layer architecture for economically optimal process control and operation

A two-layer architecture for dynamic real-time optimization (or nonlinear modelpredictive control (NMPC) with an economic objective) is presented, where the solution of the dynamic optimization problem is computed on two time-scales. On the upper layer, a rigorous optimization problem is solved with an economic objective function at a slow time-scale, which captures slow trends in process uncertainties. On the lower layer, a fast neighboring-extremal controller is tracking the trajectory in order to deal with fast disturbances acting on the process. Compared to a single-layer architecture, the two-layer architecture is able to address control systems with complex models leading to high computational load, since the rigorous optimization problem can be solved at a slower rate than the process sampling time. Furthermore, solving a new rigorous optimization problem is not necessary at each sampling time if the process has rather slow dynamics compared to the disturbance dynamics. The two-layer control strategy is illustrated with a simulated case study of an industrial polymerization process.     

Evaluation of neural network variable influence measures for process control

Decision-making frequently involves identifying how to change input parameters in a given process in order to effect a directed change in the process output. Artificial neural networks have been used extensively to model business and manufacturing processes and there are several existing neural network-based influence measures that allow a decision-maker to assess the relative impact of each variable on process performance. The purpose of this paper is to review those neural network-based measures of variable influence, and to identify the combination of those measures that results in a comprehensive approach to characterizing variable influence within a trained neural network model. We then demonstrate how this comprehensive approach can be used as a tool to guide decision makers in dynamic process control.     

OWave control chart for monitoring the process mean

In this paper a control chart for monitoring the process mean, called OWave (Orthogonal Wavelets), is proposed. The statistic that is plotted in the proposed control chart is based on weighted wavelets coefficients, which are provided through the Discrete Wavelets Transform using Daubechies $\mathit{db}2$ wavelets family. The statistical behavior of the wavelets coefficients when the mean shifts are occurring is presented, and the distribution of wavelets coefficients in the case of normality and independence assumptions is provided. The on-line algorithm of implementing the proposed method is also provided. The detection performance is based on simulation studies, and the comparison result shows that OWave control chart performs slightly better than Fixed Sample Size and Sampling Intervals control charts ($\overline{X}$, EWMA, CUSUM) in terms of Average Run Length. In addition, illustrative examples of the new control chart are presented, and an application to Tennessee Eastman Process is also proposed.     

Self-oriented control charts for efficient monitoring of mean vectors

This work presents a procedure for monitoring the centre of multivariate processes by optimising the noncentrality parameter with respect to the maximum separability between the in- and out-of-control states. Similarly to the Principal Component Analysis, this procedure is a linear transformation but using a different criterion which maximises the trace of two scatter matrices. The proposed linear statistic is self-oriented in the sense that no prior information is given, then it is monitored by two types of control charts aiming to identify small and intermediate shifts. As the control charts performances depend only on the noncentrality parameter, comparisons are made with traditional quadratic approaches, such as the Multivariate Cumulative Sum (MCUSUM), the Multivariate Exponentially Weighted Moving Average (MEWMA) and Hotelling’s T² control chart. The results show that the proposed statistic is a solution for the problem of finding directions to be monitored without the need of selecting eigenvectors, maximising efficiency with respect to the average run length.     

An exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles

This paper proposes an exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles. A computer program in Fortran is available to assist in the design of the control chart and the algorithm of the Fortran program is also given. Some useful guidelines are also provided to aid users in choosing parameters for a particular application. Simulation results on the detection performance of the proposed control chart, compared with some other competing methods show that it provides quite robust and satisfactory performance in various cases, including intercept shifts, slope shifts and standard deviation shifts. A real data example from an optical imaging system is employed to illustrate the implementation and the use of the proposed control scheme.     

The mean squared loss control problem for a partially observed Markov chain

In this article, we study the optimal control of a partially observed Markov chain for which a mean squared cost functional is minimised. Both the terminal cost and the running cost are considered. Minimum principles are established. In both cases, if the optimal control is Markov feedback, more explicit forms for the stochastic integrands and adjoint processes are obtained.     

Variable window adaptive Kernel Principal Component Analysis for nonlinear nonstationary process monitoring

On-line control of nonlinear nonstationary processes using multivariate statistical methods has recently prompt a lot of interest due to its industrial practical importance. Indeed basic process control methods do not allow monitoring of such processes. For this purpose this study proposes a variable window real-time monitoring system based on a fast block adaptive Kernel Principal Component Analysis scheme. While previous adaptive KPCA models allow only handling of one observation at a time, in this study we propose a way to fast update or downdate the KPCA model when a block of data is provided and not only one observation. Using a variable window size procedure to determine the model size and adaptive chart parameters, this model is applied to monitor two simulated benchmark processes. A comparison of performances of the adopted control strategy with various Principal Component Analysis (PCA) control models shows that the derived strategy is robust and yields better detection abilities of disturbances.     

A feedback-based implementation scheme for batch process optimization

The terminal-cost optimization of a control–affine nonlinear system leads to a discontinuous solution that can be characterized in a piecewise manner. To implement such an optimal trajectory despite disturbances and parametric uncertainty, a cascade optimization scheme is proposed in this paper, where optimal reference signals are tracked. Optimality is achieved by the appropriate definition of reference signals (input bounds, state constraints, or switching functions) to track in various sub-intervals. Furthermore, conservatism is introduced into the optimization problem to ensure satisfaction of path constraints in the presence of uncertainty. Finally, the proposed cascade optimization scheme is illustrated on a simulation of a fed-batch penicillin fermentation plant.     

A variable structure convex programming based control approach for a class of uncertain linear systems

A variable structure convex programming based control for a class of linear uncertain systems with accessible state is presented in this note. A convex programming problem is solved, on-line, by reformulating the problem in terms of a piecewise smooth penalty function, and relying on a suitable analog variable structure system implementing the gradient procedure. In this way, the controlled system reference movement, optimal with respect to a pre-specified scalar convex cost function and a set of suitable equality and inequality constraints, is generated. An inner control loop aimed at the finite time exact tracking of the reference movement is also designed. As a result, the controlled system trajectory starting in the feasible region there remains, and the optimal movement in the feasible region is proved to be an asymptotically stable equilibrium point of the controlled system.     

A discrete-time parameter estimation based adaptive actuator failure compensation control scheme

This article studies discrete-time adaptive failure compensation control of systems with uncertain actuator failures, using an indirect adaptive control method. A discrete-time model of a continuous-time linear system with actuator failures is derived and its key features are clarified. A new discrete-time adaptive actuator failure compensation control scheme is developed, which consists of a total parametrisation of the system with parameter and failure uncertainties, a stable adaptive parameter estimation algorithm, and an on-line design procedure for feedback control. This work provides a new design of direct adaptive compensation of uncertain actuator failures, using an indirect adaptive control method. Such an adaptive design ensures desired closed-loop system stability and tracking properties despite uncertain actuator failures. Simulation results are presented to show the desired adaptive actuator failure compensation performance.     

Applying fuzzy approach to develop transient probability matrix for on-line variable quality monitoring

The characteristic of interest follows a normal distribution and changes of the distribution parameters are described by a k-state Markov chain. Items are produced independently and a single item is examined at every manufactured item similar to an on-line quality procedure to monitor variables of process. In this paper the fuzzy approach has been developed to obtain the transition matrix in vagueness environment. First calculated the mass function of each state and then the possibility of probability state transaction from each state to another state have been achieved. To validate the proposed approach the five learning set data was captured from real case to form the fuzzy transition matrix of 2-state Markov chain.