Operating characteristics of X-bar charts with asymmetric control limits

When the assumptions behind the Shewhart chart are not met, policies other than the traditional 3-sigma limits may enable speedier and more economical detection of process change. If a process has unequal probabilities of downward and upward shifts, downward shifts of differing magnitude from upward shifts, and/or standard deviations after downward shifts different from those after upward shifts, then increases in the in-control average run length and decreases in the out-of-control average run length are simultaneously achievable with control limits placed at unequal distances from the process mean. The magnitude of these improvements is investigated for several types of process. The results are then extended to median charts for processes with output that is not normally distributed.     

Optimisation of a set of or principal components control charts using genetic algorithms

When a multivariate process is to be monitored, there are the options of employing a set of univariate control charts or a single multivariate chart. This paper shows how to effectively design a multivariate control scheme consisting of two or three X charts, using genetic algorithms to optimise the charts parameters. The procedure is implemented using software tools, which we designed. A complete performance comparison of the scheme with the Hotelling's T ² control chart can be made in order to help the user in choosing the most adequate option for the process under consideration. Also, if the user prefers to employ charts based on principal components rather than on the original variables, the software can be used in the same way to optimise a set of two or three control charts based on these components, and to compare their performance with the performance of the T ² chart on the principal components.     

X-bar charts or pre-control: an economic evaluation using alternative cost models

The on-line monitoring techniques of pre-control and X-bar control charts are compared, using two cost models that differ in the treatment of process variation cost. The first cost model assumes that process variation results in increased costs only when out-of-tolerance parts are made, while the second cost model uses Taguchi's loss function to quantify the cost of process variation. An example shows that the least-cost alternative depends on the cost model used. The sensitivity of the two techniques to changes in a number of process parameters is analysed for the loss function-based model. The results indicate that the most important consideration in choosing the process monitoring procedure is the assumption regarding the cost of process variation.     

Economic design of X-bar control charts for use in monitoring continuous flow processes

This paper develops the economic design of an A'-bar chart for monitoring continuous flow processes such as those encountered in refining, chemical processing and mining. The economic model permits one to optimally select the subgroup size, the sampling interval, and the control limit width based upon an economic criterion. This economic model is then applied to a realistic set of costs from the chemical industry. A sensitivity analysis is performed to illustrate the effects of incorrectly estimating the cost components of the model.     

Design of exponential control charts using a sequential sampling scheme

Control charts for monitoring the time between events can be applied in various areas. In this study, we focus on the exponential control chart and consider the phase II problem (when process parameters are known) as well as the phase I problem (when process parameters are unknown). An exponential chart designed with the conventional approach has the disadvantage that the Average Run Length (ARL) value may increase when the process deviates from the nominal state. An ARL-unbiased design approach is therefore proposed for both phase II and phase I exponential charts. A sequential sampling scheme is adopted for the phase I exponential chart. The proposed ARL-unbiased design approach has several advantages over the conventional one, as it provides a self-starting feature and can significantly improve the ARL performance. Specific guidelines are suggested regarding the time to stop updating the estimates of parameters and control limits based on the actual false alarm rate. The phase I exponential chart can be calibrated to a constant in-control ARL value for each successive event accumulated to date. Simulated and real data examples are given to demonstrate the use and efficiency of the proposed design approach.     

Generating experimental designs involving control and noise variables using genetic algorithms

Efficient estimation of response variables in a process is an important problem that requires experimental designs appropriated for each specific situation. When we have a system involving control and noise variables, we are often interested in the simultaneous optimization of the prediction variance of the mean (PVM) and the prediction variance of the slope (PVS). The goal of this simultaneous optimization is to construct designs that will result in the efficient estimation of important parameters. We construct new computer‐generated designs using a desirability function by transforming PVM and PVS into one desirability value that can be optimized using a genetic algorithm. Fraction of design space (FDS) plots are used to evaluate the new designs and six cases are discussed to illustrate the procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimal shape control of functionally graded smart plates using genetic algorithms

This paper deals with optimal shape control of functionally graded smart plate containing patches of piezoelectric sensors and actuators. The genetic algorithm (GA) is designed to search for optimal actuator voltage and displacement control gains for the shape control of the functionally graded material (FGM) plates. The work extends the earlier finite element formulations of the two leading authors, so that it can be readily treated using genetic algorithms. Numerical results have been obtained to study the effect of the shape control of the FGM plates under a temperature gradient by optimising (i) the voltage distribution for the open loop control, and (ii) the displacement control gain values for the closed loop feedback control. The effect of the constituent volume fractions of zirconia, through varying the volume fraction exponent n, on the optimal voltages and gain values has also been examined.     

Design issues for adaptive control charts

Adaptive control charts allow the components of the quality‐monitoring scheme to vary in order to obtain improved performance over non‐adaptive control charts. Research has centered on components such as the sample size, time between samples, warning limits, and control limits and has recommended a variety of schemes, many of which are optimal in some sense. In practice, there are many other adaptive schemes that are near optimal, which will still yield considerable improvement over non‐adaptive control charts. In addition, the impact of parameter estimation on adaptive control chart performance must be taken into consideration. Based on the simulation results shown here, adaptive control charts should only be used for mature processes, where a sufficient amount of Phase I data have been obtained to ensure that the estimated control limits are accurate. When evaluating control chart performance, we consider initial state performance measures for simplicity and note that the conclusions obtained here apply to steady‐state performance measures. The evaluation of performance measures is easily handled by the Markov chain approach detailed in the Appendix. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust economic-statistical design of X-bar control chart

Control charts are developed to monitor the service and production processes. The fact that many processes have uncertain parameters is a barrier to obtain the best design of the control charts. In this paper, economic statistical design (ESD) of the X-bar control chart utilising robust optimisation approach that considers interval estimates of uncertain parameters is investigated. A heuristic algorithm is developed to obtain the robust scheme of the control chart. Robust design for an industrial problem is compared with traditional ESD, and heuristic design. Numerical analyses and simulation study show that the proposed X-bar control chart offers a better approach and more reliable solutions for practitioners.     

Design optimization of composites using genetic algorithms and failure mechanism based failure criterion

In this paper, minimum weight design of composite laminates is presented using the failure mechanism based (FMB), maximum stress and Tsai–Wu failure criteria. The objective is to demonstrate the effectiveness of the newly proposed FMB failure criterion (FMBFC) in composite design. The FMBFC considers different failure mechanisms such as fiber breaks, matrix cracks, fiber compressive failure, and matrix crushing which are relevant for different loading conditions. A genetic algorithm is used for the optimization study. The Tsai–Wu failure criterion over predicts the weight of the laminate by up to 86% in the third quadrant of the failure envelope compared to FMB and maximum stress failure criteria, when the laminate is subjected to compressive–compressive loading. It is found that the FMB and maximum stress failure criteria give comparable weight estimates. The FMBFC can be considered for use in the strength design of composite structures.     

Transfer batch scheduling using genetic algorithms

This paper examines scheduling in a manufacturing system with transfer batches. Transfer batches are considered as different batches although they stem from the same job. Genetic algorithms determine the size of the transfer batches for each job and the final schedule with a makespan criterion. A novelty of the genetic algorithm developed is twin chromosome encoding, the first chromosome representing the relative size (participation ratio) of each transfer batch with respect to the whole batch; and the second chromosome applying in effect a dynamic heuristic dispatching rule representation for resolving operation antagonism. New crossover and mutation operators were employed for the first chromosome and standard operators for the second. The genetic algorithms were coded in C++ for better control. A 20 job?×?eight machine shop was used as a test case. Results favour genetic algorithms over heuristic procedures, but the latter close the gap with an increase in the number of transfer batches. Design of Experiments was used to focus on the most promising genetic algorithm parameter value combinations.     

Scheduling TV commercials using genetic algorithms

In this paper, the problem of scheduling commercial messages during the peak of viewing time of a TV channel is formulated as a combinatorial auction-based mathematical programming model. Through this model, a profitable and efficient mechanism for allocating the advertising time to advertisers is developed by which the revenue of TV channels is maximised while the effectiveness of advertising is increased. We developed a steady-state genetic algorithm to find an optimal or a near optimal solution for the proposed problem. A computational experiment was conducted for evaluating the efficiency of the proposed algorithm. A set of test problems with different sizes were generated, using the pseudo-random generation mechanism, and solved by the proposed genetic algorithm. The optimal solutions of the linear programming relaxation of these test problems were also obtained and were used for evaluating the quality of solutions obtained by the developed algorithm. The results of this computational experiment revealed the robustness of the solutions and acceptably low computational time for obtaining these solutions. The computational results also demonstrated that the proposed genetic algorithm had an appropriate ability to preserve population diversity during the search and was capable of obtaining high-quality solutions for the proposed problem.     

Monitoring automatically controlled processes using statistical control charts

Statistical process control (SPC) and automatic process control (APC) are integrated under a hierarchical scheme. The integrated scheme is called statistical and automatic process control (SAPC). SAPC is based on the comparison of the outputs of the actual system and parallel systems that model the actual system under assumed deterministic disturbances. While APC provides a continuous controller intervention, SPC acts as a supervisory controller to detect process disturbances. A cross-correlation method is used to estimate the time when the disturbance starts to affect the system as well as the type of the disturbance. After the magnitude of the disturbance is determined, a counter action is applied on the system to minimize its effect.     

Facility layout optimization using simulation and genetic algorithms

Traditionally, the objective of a facility layout problem has been to minimize the material handling cost of the manufacturing system. While it is important to reduce the amount of material handling, the traditional methods do not address the actual time at which the material is transported. In today's short cycle time production environments, the timing of material movement may have a bigger impact on the productivity of the system than its cost. In this paper, a facility layout optimization technique is presented that takes into consideration the dynamic characteristics and operational constraints of the system as a whole, and is able to solve the facility layout design problem based on a system's performance measures, such as the cycle time and productivity. Each layout solution is presented in the form of a string that is suitable for analysis by a genetic algorithm technique. These solutions are then translated into simulation models by a specially designed automated simulation model generator. Genetic algorithms are used to optimize the layout for manufacturing effectiveness while simulation serves as a system performance evaluation tool. Combined with a statistical comparison technique to reduce the simulation burden, the test results demonstrate that the proposed approach overcomes the limitations of traditional layout optimization methods and is capable of finding optimal or near optimal solutions.     

Calculating petal tools by using genetic algorithms

To pass from a spherical surface to a conic one, it is possible to use a petal tool or a small solid tool that is placed at different time intervals at several radial zones of the glass. Genetic algorithms are applied to calculate the angular sizes of the incomplete annular tools that make up the petal tools. We also present the desired wear results carried out with the petal tool that was designed on the basis of the dwell times of complete annular tools. These dwell times are calculated by using base functions that are generated with annular tools and by applying the genetic algorithms.     

Engineering design optimization using species-conserving genetic algorithms

The species conservation technique described here, in which the population of a genetic algorithm is divided into several groups according to their similarity, is inspired by ecology. Each group with similar characteristics is called a species and is centred on a dominating individual, called the species seed. A genetic algorithm based on this species conservation technique, called the species-conserving genetic algorithm (SCGA), was established and has been proved to be effective in finding multiple solutions of multimodal optimization problems. In this article, the SCGA is used to solve engineering design optimization problems. Different distance measures (measures of similarity) are investigated to analyse the performance of the SCGA. It is shown that the Euclidean distance is not the only possible basis for defining a species and sometimes may not make sense in engineering applications. Two structural design problems are used to demonstrate how the choice of a meaningful measure of similarity will help the exploration for significant designs.     

Control point policy optimization using genetic algorithms

This paper describes the application of an integrated Genetic Algorithm (GA)/Discrete Event Simulation model for selecting optimum values for Critical Point Policy (CPP) hedging time and buffer size parameters. The CPP is shown to perform well, when compared with the Critical Ratio priority rule, in terms of improving service levels, particularly when subject to conditions where buffer sizes and Takt times are required to be small. The technique developed involves buffer sizes being chosen by a GA according to a constraint on the total storage space available within the system. A method is described for reducing the number of variables that the GA needs to deal with, hence, improving the efficiency of the GA optimization process. The development and application work reported also provides further understanding into how and when the CPP should be applied.     

Synthesis of optical multilayer systems using genetic algorithms

Stochastic algorithms are a promising method for the synthesis of optical multilayer systems. Amethod based on the use of genetic algorithms is described and applied to the design of three very different optical filters. Solutions found by genetic algorithms are refined, and results are compared with those of previous publications.     

Design and implementation of CUSUM exceedance control charts for unknown location

Nonparametric control charts provide a robust alternative in practice when the form of the underlying distribution is unknown. Nonparametric CUSUM (NPCUSUM) charts blend the advantages of a CUSUM with that of a nonparametric chart in detecting small to moderate shifts. In this paper, we examine efficient design and implementation of Phase II NPCUSUM charts based on exceedance (EX) statistics, called the NPCUSUM-EX chart. We investigate the choice of the order statistic from the reference (Phase I) sample that defines the exceedance statistic. We see that choices other than the median, such as the 75th percentile, can yield improved performance of the chart in certain situations. Furthermore, observing certain shortcomings of the average run-length, we use the median run-length as the performance metric. The NPCUSUM-EX chart is compared with the NPCUSUM-Rank chart based on the popular Wilcoxon rank-sum statistic. We also study the choice of the reference value, k, of the CUSUM charts. An illustration with real data is provided.     

Design of exponential control charts based on average time to signal using a sequential sampling scheme

Exponential charts based on time-between-events (TBE) data are widely investigated and applied in various fields. The average time to signal (ATS) is used instead of the average run length to evaluate the performance of TBE charts, since the ATS involves both the number and the time of samples inspected until a signal occurs. An ATS-unbiased exponential control chart is proposed when the in-control parameter is known. Considering the need in practice to start monitoring a production process as soon as possible, a sequential sampling scheme is adopted and the in-control parameter is estimated by an unbiased and consistent estimator. Some specific guidelines to stop updating control limits are obtained from the relationship between the phase I sample size and the actual false alarm rate. Finally, two real examples are given to illustrate the implementation and efficiency of the proposed method.