Multi-criteria design of an X̄ control chart

Control chart designs are widely studied because control charts are not only costly used but also play an important role in improving firms' quality and productivity. Design of control charts refers to the selection of parameters, including sample size, control-limit width, and sampling frequency. In this paper, a possible combination of design parameters is considered as a decision-making unit; it is characterized by three attributes: hourly expected cost, average run length of process being controlled, and detection power of the chart designed with the selected parameters. Accordingly, optimal design of control charts can be formulated as a multiple criteria decision-making (MCDM) problem. To solve the MCDM problem, a solution procedure on the basis of data envelopment analysis is proposed. Finally, an industrial application is presented to illustrate the solution procedure. Also, adjustment to control chart design parameters is suggested when there are process improvements or process deteriorations.     

Economic design of autoregressive moving average control chart using genetic algorithms

When designing control charts, it is usually assumed that the observations from the process at different time points are independent. However, this assumption may not be true for some production processes, e.g., the continuous chemical processes. The presence of autocorrelation in the process data can result in significant effect on the statistical performance of control charts. Jiang, Tsui, and Woodall (2000) developed a control chart, called the autoregressive moving average (ARMA) control chart, which has been shown suitable for monitoring a series of autocorrelated data. In the present paper, we develop the economic design of ARMA control chart to determine the optimal values of the test and chart parameters of the chart such that the expected total cost per hour is minimized. An illustrative example is provided and the genetic algorithm is applied to obtain the optimal solution of the economic design. A sensitivity analysis shows that the expected total cost associated with the control chart operation is positively affected by the occurrence frequency of the assignable cause, the time required to discover the assignable cause or to correct the process, and the quality cost per hour while producing in control or out of control, and is negatively influenced by the shift magnitude in process mean.     

On the performance of the conditional decision procedure in geometric charts

To improve the performance of control charts the conditional decision procedure (CDP) incorporates a number of previous observations into the chart’s decision rule. It is expected that charts with this runs rule are more sensitive to shifts in the process parameter. To signal an out-of-control condition more quickly some charts use a headstart feature. They are referred as charts with fast initial response (FIR). The CDP chart can also be used with FIR. In this article we analyze and compare the performance of geometric CDP charts with and with no FIR. To do it we model the CDP charts with a Markov chain and find closed-form ARL expressions. We find the conditional decision procedure useful when the fraction p of nonconforming units deteriorates. However the CDP chart is not very effective for signaling decreases in p.     

On efficient use of auxiliary information for control charting in SPC

In Statistical Process Control (SPC), monitoring of the process dispersion has a major impact on the performance of processes like manufacturing, management and services. Control charts act as the most important SPC tool, used to differentiate between common and special cause variations in the process. The use of auxiliary information can enhance the detection ability of control charts and hence an efficient monitoring of process parameter(s) can be done. This study deals with the Shewhart type variability control charts based on auxiliary characteristics for the non-cascading processes, assuming stability of auxiliary parameters. The control chart structures of these variability charts are provided and their performance evaluations are carried out in terms of average run length (ARL), relative average run length (RARL) and extra quadratic loss (EQL) under the normal and t distributed process environments. The comparisons have been made among different variability charts and superiorities are established based on their detection abilities for different amounts of shifts in process dispersion. An illustrative example is also provided in support of the theory, and finally the study ends with concluding remarks and suggestions for future research.     

Enhancing the performance of CUSUM scale chart

Control charts act as the most important statistical process monitoring tool, widely used for the purpose of identifying unusual variations in process parameters. Researchers have implemented different rules to increase the sensitivity of Shewhart, CUSUM and EWMA control charts for the detection of small shifts in process location. However, for the monitoring of process scale, the use of such rules has been limited to Shewhart charts. This study proposes the implementation of sensitizing rules in CUSUM scale charts to enhance their ability to detect smaller changes in process variability. The performance of the proposed schemes is evaluated and compared with the simple scale CUSUM scheme, the EWMS chart, the M-EWMS chart and the COMB chart, in terms of run length characteristics such as average run length (ARL) and standard deviation of the run length distribution (SDRL). Control chart coefficients to set the ARL at the desired level are also provided. Two numerical examples are given to illustrate the application of the proposed schemes on practical data sets.     

Economic design of time-between-events control chart system

This article presents the economic design of the control chart system consisting of several individual control charts based on time-between-events (TBE) data for monitoring multistage manufacturing processes. The design algorithm considers all the TBE charts within a system in an integrative and optimal manner. Numerical studies show that the proposed design algorithm improves the performance characteristics (in terms of profit) considerably. The proposed control chart system is easy to understand and operate, and thus the floor operators can utilize and understand it as easily as for the traditional system.     

An economically designed Sequential Probability Ratio Test control chart for short-run production

This paper proposes an economic model for the design of an SPRT (Sequential Probability Ratio Test) chart for monitoring the process mean in short-run production. The model expresses the short-run cost per unit of operating the SPRT chart as a function of the cost parameters associated with the operation. A simple algorithm capable of optimizing the charting parameters is also proposed. The model can be used to quantify cost reductions achievable by substituting a traditional control policy by SPRT control. Numerical examples illustrate the effectiveness of the proposed procedure. It is shown that the resulting cost reduction can range from modest to substantial as the out-of-control probability of the process increases.     

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.     

New format for flowcharts

This paper proposes a new chart format as an alternative for the flow diagram variety of flowchart. This new chart format is more informative, more compact and easier to use and draw than the ANS format, and facilitates modularization in design and programming. The new chart format supports restrictions on control transfers, and clearly identifies the control structures used in structured programming. The new chart format also permits showing multiple levels of detail unambiguously in a single flowchart, and enables HIPO charts and system charts to be usefully augmented.     

Comparative study of the performance of the CuSum and EWMA control charts

This work presents a comparative study of the performance of the cumulative sum (CuSum), as well as the exponentially weighted moving average (EWMA) control charts. The objective of this research is to verify when CuSum and EWMA control charts do the best control region, in order to detect small changes in the process average. Starting from the data of a productive process, several series were simulated. CuSum and EWMA control charts were used to determine the average run length (ARL) to detect a condition out of control. ARL found by each chart which was then, compared. It was observed that the CuSum control chart practically did not sign points out of control for the levels of variation between ±1.0 standard deviation. For these variation levels the EWMA control chart was more efficient than CuSum. Among the parameters EWMA control chart the ones with constant λ=0.10 and 0.05, with the respective control limits L=2.814 and 2.625, were the ones that detected larger number of altered positions.     

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.     

Optimal linear combination of Poisson variables for multivariate statistical process control

In this paper we analyze the monitoring of p Poisson quality characteristics simultaneously, developing a new multivariate control chart based on the linear combination of the Poisson variables, the LCP control chart. The optimization of the coefficients of this linear combination (and control limit) for minimizing the out-of-control ARL is constrained by the desired in-control ARL. In order to facilitate the use of this new control chart the optimization is carried out employing user-friendly Windows© software, which also makes a comparison of performance between this chart and other schemes based on monitoring a set of Poisson variables; namely a control chart on the sum of the variables (MP chart), a control chart on their maximum (MX chart) and an optimized set of univariate Poisson charts (Multiple scheme). The LCP control chart shows very good performance. First, the desired in-control ARL (ARL₀) is perfectly matched because the linear combination of Poisson variables is not constrained to integer values, which is an advantage over the rest of charts, which cannot in general match the required ARL₀ value. Second, in the vast majority of cases this scheme signals process shifts faster than the rest of the charts.     

Applying a coupled expert system to quality control charts

Quality control charts are a common tool used for control of a manufacturing process. Expert systems can serve as a valuable tool to automate the different phases in the use of quality control charts. The authors have developed a coupled expert system to select a proper control chart, optimize the design of the selected control chart, analyze the chart to identify an out-of-control process and suggest the reason(s) for an out-of-control process. The intent of this paper is to discuss the main features of this coupled expert system.

An expert system shell called PCPLUS helps a user select the most appropriate control chart and identify the reason(s) for a process to be out-of-control. FORTRAN was used to implement the modules for design, plotting, and analysis of the selected control chart.     

Design and optimization of EWMA control charts for in-control,indifference, and out-of-control regions

The design of quality control charts is normally carried out considering a process shift size that is considered important to be detected. The EWMA control chart is one of the best available options to use when good performance is needed to detect small process shifts. This paper presents a method for design of EWMA charts for control processes, in which the detection of small shifts is not necessary, and at the same time is effective in detecting important shifts. In such cases the EWMA control chart can also be designed successfully to deal with these requirements. A Markov chain approach is also applied to determine the ARL of the modified EWMA control chart. The implementation and interpretations are provided and numerical examples are used to illustrate the application procedure. We also investigate some basic properties of the proposed scheme. Genetic algorithms have been used to carry out this design.     

Integrating economics into quality control charts

When control of a manufacturing process is needed, the common tool is Statistical Quality control (SQC). In the past, however, economic factors were the results after employing the SQC charts. Design of control charts refers to the specification of the sample size, the sampling frequency and the control limits for the chart. The authors have tested a model that uses economics as an integral part for the design of an X-bar control chart.

Douglas C. Montgomery developed a computer program for the optimal economic design of an X-bar control chart. The program is based on the cost model proposed by A.J. Duncan.

Montgomery's program was modified to select the optimal design parameters from a table of parameter values. Subroutines were developed to enable the user to enter the number of subgroups and the data points for each subgroup. The economically designed control chart is plotted using standard Graphical Kernel System (GKS) subroutines.     

Complexity reduction of a design problem in QFD using decomposition

Quality function deployment (QFD) is a cross-functional planning tool that ensures that the voice of the customer is systematically deployed throughout the product planning and design stages. Although many success applications of QFD have been reported worldwide, designers face impediments to the adoption of QFD as a product design aid. One of the difficulties associated with the application of QFD is the large size of a house of quality (HOQ) chart, which is the principal tool for QFD. It is well-known that it becomes more difficult and inefficient to manage a design project as the problem size becomes larger. This paper proposes to develop formal approaches to reducing the size of an HOQ chart using the concept of design decomposition. The decomposition approaches developed attempt to partition an HOQ chart into several smaller sub-HOQ charts which can be solved efficiently and independently. By decomposing a large HOQ chart into smaller sub-HOQ charts, the design team not only can enhance the concurrency of the design activities, but also reduce the amount of the time, effort, and cognitive burden required for the analysis. This would help to obviate the objections to the adoption of QFD as a product design aid and improve the efficiency of its use in practice.     

Measuring the performance improvement of a double generally weighted moving average control chart

This study extends the sum of squares generally weighted moving average (SS-GWMA) control chart by using the double generally weighted moving average (DGWMA) technique. The proposed expanded chart is called the sum of squares double generally weighted moving average (SS-DGWMA) control chart. Simulations are performed to evaluate the average run length (ARL) and standard deviation of run length (SDRL) of the SS-DGWMA, SS-DEWMA, and SS-GWMA charts. An extensive comparison shows that the optimal SS-DGWMA chart is superior to the optimal SS-GWMA and SS-DEWMA charts in all studied scenarios. The SS-DGWMA chart is also easy to implement and to interpret the abnormal signals.     

A neural network-based procedure for the monitoring of exponential mean

Control charts are widely used for both manufacturing and service industries. Cumulative sum (CUSUM) charts are known to be very sensitive in detecting small shifts in the mean. In this paper, we propose a neural network as an alternative approach to CUSUM charts when monitoring exponential mean. The performance of neural network was evaluated by estimating the average run lengths (ARLs) using simulation. The results obtained with simulated data suggest that control scheme based on neural network is significantly more sensitive to process shifts than CUSUM charts. This research also examines the feasibility of using CUSUM chart and neural network together in detecting process mean shifts. The results indicate that using the two methods in combination is more effective than using the methods separately.