Adaptive Charts Research Articles

A comparison study on effectiveness and robustness of control charts for monitoring process mean and variance

AbstractThis article compares the effectiveness and robustness of nine typical control charts for monitoring both process mean and variance, including the most effective optimal and adaptive sequential probability ratio test (SPRT) charts. The nine charts are categorized into three types (the type, CUSUM type and SPRT type) and three versions (the basic version, optimal version and adaptive version). While the charting parameters of the basic charts are determined by common wisdoms, the parameters of the optimal and adaptive charts are designed optimally in order to minimize an index average extra quadratic loss for the best overall performance. Moreover, the probability distributions of the mean shift δµ and standard deviation shift δσ are studied explicitly as the influential factors in a factorial experiment. The main findings obtained in this study include: (1) From an overall viewpoint, the SPRT‐type chart is more effective than the CUSUM‐type chart and type chart by 15 and 73%, respectively; (2) in general, the adaptive chart outperforms the optimal chart and basic chart by 16 and 97%, respectively; (3) the optimal CUSUM chart is the most effective fixed sample size and sampling interval chart and the optimal SPRT chart is the best choice among the adaptive charts; and (4) the optimal sample sizes of both the charts and the CUSUM charts are always equal to one. Furthermore, this article provides several design tables which contain the optimal parameter values and performance indices of 54 charts under different specifications. Copyright © 2011 John Wiley & Sons, Ltd.

Optimal inspection policy for three-state systems monitored by control charts

This paper presents the formulations of the expected long-run cost per time unit for a system monitored by a static control chart and by an adaptive control chart respectively. The static chart has a fixed sampling interval and a fixed sample size. The adaptive chart has a fixed sample size but variable sampling intervals. The system is supposed to have three states, normal working state, failure delay time state, and failed state. Two levels of repair are used to maintain the system. A minor repair is used to restore the system if a detectable defect is confirmed by an inspection. A major repair will be performed if the system fails. The expected cost per time unit for maintaining such a system is obtained. The objective of such analysis is to find an optimal sampling policy for the inspection process. An artificially generated data example and a real data example are used to compare the expected cost per time unit for both the static and adaptive control charts.

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.

Adaptive charts with sampling at fixed times under non-normality

Recently developed adaptive charts have been shown to give substantially faster detection of most process shifts than the fixed parameters charts. The “sampling at fixed times” idea can be implemented in the adaptive control charts, and from the practical viewpoint, the adaptive charts with sampling at fixed times are considered to be more convenient to administer than the traditional adaptive charts. The usual assumption for designing the control chart is that the data or measurements are normally distributed. However, this assumption may not be tenable in some production processes. The Burr distribution has been used in the literature to represent various non-normal distributions. In the present paper, the Burr distribution is employed to evaluate the adaptive charts with sampling at fixed times for non-normal populations. Base on the study, it is shown that the variable sampling interval with fixed times (VSIFT) chart and variable sampling rate with fixed times (VSRFT) chart are very sensitive to non-normality; however, the variable parameters with fixed times (VPFT) chart is relatively robust against non-normality. Under consideration of false alarm rate and the ability to detect mean shifts, the VPFT chart is a more appropriate tool for non-normal populations.

Economic design of adaptive control charts for skewed data

Recent studies have demonstrated the variable parameters (VP, i.e., variable sample sizes, sampling intervals, and/or action limit coefficients) charts have better performance than standard Shewhart (SS) control chart by statistical and economic criteria. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be true for some processes. In the present paper, the economic design for the adaptive chart is developed when the process data follow a skewed distribution. An example is presented to illustrate the solution procedure. Based on the study, it is shown that the VP chart is more effective than the other adaptive control charts. The sensitivity analysis on the input parameters and various population distributions are illustrated through a numerical example.

The Variable Parameters Control Charts for Monitoring Autocorrelated Processes

The variable parameters (VP) control chart varies all control parameters from the current sample information, and results in more effective monitoring based on statistical and economic criteria. The usual assumption for designing a control chart is that the observations from the process are independent. However, for many processes, such as chemical processes, consecutive measurements are often highly correlated. In the present article, the observations are modeled as an AR(1) process plus a random error, and the properties of the VP charts are evaluated and studied under this model. Based on the study, the VP control scheme generally has better performance in detecting small mean shifts than the standard and the other adaptive charts. However, when the observations are highly autocorrelated, the complexity of the VP chart gives a negative effect on the performance.

Adaptive CUSUM of the Q chart

The CUSUM of the Q chart, as a self-starting approach, was previously proposed for detecting process shifts when the in-control process parameters are unknown. Motivated by the recent development of the adaptive chart, this paper proposes a new self-starting approach that integrates the CUSUM of the Q chart with the feature of adaptively varying the reference value, to better detect a range of shifts with unknown process parameters. The choice of the chart parameters and the masking effect are also studied. Simulation results show that our proposed chart offers balanced protection against shifts of different magnitude, and has performance comparable to the dynamic change-point control scheme. A real example from industrial manufacturing is used to demonstrate its implementation.

Re‐evaluation of performance for adaptive charts

Purpose – The purpose of this paper is to re‐evaluate the performance of the adaptive control charts which allow some of their design parameters to change during production depending on the collected information from samples over time. Instead of employing a single performance measure (average time to signal process changes), a set of measures, associated with the inspection efficiency and effort, is taken into account in the evaluation process.

An adaptive chart for monitoring the process mean and variance

AbstractTraditionally, an $\bar{X}$ chart is used to control the process mean and an R chart is used to control the process variance. However, these charts are not sensitive to small changes in the process parameters. The adaptive $\bar{X}$ and R charts might be considered if the aim is to detect small disturbances. Due to the statistical character of the joint $\bar{X}$ and R charts with fixed or adaptive parameters, they are not reliable in identifying the nature of the disturbance, whether it is one that shifts the process mean, increases the process variance, or leads to a combination of both effects. In practice, the speed with which the control charts detect process changes may be more important than their ability in identifying the nature of the change. Under these circumstances, it seems to be advantageous to consider a single chart, based on only one statistic, to simultaneously monitor the process mean and variance. In this paper, we propose the adaptive non‐central chi‐square statistic chart. This new chart is more effective than the adaptive $\bar{X}$ and R charts in detecting disturbances that shift the process mean, increase the process variance, or lead to a combination of both effects. Copyright © 2006 John Wiley & Sons, Ltd.

Using economically designed Shewhart and adaptive ―X charts for monitoring the quality of tiles

AbstractThis paper presents the economic design of ―X control charts for monitoring a critical stage of the main production process at a tile manufacturer in Greece. Two types of ―X charts were developed: a Shewhart‐type chart with fixed parameters and adaptive charts with variable sampling intervals and/or sample size. Our prime motivation was to improve the statistical control scheme employed for monitoring an important quality characteristic of the process with the objective of minimizing the relevant costs. At the same time we tested and confirmed the applicability of the theoretical models supporting the economic design of control charts with fixed and variable parameters in a practical situation. We also evaluated the economic benefits of moving from the broadly used static charts to the application of the more flexible and effective adaptive control charts. The main result of our study is that, by redesigning the currently employed Shewhart chart using economic criteria, the quality‐related cost is expected to decrease by approximately 50% without increasing the implementation complexity. Monitoring the process by means of an adaptive ―X chart with variable sampling intervals will increase the expected cost savings by about 10% compared with the economically designed Shewhart chart at the expense of some implementation difficulty. Copyright © 2006 John Wiley & Sons, Ltd.

Weighted-loss-function control charts

This article proposes a single weighted-loss-function chart (WL chart) for monitoring the process mean and variance simultaneously in statistical process control (SPC). The weights of the losses due to mean shift and variance shift in the loss function are balanced through a weighting factor λ, so that the WL chart is considerably more effective than the unadjusted loss function chart, the joint \(\overline{X}\)&S charts and many other charts as well. The improvement in detection effectiveness will directly lead to the reduction of a number of defects in the manufacturing process when out-of-control cases occur. Moreover, the WL chart provides a platform for the further development of the Cusum chart, runs rule, or adaptive chart for monitoring both process mean and variance.

Gráficos adaptativos de controle por atributos e seu projeto na prática

Os gráficos de controle de processo com parâmetros variáveis, ou gráficos adaptativos, permitem intensificar ou relaxar o controle do processo de acordo com a informação da amostra mais recente. Sua vantagem é uma maior rapidez na detecção de causas especiais que tiram o processo de sua situação de controle. Este artigo apresenta um modelo geral para gráficos de c, np, u e p com um, dois ou todos os parâmetros de projeto (tamanho de amostra, intervalo de tempo entre amostras e largura dos limites de controle) variáveis, que proporciona ganhos de eficiência substanciais. É proposto um procedimento para escolha dos valores para os parâmetros dos gráficos na prática, apoiado em um programa em Excel (disponível a pedido) que permite selecionar, de forma rápida e simples, dentre valores práticos, aqueles que otimizam a eficiência do gráfico de controle na detecção de alterações do processo.

Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart

AbstractRecent research has shown that the adaptive control charts are quicker than the traditional static charts in detecting process shifts. This paper develops the algorithm for the optimization designs of the adaptive np control charts for monitoring the process fraction non‐conforming p. It includes the variable sample size chart, the variable sampling interval chart, and the variable sample size and sampling interval chart. The performance of the adaptive np charts is measured by the average time to signal under the steady‐state mode, which allows the shift in p to occur at any time, even during the sampling inspection. By studying the performance of the adaptive np charts systematically, it is found that they do improve effectiveness significantly, especially for detecting small or moderate process shifts. Copyright © 2004 John Wiley & Sons, Ltd.

Adaptive Control Charts for Attributes

We develop a general model for adaptive c , np , u and p control charts in which one, two or three design parameters (sample size, sampling interval and control limit width) switch between two values, according to the most recent process information. For a given in-control average sampling rate and a given false alarm rate, the adaptive chart detects changes in the process much faster than a chart with fixed parameters. Moreover, this study also offers general guidance on how to choose an effective design.

Comparing the Effectiveness of Various Bayesian X̄ Control Charts

In an attempt to improve the procedures for statistical process control many researchers have developed and proposed a variety of adaptive control charts in the last decade. The common characteristic of those charts is that one or more of the chart parameters (sampling interval, sample size,control limits) is allowed to change during operation, taking into account current sample information. Due to their flexibility, adaptive charts are more effective than their static counterparts but they are also more complex in terms of implementation. The purpose of this paper is to evaluate the economic performance of various adaptive control schemes to derive conclusions about their relative effectiveness. The analysis concentrates on Bayesian control charts used for monitoring the process mean in finite production runs. We present dynamic programming formulations and properties of the optimal solutions, which we then use to solve a number of numerical examples. The results from our comparative numerical study indicate that the chart parameter having the most positive impact on the economic performance by being adaptive is the sampling interval. It is therefore sufficient in most cases to use control charts with adaptive sampling intervals rather than other types of partially adaptive charts or the more complicated fully adaptive control charts.

Projeto econômico de cartas adaptativas para monitoramento de processos

Cartas de controle estatístico vêm sendo utilizadas com sucesso no monitoramento do desempenho de processos industriais. Nos últimos anos, diversas modificações nas cartas de Shewhart foram propostas na literatura. Tais modificações visam adaptar as cartas de controle ao monitoramento de processos com características especiais; entre elas, destacam-se as cartas adaptativas de controle. Apesar de apresentarem vantagens sobre as cartas de Shewhart, sinalizando, de maneira mais rápida, situações anômalas no comportamento dos processos, aspectos práticos relacionados à implementação de cartas adaptativas são pouco explorados na literatura. Neste artigo, propõe-se um modelo econômico para o projeto de cartas adaptativas. O modelo proposto é aplicado em um estudo de caso, no monitoramento de um processo de usinagem de peças para automóveis. No estudo de caso, o significado e a forma de determinação dos parâmetros do modelo econômico são detalhados. Esquemas adaptativos e tradicionais de controle de processo são comparados quanto a seus custos operacionais.

A Survey of Recent Developments in the Design of Adaptive Control Charts

This survey presents, in a comprehensive way, the substantial recent developments in the statistical and economic design of adaptive or dynamic charts that allow some of their parameters to change during production. After discussing several different measures of performance for these charts, the survey proceeds with a presentation of published models and results, classifying them according to the chart parameters (sampling intervals, sample sizes, and control limits) that the models allow to change dynamically. Comparisons between adaptive and static charts are provided and discussed. It is concluded that utilization of adaptive charts can increase significantly the effectiveness of process monitoring. Finally, the survey identifies gaps in the existing literature which may constitute fruitful areas for further research.

The usefulness of a weight gain spurt to identify women who will develop preeclampsia

Objective: The usefulness of adaptive centiles for weight gain as well as sudden weight gain spurts in identifying women who will develop preeclampsia was assessed. Methods: A study sample of 99 women who developed preeclampsia and a control sample of 675 women with normal pregnancies, were randomly selected. Weight gain spurts were identified by the upper bound of adaptive maternal weight centiles. Average changes in weight between successive clinic visits were also assessed. Results: Weight gain exceeding the 90 th percentile of the adaptive centiles resulted in estimated sensitivity and specificity of 52% and 66% and weight gain >0.9 kg per week between visits in 76% and 29% respectively. Of women who would develop preeclampsia identified by the adaptive chart, 62.0% exhibited abnormal weight gain prior to the onset of abnormal clinical findings. Conclusions: A sudden weight gain spurt is a far from reliable sign of impending preeclampsia. This reason for weighing women at antenatal visits appears to be unfounded.

Economic-statistical design of an adaptive [formula omitted] chart

An X ̄ chart with adaptive design parameters outperforms a traditional fixed sample-size, fixed sampling-interval X ̄ chart. However, an adaptive chart employs more resources by using a rapid mean sampling rate and a large average sample size to improve its performance. In this paper, an economic model for an adaptive chart with dual sample sizes and dual sampling intervals is developed. Using this model, the design parameters of an adaptive chart are optimized by minimizing the cost function. Constraints on the average time to signal are applied to the economic model to satisfy the required statistical properties. The adaptive chart is compared to the nonadaptive chart in terms of cost of operation and average time to signal. Sensitivity of the design parameters of the adaptive chart with respect to the operating cost and adaptive design parameters is also analyzed. An example is presented illustrating the application of the economic model. With some minor changes, the model can also be used to design a pure adaptive sample size chart or a pure adaptive sampling interval chart.