Using genetic algorithm and response surface methodology for statistically constrained optimization of VSI X-bar control charts under multiple assignable causes and non-normality

Variable sampling interval (VSI) control charts have been introduced with the aim of improving performance of traditional control charts. Usually, in the economic–statistical design of the VSI $ \overline{X} $ control charts, it is assumed that observations are normally distributed and process is subjected to only one assignable cause. However, in practice these assumptions could easily fail to hold, and results no longer could be realistic. This paper considers non-normal observations for the case of multiple assignable causes to develop a cost model for the economic design of VSI $ \overline{X} $ control chart. Being more applicable for all types of distributions, Burr distribution is employed for representing the distribution of non-normal process data. Since the proposed design consists of a complex nonlinear cost function that cannot be solved using a classical optimization method, genetic algorithm (GA) searching method as an efficient famous metaheuristic is employed to find the optimal values for the design parameters. Moreover, to improve the performances, response surface methodology is employed to calibrate GA parameters. The effectiveness of the proposed scheme is evaluated through a numerical example. Sensitivity analysis is also carried out to show the effects of cost and process parameters on the outputs of the model. Results show that in all cases, presented VSI model has better economical and statistical performances than its corresponding fixed sampling interval scheme.     

The effect of correlation on the economic design of warning limit X-bar charts

Control charts are widely applied to monitor manufacturing processes. In 1962, Page presented a modified X-bar chart with warning limits, which includes an upper and lower warning band. In 1975, Gordon and Weindling presented a cost model for determining the five parameters of a warning limit X-bar chart: i.e., the sample size, the sampling interval between successive subgroups, the control limit coefficient, the warning limit coefficient and the significant run length. When designing control charts, one usually assumes that the measurements within a sample are independently distributed. However, this assumption may not be tenable in some specific production processes. Yang and Hancock presented a correlation model to describe the correlated data in a sample. In this paper, we study the effect of correlated data on the design of warning limit X-bar charts by combining Gordon and Weindling's cost model with Yang and Hancock's correlation model. Based on the study, it is observed that among the five parameters in the economic design, only the significant run length is affected by the correlated data. Highly correlated data or independent data result in a longer run in the warning band.     

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 &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.     

Adaptive sampling interval cause-selecting control charts

This article considers the statistical adaptive process control for two dependent process steps. We construct an adaptive sampling interval Z _X control chart to monitor the quality variable produced by the first process step, and use the adaptive sampling interval Z _e control chart to monitor the specific quality variable produced by the second process step. By using the proposed adaptive sampling interval control charts, we can quickly detect and distinguish which process step is out of control. The performance of the proposed adaptive sampling interval control charts is measured by the adjusted average time to signal (AATS), which was derived by a Markov chain approach, for an out-of-control process. An empirical automobile braking system example shows the application and the performance of the proposed adaptive sampling control charts in detecting shifts in process means. Some numerical results obtained demonstrated that the performance of the proposed adaptive sampling cause-selecting control charts outperforms the fixed sampling interval cause-selecting control charts.     

Bootstrap method approach in designing multi-attribute control charts

In a production process, when the quality of a product depends on more than one correlated characteristic, multivariate quality control techniques are used. Although multivariate statistical process control is receiving increased attention in the literature, little work has been done to deal with multi-attribute processes. In monitoring the quality of a product or process in multi-attribute environments in which the attributes are correlated, several issues arise. For example, a high number of false alarms (type I error) occur and the probability of not detecting defects (type II error) increases when the process is monitored by a set of independent uni-attribute control charts. In this paper, to overcome these problems, first we develop a new methodology to derive control limits on the attributes based on the bootstrap method in which we build simultaneous confidence intervals on the attributes. Then, based upon the in-control and out-of-control average run length criteria we investigate the performance of the proposed method and compare it with the ones from the Bonferroni and Sidak’s procedure using simulation. The results of the simulation study show that the proposed method performs better than the other two methods. At the end, we compare the bootstrap method with the T ² control chart for attributes.     

Economic-statistical design of MC1 control charts

An economic-statistical design is presented to determine the optimal subgroup size, sampling frequency, the reference value and the control limit parameter for multivariate cumulative sum (MCUSUM) control charts based on the multivariate CUSUM 1 (MC1) method. To illustrate the solution procedure, a numerical example is presented and the sensitivity analysis is studied.     

Pattern recognition for statistical process control charts

Control charts are important statistical process control tools for determining whether a process is run in its intended mode or in the presence of unnatural patterns. Patterns displayed on control charts can provide information about the process. This paper describes the development of a pattern recognition system designed to detect and analyse various patterns that can occur on statistical quality control charts. The system looks not only for simple patterns, such as trend, shift and stratification, but also for superimposed patterns, such as trend + shift. The effect of noise associated with individual patterns is also analysed. The benefits of the approach compared with the alternatives are discussed.Notation N _i ith value of the noise series - N _T noise tolerance - x _i ith data item from a number sequence - r _i seed for random number simulation - adjacent difference - standard deviation - mean of the data - A slope of a straight line - B constant - C constant - i indexing integer - j indexing integer - k total number of samples - l starting point of a pattern on control chart - m ending point of a pattern on control chart - n size of samples - ptn pointer to the pattern identified - slope slope for trend patterns - X normally distributed variate arising from simulation - CL centre-line - LCL lower control limit - LOSL lower one-sigma limit - LWL lower warning limit - UCL upper control limit - UOSL upper one-sigma limit - UWL upper warning limit     

质量控制图在线智能诊断分析系统

在计算机集成制造系统环境下,为了有效实现工序质量控制,提出了质量控制图的在线智能诊断分析系统框架,它由控制图模式识别、参数估计、专家诊断分析系统和加工参数调整系统四个模块组成。在该系统中,采用了一种适用于模式识别与分类的新型神经网络模型——局部有监督特征映射网络,将其应用于该系统的控制图模式识别和参数估计中。仿真实验和应用实例表明,识别和分类结果与实际相符,并可以保证实时性。     

Cause-selecting control charts based on Huber’s M-estimator

Cause-selecting chart (CSC) is effective in monitoring and diagnosing multistage processes. It discriminates between the overall and specific qualities by establishing the relationship between input and output measurements. In practice, the model relating the input and output variables must be estimated. To this end, historical data are used, which often contain outliers. The presence of outliers has a deleterious effect on the control charting procedure. To alleviate the encountered problem, a robust monitoring approach based on Huber’s M-estimator is proposed. Subsequently, the performance of the robust and non-robust CSCs is investigated using the average run length criterion while conducting a simulation study. The results reveal that the Huber-based CSC is superior to the traditional CSC due to its prompt detection of out-of-control conditions.     

Economic design of two-stage control charts with skewed and dependent measurements

In many instances, the cost is high to monitor primary quality characteristic called performance variable, but it could be more economical to monitor its surrogate. To cover asymmetric processes in an alternating fashion of two-stage charting design using either performance variable or surrogate variable, both process variables are modeled by a skew normal distribution, respectively. The proposed two-stage control charts are constructed with an economic viewpoint using Markov chain approach. Two algorithms are provided to implement the proposed charting method. The application of the proposed charting method and its advantages over the existing methods are presented through an illustrating example.     

测量系统能力对过程监测效果的影响分析

测量系统的重复性和再现性变异是测量值波动的一个重要来源,它对于过程监测的效果控制图会造成影响.基于测量系统的重复性和再现性分析,讨论了测量系统能力对监测过程的(X)控制图性能的影响,结果表明符合要求的测量系统对(X)控制图的性能影响不是很明显,否则影响较大,并通过一个仿真示例验证了该结果.     

双抽样均值—标准差联合控制图的构建及参数设计

在参考双抽样均值控制图及双抽样标准差控制图的基础上,构建了双抽样均值一标准差联合控制图.建立了控制图参数设计的优化模型,用以监控生产过程质量,并通过遗传算法完成了模型求解.采用马尔科夫链方法,完成了联合控制图平均运行长度性能指标的计算.基于该指标,通过两阶段抽样和可变抽样样本及抽样区间均值-标准差联合控制图的性能对比,分析验证了该控制图的性能优势.     

Condition monitoring scheme via one-class support vector machine and multivariate control charts

A condition-based maintenance (CBM) has been widely employed to reduce maintenance cost by predicting the health status of many complex systems in prognostics and health management (PHM) framework. Recently, multivariate control charts used in statistical process control (SPC) have been actively introduced as monitoring technology. In this paper, we propose a condition monitoring scheme to monitor the health status of the system of interest. In our condition monitoring scheme, we first define reference data set using one-class support vector machine (OC-SVM) to construct the control limit of multivariate control charts in phase I. Then, parametric control chart or non-parametric control chart is selected according to the results from multivariate normality tests. The proposed condition monitoring scheme is applied to sensor data of two anemometers to evaluate the performance of fault detection power.

     

An economic design for variable sampling interval MA control charts

Most of the studies done on the economic design of control charts focus on a fixed-sampling interval (FSI); however, it has been discovered that variable-sampling-interval (VSI) control charts are substantially quicker in detecting shifts in the process than FSI control charts due to a higher frequency in the sampling rate when a sample statistic shows some indication of a process change. In this paper, an economic design for a VSI moving average (MA) control chart is proposed. The results of a numerical example adopted from an actual case indicate that the loss cost of VSI MA control charts is consistently lower than that of the FSI scheme.Design variables n Sampling size for each moving plot - h_a Subsequent sampling interval when preceding sample mean is located at sub-control region I_a, a=1,2,..., - Number of different sampling-interval lengths, 2 - k_a Threshold limit expressed in units of - k₁ Control limit expressed in units of Parameters related to assignable cause µ₀ Target mean - True-process standard deviation - Magnitude of an assignable cause expressed in units of - Occurrence rate of an assignable cause per unit timeCost and technical parameters D Average time taken to find and repair an assignable cause after detection - e Time for a sample to be taken, transmitted to laboratory, and results phoned back to process control room - M Income reduction when =₀+ - T Average cost of looking for an assignable cause when a false alarm occurs - W Average cost of looking for and repairing an assignable cause when one does exist - F_c Fixed cost per subgroup of sampling, inspecting, evaluating and plotting - V_c Variable cost per subgroup of sampling, inspecting, evaluating and plotting     

Monitoring process variability using exponentially weighted moving sample variance control charts

Exponentially weighted moving average (EWMA) control charts are regarded as one of the most convenient tools in detecting small process shifts. Although EWMA control charts have been extensively used to monitor the mean of quality characteristics, there are few studies concentrating on the monitoring of process variability by using weighted moving control charts. In this paper, we propose an exponentially weighted moving sample variance (EWMSV) control chart for monitoring process variability when the sample size is equal to 1. The results are compared numerically with other similar methods using the average run length (ARL). Through an example, the practical considerations are presented to implement EWMSV control charts.     

An evolutionary economic-statistical design for VSI X control charts under non-normality

Since Reynolds et al. [1] proposed the variable sampling interval (VSI) control chart, the statistical properties of the chart have been discussed and shown to be better than the traditional control chart in which the sampling intervals length are fixed. However, the VSI charts are, like the traditional charts, still costly when they are used for the prevention of defective products. For this reason, an appropriate design is necessary before it is used. In this paper, a VSI control chart is used for monitoring non-normal process data, which is widely encountered in practice. Then, a cost-quality model based on the Burr distribution is proposed for constructing an economic-statistical design for the VSI chart. The design of the chart has been developed considering the optimisation of the cost function in this model posed by statistical constraints. The design parameters can be derived through the evolutionary search method, and the overall finding indicates that the designed VSI chart always outperforms the traditional control chart with respect to the expected cost per unit time. This model is also suitable for normally distributed data; thus, it is suitable for a general application.     

生产系统维修策略和控制图经济设计研究综述

在生产系统的产品质量保证过程中,设备维修管理与统计过程控制是两种常用手段和方法。在分析设备维修管理和统计过程控制对生产系统的产品质量和经济成本影响基础上,重点从经济性角度按照维修策略经济设计、控制图经济设计,以及维修策略和控制图联合经济设计三个知识模块,对生产质量保证管理系统的经济性设计研究现状进行了梳理与评述,并提出了未来研究的努力方向。     

An enhancement of DSI X̄ control charts using a fuzzy-genetic approach

A traditional control chart used to monitor a process draws the process data at a fixed sampling rate, while a variable sampling interval (VSI) control chart varies the sampling rate as a function of on-line process data. In such a sampling policy, a higher sampling rate is adopted when there is suspicion of a change in a process. Therefore, it is able to detect the process change faster than traditional control chart, and thus has been much accepted for use. Nevertheless, the binary suspicious grade used in VSI policy to specify the sampling rate is not detailed enough to explain the acquired information from process data. As a result, this paper aims to refine the suspicious grade and sampling interval lengths to increase the detection ability of VSI charts. This study first establishes a composition function on two sides of the control chart by introducing the concept of fuzzily suspicious grade to specify the sampling rate. Then, genetic algorithms (GAs) is used to adjust the values of the parameters in this composition function to enhance the dual-sampling-interval (DSI) charts-one type of the VSI charts in common use-in terms of average time to signal (ATS) for process mean shift. In addition, some statistical properties of the enhanced DSI charts as well as performance comparison to traditional DSI charts are provided and analysed.