监控均值标准差的可变抽样区间EWMA图经济设计

为了在提高过程监控效率的同时降低过程监控费用,针对同时监控过程均值和标准差变化的情形,研究可变抽样区间的指数加权移动平均控制图的经济设计问题.首先建立可变抽样区间,同时监控均值标准差指数加权移动平均控制图；其次对其进行经济设计,使单位时间期望费用函数最小,以确定控制图参数的最优值；然后利用遗传算法来寻找经济模型的参数最优解；最后对可变抽样区间同时监控均值标准差指数加权移动平均控制图的经济模型进行灵敏度分析和最优性分析.通过最优性分析得出结论:基于经济模型设计的可变抽样区间指数加权移动平均控制图比传统的控制图具有较小的费用.     

变采样间隔自适应EWMAt控制图统计设计

针对平滑系数固定的EWMAt控制图失控状态下平均报警时间长的问题,提出一种变采样间隔、自适应平滑系数的EWMAt(VSI-AEWMAt)控制图。平滑系数的自适应特性加强了EWMAt控制图对大偏移的检测能力,变采样间隔特性缩短了EWMAt控制图的平均报警时间。采用Markov链方法计算VSI-AEWMAt控制图的平均报警时间,给出了VSI-AEWMAt控制图的参数优化算法。通过仿真分析比较了VSI-AEWMAt控制图与VSI-EWMAt控制图的统计性能,结果表明VSI-AEWMAt控制图的性能优于VSI-EWMAt控制图。     

An improved SPRT control chart for monitoring process mean

The sequential probability ratio test (SPRT) chart is a desirable tool for monitoring manufacturing processes due to its high effectiveness. It is especially suitable for applications where testing is very expensive or destructive, such as the automobile airbags test and unaxial tensile test. This article proposes a design algorithm for the SPRT chart in which the reference value (γ) of the SPRT chart is optimized. The design algorithm increases the overall effectiveness of the SPRT chart by more than 10% on average. Moreover, the improvement in detection effectiveness is achieved without any additional difficulty in implementation. A design table is also provided to facilitate quality engineers to design the SPRT chart.     

The run sum t control chart for monitoring process mean changes in manufacturing

The $ \overline{X} $ type charts are not robust against estimation errors or changes in process standard deviation. Thus, the t type charts, like the t and exponentially weighted moving average (EWMA) t charts, are introduced to overcome this weakness. In this paper, a run sum t chart is proposed, and its optimal scores and parameters are determined. The Markov chain method is used to characterize the run length distribution of the run sum t chart. The statistical design for minimizing the out-of-control average run length (ARL₁) and the economic statistical design for minimizing the cost function are studied. Numerical results show that the t type charts are more robust than the $ \overline{X} $ type charts for small shifts, in terms of ARL and cost criteria, with respect to changes in the standard deviation. Among the t type charts, the run sum t chart outperforms the EWMA t chart for medium to large shifts by having smaller ARL₁ and lower minimum cost. The run sum t chart surpasses the $ \overline{X} $ type charts by having lower ARL₁ when the charts are optimally designed for large shifts but the run sum $ \overline{X} $ and EWMA $ \overline{X} $ prevail for small shifts. In terms of minimum cost, the $ \overline{X} $ type charts are superior to the t type charts. As occurrence of estimation errors is unpredictable in real process monitoring situations, the run sum t chart is an important and useful tool for practitioners to handle such situations.     

过程均值偏移随机的EWMA控制图优化设计

针对过程均值偏移随机的情况,提出一种统计经济最优的指数加权移动平均控制图优化设计方法。该方法将过程受控、失控未检出、失控被检出并进行恢复这三个阶段定义为一个周期,分析了三个阶段的平均时长及质量成本构成,通过计算产品质量特性超出规格界限的概率量化缺陷产品所造成的质量损失,以单位时间内期望成本最小为目标建立指数加权移动平均控制图优化模型并设计了遗传算法,优化了样本容量、采样间隔、平滑界限和控制界限等参数。通过与休哈特均值控制图、传统指数加权移动平均控制图等进行对比验证了该模型的优越性。     

A new adaptive control chart for monitoring process mean and variability

Traditionally, an $\bar{X}$ chart is used to control the process mean, and an R chart is used to control the variance. However, these charts are not sensitive to the small shifts in the processes. The adaptive charts might be considered if the aim is to detect process changes quickly. In this paper, we propose a new adaptive single control chart which integrates the exponentially weighted moving average procedure with the generalized likelihood ratio test statistics for jointly monitoring both the process mean and variability. This new chart is effective in detecting the disturbances that shift the process mean, increase or decrease the process variance, or lead to a combination of both effects.     

The variable sample size t control chart for monitoring short production runs

Starting the online monitoring of a quality characteristic by means of a control chart at the beginning of a short production run is often a challenging issue for quality practitioners: in fact, the frequent absence of preliminary information prevents from getting a precise estimate of the characteristic mean and standard deviation. Furthermore, for short runs having a finite rolling horizon, the number of inspections scheduled within the run can be too small to get sufficient samples allowing the phase I implementation of the chart to be completed. Recently, t control charts have been proposed as efficient means to overcome this problem because they do not need any phase I tentative control limits definition or preliminary process knowledge. In this paper, a variable sample size (VSS) version of the t chart is proposed. Adaptive control charts have been implemented with success in long runs: here, the performance of the variable sample size strategy is investigated for a chart used in a short run. The statistical performance of the VSS t chart is compared with the one of the fixed-parameter (FP) t chart for both scenarios of fixed and unknown shift size, with the latter situation being frequent in short-run manufacturing environments. An extensive numerical investigation reveals the potential benefits of the proposed chart. When the statistical design is optimized with respect to a fixed value of the shift size δ, the VSS t chart has a better statistical performance than the FP t chart for moderate to large values of δ. Conversely, for the unknown shift size condition, the VSS t chart always outperforms the FP t chart for in-control average sample sizes ASS₀?>?7. An illustrative example shows the implementation of the VSS during the production of a finite lot of mechanical parts.     

An integrated supervised learning solution for monitoring process mean vector

When an out-of-control condition is detected by a control chart, a search begins to identify and eliminate the source(s) of the signal. Identification of the time when a process first changed is an important step in root cause analysis which helps a process engineer to eliminate the source(s) of assignable cause effectively. The time when a change takes place in the process is referred to as the change point. In multivariate environment, since there is more than one variable involved, then root cause analysis is relatively harder compared to the case of univariate because it is not clear exactly which variable has contributed to the out-of-control condition and in what direction its mean has shifted. Hence, a procedure that identifies the change point, performs diagnostic analysis, and specifies the direction of the shift in the mean of the contributing variable(s) all simultaneously could help to conduct root cause analysis effectively. Although different multivariate methods exist in the literature that allow to either estimate change point in the process mean vector or identify the contributing variables leading to the out-of-control condition, but in this research, an integrated supervised learning solution is proposed, which helps to (1) detect of an out-of-control condition, (2) identify the change point leading to shift in the mean vector, (3) specify the variable(s) contributing to the out-of-condition, and (4) identify the direction of the shift in the mean of each contributing variable simultaneously. A real case study is used to evaluate and compare the performance of the proposed integrated approach to existing methods in the literature.     

A synthetic control chart for monitoring process dispersion with sample range

A synthetic control chart for monitoring the changes in the standard deviation of a normally distributed process is proposed in this paper. The synthetic chart consists of the sample range (R) chart and the conforming run-length (CRL) chart. The R chart can be viewed as a special case of the synthetic chart. The operation, design and performance of this chart are described. Average run- length comparisons between other procedures and the synthetic chart are presented. It indicates that the synthetic chart is a good alternative for monitoring process dispersion. The variable sampling interval (VSI) schemes, as an enhancement to the synthetic chart, are discussed to further improve the chart performance. An example is presented to illustrate the application of synthetic chart and its VSI scheme.     

Generally weighted moving average control chart for monitoring process variability

Most applications of the EWMA control chart for monitoring processes depend on detecting shifts in the process mean. The problem of detecting an increase in process variability, which can also strongly affect the quality of products, is perhaps more important. When a process moves from the pilot phase to the production phase, the mean may not shift but the variation will probably increase because new sources of variation are introduced, including new people and materials. A simulation is performed to evaluate the ARL to false alarm and to monitor the change in the process variability of the EWMA control chart and the GWMA control chart. An extensive comparison reveals that the GWMA control chart is more sensitive than the EWMA control chart in monitoring the variance of a process. The results of this study can be applied to monitor the process variability in automated industries.     

A CUSUM scheme with variable sample sizes for monitoring process shifts

The cumulative sum scheme (CUSUM) and the adaptive control chart are two approaches to improve chart performance in detecting process shifts. A weighted loss function CUSUM scheme (WLC) is able to monitor both the mean shift and the increasing variance shift by manipulating a single chart. This paper investigates the WLC scheme with a variable sample sizes (VSS) feature. A design procedure is firstly proposed for the VSS WLC scheme. Then, the performance of the chart is compared with that of four other competitive control charts. The results show that the VSS WLC scheme is more powerful than the other charts from an overall viewpoint. More importantly, the VSS WLC scheme is simpler to design and operate. A case study in the manufacturing industry is used to illustrate the chart application. The proposed VSS WLC scheme suits the scenario where the strategy of varying sample sizes is feasible and preferable to pursue a high capability of detecting process variations.     

Economical operation of the C pm control chart for monitoring process capability index

Process capability indices are widely used to provide the evaluation measure of a process. Especially, the process capability index C _pm , which is defined by the range of the process standard specification limits and the deviation from a target value, is called the Taguchi index. Boyles has investigated the statistical characteristics of the estimator $\hat{C}_{pm}$ , and also proposed a technique for the C _pm control chart. Since the process capability index C _pm is based on the concept of the Taguchi’s quality loss, the process capability index C _pm already includes an economical concept. In this article, we evaluate an operating cost consisting of the sampling cost, the sample cost, and the quality loss of failing to detect an out-of-control state when the C _pm control chart is used. Then, we derive an optimal operating plan by sample size and sampling interval in order to minimize the ceiling value of the operating cost based on the min–max criterion.     

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     

Design and application of exponential chart for monitoring time-between-events data under random process shift

Exponential charts based on time-between-events (TBE) data were developed for monitoring high-yield process like the process which has achieved six-sigma quality level and has recently shown to be very useful in manufacturing systems, in reliability and maintenance monitoring, and also in service-related applications in general. This article develops an economic model of the exponential chart (known as TBE_random chart) for monitoring time-between-events data; the design algorithm considers the random characteristic of the process shifts and therefore better reflects the real process conditions. The probability distribution of the random process shift is modeled by a Rayleigh distribution based on the sample data acquired during the operation of the control chart. The design of the proposed control chart scheme is demonstrated, and the properties are compared with that of other exponential charts. The results of the numerical studies show that the consideration of the random process shift in designing an exponential chart provides an excellent in-control stability of the charting scheme, which in turn helps in saving time and cost for searching the false alarms. The proposed control chart is easy to understand and operate, and thus the floor operators can utilize and understand it as easily as with a traditional charting scheme.     

Identifying the mean step change of UBM chart

The traditional control charts are developed based on the assumption that the successive observations are independent and identically distributed. In some processes, the independence assumption is violated when there is autocorrelation between observations. To solve this problem, two methods, classified as model-based and model-free, could be applied. When a control chart alarms an assignable cause, it is essential to detect the process change point in order to remove the root cause. In the presence of autocorrelated data, different methods for change-point identification have been applied only for model-based methods. Hence, this is considered as the research gap and an attempt is made to fill this gap by applying maximum likelihood function in unweighted batch mean control chart, one of the most applied model-free methods. In this article, an estimator is presented to determine the change point for the first-order autoregressive process, AR(1). When a real change occurs, the performance of proposed estimator is evaluated through simulation.     

A new EWMA monitoring design for multivariate quality control problem

In this paper, a new approach is proposed to detect shifts of a multivariate quality control system. To do this, first, the decomposition method in multivariate normal distribution is introduced. Then, a control statistics is defined, and its properties are explained. In order to understand the proposed methodology and to evaluate its performance, a numerical example is provided by simulation. Moreover, the in- and out-of-control average run length of the proposed method are compared with the ones from the well-known multivariate cumulative sum and multivariate exponential weighted moving average in different scenarios of shifts. The results of the simulation study show that the proposed methodology performs better than the other methods in detecting the shifts of the standard deviation and correlation.     

Double sampling \overline{X} control chart for a first-order autoregressive moving average process model

In this paper, we consider the double sampling (DS) $\overline{X} $ control chart for monitoring processes in which the observations can be represented as a first-order autoregressive moving average (ARMA(1, 1)) model. The properties of the DS $\overline{X} $ control chart with the sampling intervals driven by the rational subgroup concept are studied and compared with the Shewhart chart and the variable sample size (VSS) chart, both properly modified to account for the serial correlation. Numerical results show that the correlation within subgroups has a significant impact on the properties of the charts. For processes with low to moderate correlation levels, the DS $\overline{X} $ chart is substantially more efficient in detecting process mean shifts.