可变样本容量和抽样区间的质量控制图

常规控制图是每隔固定时间从过程抽取固定容量的样本对过程进行监督,本文根据Ｐｒａｂｈｕ等的联合可变样本容量和抽样区间的ｘ图的模型设计可变样本容量和抽样区间的中位值ｘ和极差Ｒ控制图,计算了在可变样本容量和抽样区间下发信号前的平均时间,并同常规、可变样本容量与可变抽样区间图作比较。所设计的ｘ和Ｒ图能缩短过程失控时间而减少不合格品数。     

Q控制图灵敏性分析

对过程均值未知,过程标准偏差已知情况下的单值Q控制图与均值Q控制图检测过程均值一次偏移的灵敏性进行了分析.结果表明:在过程初始阶段,单值Q图的灵敏性要高于均值Q控制图.在过程初始阶段,建立单值Q控制图监测过程波动,累积一定数量的样本后,建立均值Q控制图监视过程波动.两种Q控制图互为补充,共同用于监视过程波动更有效.     

面向质量目标的Q控制图设计

针对大批量生产开始阶段的过程监控,提出了一种基于预定质量目标的Q控制图监控方法.其基本思路是利用面向质量目标的统计公差技术与Q控制图相结合应用,以实现大批量过程开始阶段均值和方差未知时面向质量目标的过程监控.基于质量目标建立统计公差(CP*,k*),并将该统计公差转化为基于给定置信概率的对CP和k的估计值的判定条件.通过案例分析,面向质量目标的Q控制图能够在过程保持受控状态的前提下以一定置信概率保证质量目标.     

具有可变抽样区间的残差MEWMA控制图

为了提高控制图监控多元自相关过程小波动的效率,研究具有可变抽样区间(VSI)的残差MEWMA控制图。首先,对残差MEWMA控制图进行可变抽样区间设计,用蒙特卡罗模拟方法计算其平均报警时间。其次,对所设计的可变抽样区间残差MEWMA与固定抽样区间的残差MEWMA进行比较研究。结果表明,可变抽样区间残差MEWMA控制图监控效率优于固定抽样区间的残差MEWMA控制图,能更快地发现过程中的变化。然后,通过对比研究得出,VSI残差MEWMA控制图的受控性能优于VSI MEWMA控制图。最后,研究平滑系数对过程监控性能的影响,得出过程波动较小时,采用较小的平滑系数;分析自相关系数对过程监控性能的影响关系,得出对于相同波动,相关系数越小,VSI MEWMA残差控制图的监控效果越好。     

Q控制图初始性能的改进

针对单值Q控制图在过程初始阶段所面临的突出问题,即检出力不强的弱点,提出一种改进单值Q控制图初始性能的质量控制图。它是建立在贝叶斯预测理论的基础上,应用在过程方差是未知的稳态生产过程的条件下。对控制图处于稳态和过程均值发生偏移时的性能及基于贝叶斯模型先验估计值对控制图的影响进行了讨论,结果表明控制图的特性适用于监视稳定生产过程的初始阶段,而这种特性恰好弥补了Q控制图在初始阶段性能不佳的弱点。     

子样本数较少时的中位值控制图

本文设计样本数较少时中位值图的控制限，道德导出了与中位值有关的统计量的分布，然后给出中位值图控制限的公式，将算得的系数列成表，该中位值控制图已应用于小批量的生产过程。     

非对称抽样区间x^-图

许多生产过程不满足休哈特图所基于的假设,过程均值向上飘移与向下飘移的发生具有不等概率,向上漂移幅度不同于向下漂移幅度.提出一种非对称抽样区间(x)图来监控此类过程,计算了控制图的效率测度--平均报警时间,与对称抽样区间图及非对称控制限图的比较显示此方案可以更快发现过程的变化.     

可变抽样区间不合格品数控制图

分析了休哈特控制图的不足,设计出具有两种抽样区间长度的可变抽样区间(VSI)np图,当点子接近控制限时,使用较短的抽样区间;当点子接近目标值时,使用较长的抽样区间.若点子超出控制限,则与固定抽样区间控制图(FSI)一样发出信号.同时还计算了在可变抽样区间下发信号前的平均时间,并与固定抽样区间np图进行比较,所设计的VSI控制图能缩短过程失控时间,从而可减少不合格品数.     

CUSUM控制图的一种优化设计方法研究

提出了一种以田口质量损失函数最小为目标的CUSUM控制图优化设计方法，建立了优化设计理论模型，提出了优化分析的流程，进行了实例分析和验证。     

控制图在扭矩扳子比对过程中的应用

通过建立控制图分析了扭矩扳子在比对过程中的质量控制结果。主要介绍了平均值-标准偏差控制图（xˉ-s图）的应用,以监视比对过程中数据的质量;根据控制图提供异常值的有关信息,采取相应纠正措施,使比对的测量过程处于统计控制状态。文章还从选择合适的控制图、测量频次的确定、绘制控制图的顺序、失控后的处置等方面分析讨论了实际操作中需要注意的问题,为计量人员开展扭矩扳子的测量工作提供参考。     

Optimal Design of VSI ―X Control Charts for Monitoring Correlated Samples

This paper develops an economic design of variable sampling interval (VSI)―X control charts in which the next sample is taken sooner than usual if there is an indication that the process is off‐target. When designing VSI―X control charts, the underlying assumption is that the measurements within a sample are independent. However, there are many practical situations that violate this hypothesis. Accordingly, a cost model combining the multivariate normal distribution model given by Yang and Hancock with Bai and Lee's cost model is proposed to develop the design of VSI charts for correlated data. An evolutionary search method to find the optimal design parameters for this model is presented. Also, we compare VSI and traditional ―X charts with respect to expected cost per unit time, utilizing hypothetical cost and process parameters as well as various correlation coefficients. The results indicate that VSI control charts outperform the traditional control charts for larger mean shift when correlation is present. In addition, there is a difference between the design parameters of VSI charts when correlation is present or absent. Copyright © 2005 John Wiley & Sons, Ltd.     

Control Charts for Monitoring Field Failure Data

One responsibility of the reliability engineer is to monitor failure trends for fielded units to confirm that pre‐production life testing results remain valid. This research suggests an approach that is computationally simple and can be used with a small number of failures per observation period. The approach is based on converting failure time data from fielded units to normal distribution data, using simple logarithmic or power transformations. Appropriate normalizing transformations for the classic life distributions (exponential, lognormal, and Weibull) are identified from the literature. Samples of size 500 field failure times are generated for seven different lifetime distributions (normal, lognormal, exponential, and four Weibulls of various shapes). Various control charts are then tested under three sampling schemes (individual, fixed, and random) and three system reliability degradations (large step, small step, and linear decrease in mean time between failures (MTBF)). The results of these tests are converted to performance measures of time to first out‐of‐control signal and persistence of signal after out‐of‐control status begins. Three of the well‐known Western Electric sensitizing rules are used to recognize the assignable cause signals. Based on this testing, the ―X‐chart with fixed sample size is the best overall for field failure monitoring, although the individual chart was better for the transformed exponential and another highly‐skewed Weibull. As expected, the linear decrease in MTBF is the most difficult change for any of the charts to detect. Copyright © 2005 John Wiley & Sons, Ltd.     

Linking EWMA p Charts and the Risk Adjustment Control Charts

This paper develops an adaptive exponentially weighted moving average (EWMA) chart that can be used as either a p chart for monitoring significant departures from in‐control non‐homogenous probabilities of failure or success or a risk‐adjusted control chart for success or failure of an event. An example of a risk adjustment process is monitoring the performance of a particular surgery over time where we need to adjust for the temporal changes in patient case mix. If the magnitude of this shift is known in advance, as would be the case in some hypothesis testing applications, then the paper offers a way of selecting the appropriate exponential weights to be efficient at detecting such a variable shift. The adaptive EWMA p chart is tested using extensive simulations. Processes for its efficient design are offered. The example application offers practitioners a means of evaluating a trial in real time rather than the traditional approach of evaluating the trial at the end of the study period. This is helpful in deciding how long the trial should run as well as potentially adapting the design over time as more is understood about the trial uncertainties. This may be particularly useful in evaluating expensive trials. Copyright © 2016 John Wiley & Sons, Ltd.     

Adapting EWMA Control Charts for Batch-Correlated Data

Batch production is common in the chemical and process industries. This article demonstrates how EWMA charts should be modified to account for substantial batch-to-batch variation. A batch-correlation model is considered, and methods of estimation and hypothesis testing for the batch-correlation coefficient are developed. This discussion is most appealing for production processes in which items are processed in batches but are related within batch.     

Type II Errors of Demerit Control Charts

Complex products may present more than one type of defect. A demerit control chart is a useful tool for monitoring different types of defects in a single chart while taking into account different levels of severity. Traditionally, control limits have been established based on standard deviations from the centerline assuming normality. These limits were improved upon by approaches to finding the exact distribution of the demerit statistic and establishing probability-based limits. With respect to Type I error, probability-based limits have been shown to outperform traditional limits. Now, again with exact distributions, we consider Type II errors as well when establishing control limits for different shifts, means and weights.     

Shewhart Control Charts for Monitoring Reliability with Weibull Lifetimes

In this paper, we present Shewhart‐type and S² control charts for monitoring individual or joint shifts in the scale and shape parameters of a Weibull distributed process. The advantage of this method is its ease of use and flexibility for the case where the process distribution is Weibull, although the method can be applied to any distribution. We illustrate the performance of our method through simulation and the application through the use of an actual data set. Our results indicate that and S² control charts perform well in detecting shifts in the scale and shape parameters. We also provide a guide that would enable a user to interpret out‐of‐control signals. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparison of Multivariate Control Charts for Process Dispersion

In this article we compare four multivariate control charts for process dispersion in the retrospective analysis of a historical data set. Among the schemes compared, a new control chart based on a robust estimation of the variance-covariance matrix proved to be very effective in detecting changes in the process dispersion matrix.     

Conditional Control Charts for Weibull Quantiles Under Type II Censoring

In this article, we propose control charts for the quantiles of the Weibull distribution, for type II censored data, based on the distribution of a pivotal quantity conditioned on ancillary statistics. These control charts must be considered as alternatives to bootstrap type control charts. We derive an analytical form of the conditional distribution function of the monitored statistic and we use this function to propose ARL‐unbiased control limits. We further demonstrate that the proposed conditional chart have a general analytical form for the ARL that can be evaluated numerically without use of simulations and we also show that these charts perform at least as well as the bootstrap type ones. We finally apply the conditional charts to a dataset on the strength of carbon fibers to detect shifts in a specified Weibull quantile. Copyright © 2014 John Wiley & Sons, Ltd.     

Multivariate Profile Charts for Statistical Process Control

The multivariate profile (MP) chart is a new control chart for simultaneous display of univariate and multivariate statistics. It is designed to analyze and display extended structures of statistical process control data for various cases of grouping, reference distribution, and use of nominal specifications. For each group of observations, the scaled deviations from reference values are portrayed together as a modified profile plot symbol. The vertical location of the symbol is determined by the multivariate distance of the vector of means from the reference values. The graphical display in the MP chart enjoys improved visual characteristics as compared with previously suggested methods. Moreover, the perceptual tasks required by the use of the MP chart provide higher accuracy in retrieving the quantitative information. This graphical display is used to display other combined univariate and multivariate statistics, such as measures of dispersion, principal components, and cumulative sums     

Improved Phase I Control Charts for Monitoring Times Between Events

In many situations, the times between certain events are observed and monitored instead of the number of events particularly when the events occur rarely. In this case, it is common to assume that the times between events follow an exponential distribution. Control charts are one of the main tools of statistical process control and monitoring. Control charts are used in phase I to assist operating personnel in bringing the process into a state of statistical control. In this paper, phase I control charts are considered for the observations from an exponential distribution with an unknown mean. A simulation study is carried out to compare the in‐control robustness and out‐of‐control performance of the proposed chart. It is seen that the proposed charts are considerably more in‐control robust than two competing charts and have comparable out‐of‐control properties. Copyright © 2014 John Wiley & Sons, Ltd.