A sum of squares double exponentially weighted moving average chart

The sum of squares double exponentially weighted moving average (SS-DEWMA) chart is proposed to improve the performance of the single SS-EWMA chart, in the detection of initial out-of-control signals. The SS-DEWMA chart uses the sum of squares statistic and it simultaneously monitors the process mean and variance in a single chart. A simulation study is conducted to show that the optimal SS-DEWMA chart provides better zero state average run length (ARL) and standard deviation of the run length (SDRL) performances than the optimal SS-EWMA chart. In addition, as suggested by one of the reviewers, the cyclical steady state ARLs and SDRLs of the SS-DEWMA and SS-EWMA charts are compared, where it is found that the former did not perform as well as the latter. Note that to the best of the authors’ knowledge, a study on DEWMA type charts’ steady state ARL and SDRL performances has yet to be made in the literature. A situation in which the SS-DEWMA chart could be more useful than the SS-EWMA chart is explained in Sections 4 and 6.     

Optimal design of the double sampling X¯ chart with estimated parameters based on median run length

The double sampling (DS) chart when the process parameters are unknown and have to be estimated from a reference Phase-I dataset is studied. An expression for the run length distribution of the DS chart is derived, by conditioning and taking parameter estimation into account. Since the shape and the skewness of the run length distribution change with the magnitude of the mean shift, the number of Phase-I samples and sample sizes, it is shown that the traditional chart’s performance measure, i.e. the average run length, is confusing and not a good representation of a typical chart’s performance. To this end, because the run length distribution is highly right-skewed, especially when the shift is small, it is argued that the median run length (MRL) provides a more intuitive and credible interpretation. From this point of view, a new optimal design procedure for the DS chart with known and estimated parameters is developed to compute the chart’s optimal parameters for minimizing the out-of-control MRL, given that the values of the in-control MRL and average sample size are fixed. The optimal chart which provides the quickest out-of-control detection speed for a specified shift of interest is designed according to the number of Phase-I samples commonly used in practice. Tables are provided for the optimal chart parameters along with some empirical guidelines for practitioners to construct the optimal DS charts with estimated parameters. The optimal charts with estimated parameters are illustrated with a real application from a manufacturing company.     

基于多重相关状态采样的多元EWMA控制图

为提高控制图的监测效率,提出了一种基于多重相关状态采样的多元EWMA控制图,并利用改进后的马尔可夫链方法计算控制图的平均运行长度。根据不同参数下控制图的平均运行长度,分析了控制图在失控和受控状态下的性能表现,并与其它多元EWMA控制图进行比较。模拟结果表明,该控制图具有良好的监测能力。最后用一组模拟数据来说明该方法的使用。     

基于符号秩统计量的非参数阶段累积和控制图

控制图是现代工业生产中常用的质量控制方法,传统控制图通常在数据服从正态分布的情况下进行研究。然而,在实际生产过程中,数据的正态分布假设并不总是成立,且有时分布的情况未知。针对这一状况,可以采用非参数控制图对生产过程进行监控。本文提出了一种基于Wilcoxon符号秩统计量的非参数阶段累积和控制图,通过对非参数累积和控制图的结构进行调整,使得所提出的控制图在监测不同范围的位置偏移时更加灵敏。通过模拟分析了该控制图的受控与失控表现,并与其他非参数控制图进行了比较.结果表明,本文提出的方法具有良好的监控效果。     

A new monitoring design for uni-variate statistical quality control charts

In this research, an iterative approach is employed to analyze and classify the states of uni-variate quality control systems. To do this, a measure (called the belief that process is in-control) is first defined and then an equation is developed to update the belief recursively by taking new observations on the quality characteristic under consideration. Finally, the upper and the lower control limits on the belief are derived such that when the updated belief falls outside the control limits an out-of-control alarm is received. In order to understand the proposed methodology and to evaluate its performance, some numerical examples are provided by means of simulation. In these examples, the in and out-of-control average run lengths (ARL) of the proposed method are compared to the corresponding ARL’s of the optimal EWMA, Shewhart EWMA, GEWMA, GLR, and CUSUM[11] methods within different scenarios of the process mean shifts. The simulation results show that the proposed methodology performs better than other charts for all of the examined shift scenarios. In addition, for an autocorrelated AR(1) process, the performance of the proposed control chart compared to the other existing residual-based control charts turns out to be promising.     

Simple linear profiles monitoring in the presence of within profile autocorrelation

Quality of some processes or products can be characterized effectively by a function referred to as profile. Many studies have been done by researchers on the monitoring of simple linear profiles when the observations within each profile are uncorrelated. However, due to spatial autocorrelation or time collapse, this assumption is violated and leads to poor performance of the proposed control charts. In this paper, we consider a simple linear profile and assume that there is a first order autoregressive model between observations in each profile. Here, we specifically focus on phase II monitoring of simple linear regression. The effect of autocorrelation within the profiles is investigated on the estimate of regression parameters as well as the performance of control charts when the autocorrelation is overlooked. In addition, as a remedial measure, transformation of Y-values is used to eliminate the effect of autocorrelation. Four methods are discussed to monitor simple linear profiles and their performances are evaluated using average run length criterion. Finally, a case study in agriculture field is investigated.     

ARL properties of a sample autocorrelation chart

There are several statistical process control (SPC) methods for detecting the presence of special causes of variation when process observations are inherently autocorrelated. Most of these methods, however, focus on studying changes in the mean or variance of a time series as a signal of the presence of these special causes. It is seldom emphasized in the quality literature that such causes of variation are manifested not only by changes in the mean or variance of a time series but also by the changes in its stochastic behavior. A method that specifically focuses on monitoring this tupe of change is the sample autocorrelation chart (SACC). The SACC is claimed to be capable of detecting changes in mean, variance and stochastic behavior of a series, but no detailed studies have been reported concerning such properties. In this paper, we conduct Monte Carlo experiments to analyze the average run length (ARL) properties of the SACC. The results show that, in comparison with the existing techniques for monitoring autocorrelated processes, the SACC is less sensitive in detecting mean and variance shifts but very competitive in detecting changes in the parameters of an ARMA model.     

基于协变量信息的自适应MEWMA控制图

在统计过程控制中,质量变量通常会受到许多协变量因素的影响,充分利用协变量的有用信息可以进一步提高控制图的灵敏度,因此提出一种新的自适应多元EWMA控制图,并计算ARL进行比较。在MEWMA控制图的基础上引入一个权重函数,根据协变量的有用信息自适应的调节统计量的加权参数：当收集到的协变量信息发生偏移时,选择较大的加权参数,更关注当前和附近时间点观测值的偏移程度;反之则选择较小的参数。大量数值模拟分析表明,充分利用协变量中的有用信息之后,监控效果明显优于MEWMA、MCUSUM控制图。     

A combined synthetic and np scheme for detecting increases in fraction nonconforming

The applications of attribute control charts cover a wide variety of manufacturing processes in which quality characteristics cannot be measured on a continuous numerical scale or even a quantitative scale. The np control chart is an attribute chart used to monitor the fraction nonconforming p of a process. This chart is effective for detecting large process shifts in p. The attribute synthetic chart is also proposed to detect p shifts. It utilizes the information about the time interval or the Conforming Run Length (CRL) between two nonconforming samples. During the implementation of a synthetic chart, a sample is classified as nonconforming if the number d of nonconforming units falls beyond a warning limit. Unlike the np chart, the synthetic chart is more powerful to detect small and moderate p shifts. This article proposes a new scheme, the Syn-np chart, which comprises a synthetic chart and an np chart. Since the Syn-np chart has both the strength of the synthetic chart for quickly detecting small p shifts and the advantage of the np chart of being sensitive to large p shifts, it has a better and more uniform overall performance. Specifically, it is more effective than the np chart and synthetic chart by 73% and 31%, respectively, in terms of Weighted Average of Average Time to Signal (WAATS) over a wide range of p shifts under different conditions.     

A control chart based on likelihood ratio test for detecting patterned mean and variance shifts

Control charts based on generalized likelihood ratio test (GLRT) are attractive from both theoretical and practical points of view. Most of the existing works in the literature focusing on the detection of the process mean and variance are almost based on the assumption that the shifts remain constant over time. The case of the patterned mean and variance changes may not be well discussed. In this research, we propose a new control chart which integrates the exponentially weighted moving average (EWMA) procedure with the GLRT statistics to monitor the process with patterned mean and variance shifts. The attractive advantage of our control chart is its reference-free property. Due to the good properties of GLRT and EWMA procedures, our simulation results show that the proposed chart provides quite effective and robust detecting ability for various types of shifts. The implementation of our proposed control chart is illustrated by a real data example from chemical process control.     

Modified procedures for change point monitoring in linear models

Monitoring on-line data to detect change point as early as possible is an important issue. It is shown that the existing CUSUM test is inefficient to quickly give an alarm when change point does not occur at the early stage of monitoring. In this paper we propose a set of new monitoring procedures to detect coefficients and error variance change in linear regression models. Our proposed modification, which uses a bandwidth parameter to change the beginning time of monitoring, can detect change point more quickly even if it occurs after a relative longer monitoring time. Simulations suggest that the modified procedures compared with the CUSUM test have the same null distribution but higher power and shorter average run length. In particular, we illustrate the effectiveness of our procedures by IBM stock data and Thailand/U.S. foreign exchange rate data.