Approximate design and performance of the robust control charts for monitoring dispersion in Phase I

This article designs and studies the approximate performance of robust dispersion charts, namely, MAD chart, S_n chart, and Q_n chart, in Phase I analysis (recently developed in the literature). The proposed limits are based on false alarm probability for monitoring the dispersion of a process in Phase I analysis. The charting constants are determined to achieve the required nominal FAP (FAP₀). The performance of these structures is evaluated in (i) the attained false alarm rate and (ii) the probability of signals for out‐of‐control situations. The analysis shows that the proposed design of Phase I robust dispersion charts correctly controls the FAP and shows a good performance in detecting the shifts in the process variation. An illustrative example is used to explain the practical implementation of these limits.     

The Phase I Dispersion Charts for Bivariate Process Monitoring

Multivariate control charts are usually implemented in statistical process control to monitor several correlated quality characteristics. Process dispersion charts are used to determine the stability of process variation (which is typically done before monitoring the process location/mean). A Phase‐I study is generally used when population parameters are unknown. This article develops Phase‐I |S| and |G| control charts, to monitor the dispersion of a bivariate normal process. The charting constants are determined to achieve the required nominal false alarm probability (FAP₀). The performance of the proposed charts is evaluated in terms of (i) the attained false rate and (ii) the probability of signaling for out‐of‐control situations. The analysis shows that the proposed Phase‐I bivariate charts correctly control the FAP (the false alarm probability) and detect a shift occurring in the bivariate dispersion matrix with adequate probability. An example is given to explain the practical implementation of these charts. Copyright © 2015 John Wiley & Sons, Ltd.     

On the Performance of Phase‐I Bivariate Dispersion Charts to Non‐Normality

A phase‐I study is generally used when population parameters are unknown. The performance of any phase‐II chart depends on the preciseness of the control limits obtained from the phase‐I analysis. The performance of phase‐I bivariate dispersion charts has mainly been investigated for bivariate normal distribution. However, this assumption is seldom fulfilled in reality. The current work develops and studies the performance of phase‐I |S| and |G| charts for monitoring the process dispersion of bivariate non‐normal distributions. The necessary control charting constants are determined for the bivariate non‐normal distributions at nominal false alarm probability (FAP₀). The performance of these charts is evaluated and compared in a situation when samples are generated by bivariate logistic, bivariate Laplace, bivariate exponential, or bivariate t₅ distribution. The analysis shows that the proper consideration to underlying bivariate distribution in the construction of phase‐I bivariate dispersion charts is very important to give a real picture of in or out of control process status. Copyright © 2016 John Wiley & Sons, Ltd.     

A Bivariate Semiparametric Control Chart Based on Order Statistics

In this article, a new bivariate semiparametric Shewhart‐type control chart is presented. The proposed chart is based on the bivariate statistic (X_(r), Y_(s)), where X_(r) and Y_(s) are the order statistics of the respective X and Y test samples. It is created by considering a straightforward generalization of the well‐known univariate median control chart and can be easily applied because it calls for the computation of two single order statistics. The false alarm rate and the in‐control run length are not affected by the marginal distributions of the monitored characteristics. However, its performance is typically affected by the dependence structure of the bivariate observations under study; therefore, the suggested chart may be characterized as a semiparametric control chart. An explicit expression for the operating characteristic function of the new control chart is obtained. Moreover, exact formulae are provided for the calculation of the alarm rate given that the characteristics under study follow specific bivariate distributions. In addition, tables and graphs are given for the implementation of the chart for some typical average run length values and false alarm rates. The performance of the suggested chart is compared with that of the traditional χ² chart as well as to the nonparametric SN² and SR² charts that are based on the multivariate form of the sign test and the Wilcoxon signed‐rank test, respectively. Finally, in order to demonstrate the applicability of our chart, a case study regarding a real‐world problem related to winery production is presented. Copyright © 2016 John Wiley & Sons, Ltd.     

A New Statistical High‐Quality Process Monitoring Method: The Counted Number Between Omega‐Event Control Charts

Control chart techniques for high‐quality process have attracted great attention in modern precision manufacturing. Traditional control charts are no longer applicable because of high false alarm rate. To solve this problem, in this article a new statistical process monitoring method, the counted number between omega‐event statistical process control charts, abbreviated as CBΩ charts, is proposed. The phrase omega event denotes that one observation falls into some certain interval and the CBΩ chart is to monitor the number of consecutive parts between successive r omega events. On the basis of CBΩ charts, a dual‐CBΩ monitoring scheme is developed. This scheme sets up two CBΩ charts with symmetrical omega events, (μ + ?σ, + ∞) and (? ∞, μ ? ?σ), respectively. The performance of CBΩ charts and dual‐CBΩ monitoring is investigated. Dual‐CBΩ monitoring has shown its capability in detecting both mean and variance shift and convenience in implementation compared with other traditional charts. Dual‐CBΩ monitoring can reduce false alarm rate greatly without introducing an unacceptable loss of sensitivity in detecting out‐of‐control signals in high‐quality process control. Copyright © 2011 John Wiley & Sons, Ltd.     

Support-Vector-Machine-Based False Alarm Filter of Mechatronic Built-in Test

Diagnosing intermittent fault is an important approach to reduce built-in test（BIT） false alarms. Aiming at solving the shortcoming of the present diagnostic method of intermittent fault, and according to the merit of support vector machines （ SVM） which can be trained with a small-sample, an SVM-based diagnostic model of 3 states that include OK state, intermittent state and faulty state is presented. With the features based on the reflection coefficients of an alarm rate （ AR ） model extracted from small vibration samples, these models are trained to diagnose intermittent faults. The experimental results show that this method can diagnose multiple intermittent faults accurately with small training samples and BIT false alarms are reduced.     

Phase II Shewhart‐type Control Charts for Monitoring Times Between Events and Effects of Parameter Estimation

Monitoring times between events (TBE) is an important aspect of process monitoring in many areas of applications. This is especially true in the context of high‐quality processes, where the defect rate is very low, and in this context, control charts to monitor the TBE have been recommended in the literature other than the attribute charts that monitor the proportion of defective items produced. The Shewhart‐type t‐chart assuming an exponential distribution is one chart available for monitoring the TBE. The t‐chart was then generalized to the t_r‐chart to improve its performance, which is based on the times between the occurrences of r (≥1) events. In these charts, the in‐control (IC) parameter of the distribution is assumed known. This is often not the case in practice, and the parameter has to be estimated before process monitoring and control can begin. We propose estimating the parameter from a phase I (reference) sample and study the effects of estimation on the design and performance of the charts. To this end, we focus on the conditional run length distribution so as to incorporate the ‘practitioner‐to‐practitioner’ variability (inherent in the estimates), which arises from different reference samples, that leads to different control limits (and hence to different IC average run length [ARL] values) and false alarm rates, which are seen to be far different from their nominal values. It is shown that the required phase I sample size needs to be considerably larger than what has been typically recommended in the literature to expect known parameter performance in phase II. We also find the minimum number of phase I observations that guarantee, with a specified high probability, that the conditional IC ARL will be at least equal to a given small percentage of a nominal IC ARL. Along the same line, a lower prediction bound on the conditional IC ARL is also obtained to ensure that for a given phase I sample, the smallest IC ARL can be attained with a certain (high) probability. Summary and recommendations are given. Copyright © 2014 John Wiley & Sons, Ltd.     

Monitoring a fraction with easy and reliable settings of the false alarm rate

Monitoring a fraction arises in many manufacturing applications and also in service applications. The traditional p‐chart is easy to use and design but is difficult to achieve the desired false alarm rate. We propose a two‐sided CUSUM Arcsine method that achieves both large and small desired false alarm rates for an in‐control probability anywhere between 0 and 1. The parameters of the new method are calculated easily, without tables, simulation, or Markov chain analysis used by many of the existing methods. The proposed method detects increases and decreases and works for constant and Poisson distributed sample sizes. The CUSUM Arcsine also has a superior sensitivity compared with other easily designed existing methods for monitoring Binomial distributed data. This paper includes an extensive literature review and a taxonomy of the existing monitoring methods for a fraction. Copyright © 2009 John Wiley & Sons, Ltd.     

On Constructing Retrospective ―X Control Chart Limits

In this paper, we address the issue of constructing retrospective ―X control chart limits so as to control the overall probability of a false alarm at a desired level. The standard approach for constructing limits is shown to result in a large overall probability of a false alarm. We propose that an established technique, the analysis of means (ANOM), be used for constructing the retrospective control limits, especially when the subgroup size is small. We compare the performance of the ANOM control limits with that of Bonferroni‐adjusted standard limits through Monte Carlo simulation experiments, and make recommendations as to when each approach can be used. Copyright © 2004 John Wiley & Sons, Ltd.     

Intermittent failure process and false alarm interaction modelling of threshold-based monitoring built-in tests (BITs)

Built-in tests (BITs) are widely used in manufacturing and production systems to find whether system failures occur, whereas the problem of BIT false alarms caused by intermittent failures adds to much trouble for the precise failure detection and diagnosis. Fighting with false alarms caused by intermittent failures is an urgent issue. However, the nature and temporal regularity of intermittent failures are not fully exploited, as well as the relationship between intermittent failure and BIT false alarms. The present paper introduces the method of constructing failure test profile for false alarm assessments. Probabilistic models are proposed of the failure evolution process, as well as the interactions between intermittent failures and false alarms. The false alarm time expectation is derived with the given model, serving as the foundation for the optimisation problem to find the best test threshold to enable the highest BIT capability. A numerical analysis is made to illustrate the proposed model and examine the threshold determination method. An application study is also carried out to show how the model can be applicable in real engineering practices.     

DETECTING EFFECTIVENESS MEASURED BY AURL

This communication addresses the problem of comparing the effectiveness of different control-charting schemes. The measure of average unit run length (AURL) is used to compare the effectiveness of the x-bar charts and the R charts with different sampling frequencies and different sample sizes. Since the trade-off between the frequency of false alarm and the detecting effectiveness is the most critical issue in the design of the control charts, we adjust the control limits of the charts in order to conduct the fair comparisons based on equal frequency of false alarm. © 1997 by John Wiley & Sons, Ltd.     

诊断间歇故障降低BIT虚警

间歇故障的存在及影响是产生BIT(Built-in Test)虚警的一个重要原因,为降低间歇故障引起的虚警,提出一种三状态方法,利用双阈值来区分系统的正常、间歇、永久故障三种状态,并分析得到间歇故障对BIT影响的定量关系,与传统两状态方法相比,基于三状态方法的BIT通过诊断间歇故障,不仅有效地抑制间歇故障引起的虚警,而且还能提高故障检测率。     

一种有效降低红外预警系统虚警率的检测算法

为了解决红外预警系统在受到地物、云层、飞鸟等干扰点的影响下,目标探测虚警率高的问题,提出一种基于目标点角坐标变化的检测算法.该算法是先通过分析系统扫描到的目标点角速度变化情况,将可能的目标点从含有噪声的背景中分离出来;然后利用内点惩罚函数及最速下降法相结合的最优值算法求出每个目标点的航路;最后,对航路的真实性进行判断,从而检测出运动目标.通过实验证明了该算法抗噪声干扰能力强,易于硬件实现,能够有效地降低红外预警系统的虚警率.     

An Evaluation of Wheeler's Method for Monitoring the Rate of Rare Events

Its wide application in practice makes the monitoring of the rate of rare events a popular research topic. Recently a researcher proposed plotting the counts between events on an individuals X‐chart with an upper control limit to detect process improvement and plotting the reciprocals of the counts on an X‐chart to detect process deterioration. He also used the median as the center line and the median moving range to obtain control limits in both control charts to address the problem of the standard deviation estimate inflation caused by extreme values. In our paper, we investigated the statistical performance of the four proposed approaches using simulation. We find using the mean results in a high proportion of ineffective control limits, while using the median avoids the issue of ineffective control limits but produces an unacceptably high proportion of false alarms. Copyright © 2016 John Wiley & Sons, Ltd.     

On the Use of the Expected ARL Metric for Control Charts Based on Estimated Parameters

At the origination of the Shewhart control chart, it was assumed that the process parameters were known. The in‐control Average Run Length (ARL) and the probability of having a false alarm (P) were introduced as metrics to indicate the in‐control performance. These two metrics are related when the process data are i.i.d. normally distributed: the ARL equals 1/P. When the process parameters are unknown and have to be estimated, a similar relation holds for each estimated control chart, but the relation between the expected ARL (the average of the ARLs of all possible estimated charts) and the expectedP is different. Control charts based on estimates are often designed such that the in‐control ARL equals a predefined value. This paper shows that the expected in‐control ARL is a less suitable design criterion. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic probability control limits for CUSUM charts for monitoring proportions with time-varying sample sizes

We consider the problem of monitoring a proportion with time-varying sample sizes. Control charts are generally designed by assuming a fixed sample size or a priori knowledge of a sample size probability distribution. Sometimes, it is not possible to know, or accurately estimate, a sample size distribution or the distribution may change over time. An improper assumption for the sample size distribution could lead to undesirable performance of the control chart. To handle this problem, we propose the use of dynamic probability control limits (DPCLs) which are determined successively as the sample sizes become known. The method is based on keeping the conditional probability of a false alarm at a predetermined level given that there has not been any earlier false alarm. The control limits dynamically change, and the in-control performance of the chart can be controlled at the desired level for any sequence of sample sizes. The simulation results support this result showing that there is no need for any assumption of a sample size distribution with the use of this proposed approach.     

An efficient double exponentially weighted moving average Benjamini‐Hochberg control chart to control false discovery rate

A control chart based on double exponentially weighted moving average and Benjamini‐Hochberg multiple testing procedure is proposed that controls the false discovery rate (FDR). The proposed control chart is based on probabilities (or P values) to accept or reject the null hypothesis of the underlying process is in control. To make a decision, instead of using only the current probability, previous “m” probabilities are considered. The performance of the control chart is evaluated in terms of average run length (ARL) using Monte Carlo simulations. Procedure for estimation of parameters used in the control chart is also discussed. The proposed control chart is compared with previous control charts and found to be more efficient in controlling the false discovery rate.     

Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes

The nonparametric (distribution-free) control charts are robust alternatives to the conventional parametric control charts when the form of underlying process distribution is unknown or complicated. In this paper, we consider two new nonparametric control charts based on the Hogg–Fisher–Randle (HFR) statistic and the Savage rank statistic. These are popular statistics for testing location shifts, especially in right-skewed densities. Nevertheless, the control charts based on these statistics are not studied in quality control literature. In the current context, we study phase-II Shewhart-type charts based on the HFR and Savage statistics. We compare these charts with the Wilcoxon rank-sum chart in terms of false alarm rate, out-of-control average run-length and other run length properties. Implementation procedures and some illustrations of these charts are also provided. Numerical results based on Monte Carlo analysis show that the new charts are superior to the Wilcoxon rank-sum chart for a class of non-normal distributions in detecting location shift. New charts also provide better control over false alarm when reference sample size is small.     

Economic Design Approach for an SPC Inspection Procedure Implementing The Adaptive C Chart

The present paper proposes a design approach for a statistical process control (SPC) procedure implementing a c control chart for non‐conformities, with the aim to minimize the hourly total quality‐related costs. The latter take into account the costs arising from the non‐conforming products while the process is in‐control and out‐of‐control, for false alarms, for assignable cause locations and system repairs, for sampling and inspection activities and for the system downtime. The proposed economic optimization approach is constrained by the expected hourly false alarms frequency, as well as the available labor resource level. A mixed integer non‐linear constrained mathematical model is developed to solve the treated optimization problem, whereas the Generalized Reduced Gradient Algorithm implemented on the solver of Microsoft Excel is adopted to resolve it. In order to illustrate the application of the developed procedure, a numerical analysis based on a fractional factorial design scheme, to investigate on the influence of several operating and costs parameters, is carried out, and the related considerations are given. Finally, the obtained results show that only few parameters have a meaningful effect on the selection of the optimal SPC procedure. Copyright © 2013 John Wiley & Sons, Ltd.     

Designing Phase I Shewhart X¯charts: Extended tables and software

Control charts play an important role in Phase I studies, which are conducted to establish process control and generate reference data for parameter estimation and calculation of prospective (Phase II) control limits. Researchers have tabulated the necessary charting constants for the normal theory–based Phase I Shewhart $\overline{X}$ chart for the process mean to achieve a desired nominal false alarm probability given the number of Phase I subgroups, m, up to 15. However, in practice, when parameters are estimated, the currently recommended number of Phase I subgroups is much larger than covered by their tables. Recognizing the need and taking advantage of some recently available software and computing resources, an extension to these tables is provided for m = 3(1)10 , 15(5)30 , 50(25)300 and n = 3 , 5 , 7 , 10. In addition to the tables, an R program is provided to calculate the charting constant, on demand, for user‐given values of nominal false alarm probability, m, and n. An appendix shows the details of how the program should be used.