A combined control scheme for monitoring the frequency and size of an attribute event

A traffic accident can be considered as an example of the attribute events, and the number of the injured in each accident is called the event size. Some control charts have been developed for monitoring either the time interval (T) between the occurrences of an event or the event size (C) in each occurrence. This article studies the statistical monitoring of the attribute events in which T and C are monitored simultaneously and C is an integer. Essentially, it integrates a T chart and a C chart, and is therefore referred to as a T&C scheme. Our studies show that the new chart is more effective than an individual T chart or C chart for detecting the out-of-control status of the event, in particular for detecting downward shifts (sparse occurrence and/or small size). Another desirable feature of the T&C scheme is that its detection effectiveness is more invariable against different types of shifts (i.e. T shift, C shift and joint shift in T&C) compared with an individual T or C chart. The improvement in performance is achieved due to the simultaneous monitoring of T and C. The T&C scheme can be applied in manufacturing systems and especially in non-manufacturing sectors (e.g. supply chain management, health care industry, disaster management and security control).     

Mean residual life ordering

A new partial ordering among life distributions in terms of their mean residual life is introduced. This ordering is weaker than the hazard rate ordering but it is stronger than the variability ordering. Characterizations of the DMRL and NBUE distribution are given.     

A Semi‐empirical Bayesian Chart to Monitor Weibull Percentiles

This paper develops a Bayesian control chart for the percentiles of the Weibull distribution, when both its in‐control and out‐of‐control parameters are unknown. The Bayesian approach enhances parameter estimates for small sample sizes that occur when monitoring rare events such as in high‐reliability applications. The chart monitors the parameters of the Weibull distribution directly, instead of transforming the data as most Weibull‐based charts do in order to meet normality assumption. The chart uses accumulated knowledge resulting from the likelihood of the current sample combined with the information given by both the initial prior knowledge and all the past samples. The chart is adapting because its control limits change (e.g. narrow) during Phase I. An example is presented and good average run length properties are demonstrated.     

A Robust Control Chart for Monitoring the Mean of an Autocorrelated Process

Residual control charts are frequently used for monitoring autocorrelated processes. In the design of a residual control chart, values of the true process parameters are often estimated from a reference sample of in-control observations by using least squares (LS) estimators. We propose a robust control chart for autocorrelated data by using Modified Maximum Likelihood (MML) estimators in constructing a residual control chart. Average run length (ARL) is simulated for the proposed chart when the underlying process is AR(1). The results show the superiority of the new chart under several situations. Moreover, the chart is robust to plausible deviations from assumed distribution of errors.     

Variable Sampling Interval Cumulative Count of Conforming Chart with Runs Rules

The cumulative count of conforming (CCC) chart is effective in detecting very low fraction of nonconforming items for high yield manufacturing processes. In this study, a combination of runs rules and variable sampling interval feature is proposed to a lower sided CCC chart by inspecting the items one by one. The performance measures of the control chart are derived by using the Markov chain approach. The numerical comparisons show that the performance of the CCC chart can be improved by adding the runs rules and varying the sampling interval.     

A new adaptive EWMA control chart using auxiliary information for monitoring the process mean

The adaptive memory-type control charts, including the adaptive exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, have gained considerable attention because of their excellent speed in providing overall good detection over a range of mean shift sizes. In this paper, we propose a new adaptive EWMA (AEWMA) chart using the auxiliary information for efficiently monitoring the infrequent changes in the process mean. The idea is to first estimate the unknown process mean shift using an auxiliary information based mean estimator, and then adaptively update the smoothing constant of the EWMA chart. Using extensive Monte Carlo simulations, the run length profiles of the AEWMA chart are computed and explored. The AEWMA chart is compared with the existing control charts, including the classical EWMA, CUSUM, synthetic EWMA and synthetic CUSUM charts, in terms of the run length characteristics. It turns out that the AEWMA chart performs uniformly better than these control charts when detecting a range of mean shift sizes. An illustrative example is also presented to demonstrate the working and implementation of the proposed and existing control charts.     

Bivariate copulas on the Hotelling's T2 control chart

In this paper, we propose five types of copulas on the Hotelling's T² control chart when observations are from exponential distribution and use the Monte Carlo simulation to compare the performance of the control chart, which is based on the Average Run Length (ARL) for each copula. Five types of copulas function for specifying dependence between random variables are used and measured by Kendall's tau. The results show that the copula approach can be fitted the observation and we can use copula as an option for application on Hotelling's T² control chart.     

Univariate fast initial response statistical process control with taut strings

We present a novel real-time univariate monitoring scheme for detecting a sustained departure of a process mean from some given standard assuming a constant variance. Our proposed stopping rule is based on the total variation of a nonparametric taut string estimator of the process mean and is designed to provide a desired average run length for an in-control situation. Compared to the more prominent CUSUM fast initial response (FIR) methodology and allowing for a restart following a false alarm, the proposed two-sided taut string (TS) scheme produces a significant reduction in average run length for a wide range of changes in the mean that occur at or immediately after process monitoring begins. A decision rule for when to choose our proposed TS chart compared to the CUSUM FIR chart that takes into account both false alarm rate and average run length to detect a shift in the mean is proposed and implemented. Supplementary materials are available online.     

一种新颖实用的PLC防盗系统

PLC可编程控制器以其软件简单易学、使用简便、抗干扰能力强、运行可靠等优点在工业控制领域得到了广泛的运用.提出了一种基于PLC控制部件为核心的防盗系统方案,并对系统各部件的设置进行了较为详细的说明.     

Sequential monitoring of high-dimensional time series

In the paper we derive new types of multivariate exponentially weighted moving average (EWMA) control charts which are based on the Euclidean distance and on the distance defined by using the inverse of the diagonal matrix consisting of the variances. The design of the proposed control schemes does not involve the computation of the inverse covariance matrix and, thus, it can be used in the high-dimensional setting. The distributional properties of the control statistics are obtained and are used in the determination of the new control procedures. Within an extensive simulation study, the new approaches are compared with the multivariate EWMA control charts which are based on the Mahalanobis distance.