Cumulative Sum Control Charts for Monitoring Weibull‐distributed Time Between Events

The Weibull distribution can be used to effectively model many different failure mechanisms due to its inherent flexibility through the appropriate selection of a shape and a scale parameter. In this paper, we evaluate and compare the performance of three cumulative sum (CUSUM) control charts to monitor Weibull‐distributed time‐between‐event observations. The first two methods are the Weibull CUSUM chart and the exponential CUSUM (ECUSUM) chart. The latter is considered in literature to be robust to the assumption of the exponential distribution when observations have a Weibull distribution. For the third CUSUM chart included in this study, an adjustment in the design of the ECUSUM chart is used to account for the true underlying time‐between‐event distribution. This adjustment allows for the adjusted ECUSUM chart to be directly comparable to the Weibull CUSUM chart. By comparing the zero‐state average run length and average time to signal performance of the three charts, the ECUSUM chart is shown to be much less robust to departures from the exponential distribution than was previously claimed in the literature. We demonstrate the advantages of using one of the other two charts, which show surprisingly similar performance. Copyright © 2014 John Wiley & Sons, Ltd.     

Performance study of change-point detection thresholds for cumulative sum statistic in a sequential context

Sequential detection is based on a recursive statistic and a threshold it must reach to report a change. In this paper, we consider the score-based cumulative sum statistic and propose to evaluate the detection performance of some thresholds on simulated data. Three thresholds come from the literature: the Wald constant, the empirical constant, and the conditional empirical instantaneous threshold (the latter two are built by a simulation-based procedure). Two new thresholds are built by a simulation-based procedure: the first one is instantaneous, the second is a dynamical version of the previous one. The thresholds' performance measured by an estimation of the mean time between false alarm (MTBFA) and the average detection delay (ADD) are evaluated on independent and autocorrelated data for several scenario, according to the detection objective and the real change in the data. The simulations allow us to compare the difference between the thresholds' results and to see that their performances prove to be robust when a parameter of the prechange regime is misestimated or when the data independence assumption is violated. We found also that the conditional empirical threshold is the best at minimizing the detection delay while maintaining the given false alarm rate. However, on real data, we suggest to use the dynamic instantaneous threshold because it is the easiest to build for practical implementation.     

Discussion

In this discussion, we give a short overview of some of the uses of artificial neural networks in practice. This is not intended to be an exhaustive list, but it includes some widely used industrial examples with which we are familiar. From our experience, we also attempt to point out why they are used and what the relative advantages and disadvantages of using a neural network over a traditional statistical method might be.     

Adaptive nonparametric CUSUM scheme for detecting unknown shifts in location

In this paper, we provide a sequential rank-based adaptive nonparametric cumulative sum control chart for detecting a range of shifts in the location parameter. This chart is a self-starting scheme, and thus can be used to monitor processes at the start-up stages rather than having to wait for the accumulation of sufficiently large calibration samples. It does not require any prior knowledge of the underlying distribution. The choice of the chart parameters is studied and a simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also efficiently detects various magnitudes of shifts. An illustrative example is also given to introduce the implementation of this proposed control chart.     

Detecting Change Points by Fourier Analysis

The cumulative sum (CUSUM) is a basic diagnostic tool in the analysis of change-point data. It is shown that Fourier analysis of the CUSUM can be a useful supplementary tool in such analyses. The technique is applied to three data sets that have appeared previously in the statistical literature.     

Development of a real-time non-intrusive appliance load monitoring system: An application level model

The research “Behavior Change and Energy Use” (US Department of Energy and Climate Change, 2011) [1] shows that with better information in the monthly electricity bill, the Energy Performance Certificate (EPC) can encourage people to reduce their energy usage. That is why smart meters - the emerging technology to help people to know their monthly energy consumption, are gradually replacing mechanical power meters. In this paper, we investigate a special energy monitoring process named Non-Intrusive Appliance Load Monitoring (NIALM), which is potentially the best method to give consumers pertinent information with respect to power consumption. However, real-time feedback feature in a low cost NIALM system is still a big challenge in such technology because of the complication in NIALM’s algorithms. System on Chip (SoC) technology can solve this challenge. Besides including high-speed interconnection and multi-processors, integrating Field-Programmable Gate Array (FPGA) into SoCs may be the most important evolution, which provides developers a powerful tool to develop a low cost but high performance system. Therefore, in this paper we proposed a development of a real-time NIALM system based on the SoC with FPGA acceleration.     

平稳过程趋势项变点的CUSUM检验

对平稳过程趋势项中的变点检测问题,基于最小二乘估计残差构造CUSUM型统计量.同时,在原假设下得到了其渐近分布,在备择假设下证明了该检验的容许性.蒙特卡罗数值模拟表明,文中所给检验在检验趋势项系数变点时具有较好的势,且犯第一类错误的概率较小.     

ON‐LINE MONITORING OF POLLUTION CONCENTRATIONS WITH AUTOREGRESSIVE MOVING AVERAGE TIME SERIES

The concentration of aerosol particles, largely caused by traffic volume and often enhanced during temperature inversion episodes in the cold season, can be a concern for human health in the urban environment. This particulate matter is typically recorded as PM₁₀, the total mass of particles below 10 μm in diameter. It is suspected that, within the PM₁₀ class, ultrafine particles ( < 100 nm) may be responsible for causing respiratory and cardiovascular diseases. Because of their low mass, ultrafine particles are hard to detect, and researchers try to utilize PM₁₀ in combination with nitrogen oxides NO_x and other trace gases to monitor their dynamic evolution. To meet pollution standards set by national government and European Union regulation, the city of Klagenfurt, Austria, began using calcium magnesium acetate as a deicer on 11 January 2012, hoping to literally glue pollutants to the ground and thereby reducing pollution concentrations. With the statistical methodology developed in this article, the dynamic evolution of PM₁₀ and NO_x is traced for the time period starting 4 January and ending 25 January 2012, and a change in dynamics is found. The findings are based on on‐line monitoring procedures that sequentially detect structural breaks in the mean and the parameter values of an autoregressive moving average process. These are defined in terms of model residuals and one‐step ahead predictors. Theoretical properties are studied, and a simulation study shows that the proposed procedures work well in finite samples.     

Parameter change test for random coefficient integer-valued autoregressive processes with application to polio data analysis

Abstract.  In this paper, we consider the problem of testing for a parameter change in a first-order random coefficient integer-valued autoregressive [RCINAR(1)] model. We employ the cumulative sum (CUSUM) test based on the conditional least-squares and modified quasi-likelihood estimators. It is shown that under regularity conditions, the CUSUM test has the same limiting distribution as the supremum of the squares of independent Brownian bridges. The CUSUM test is then applied to the analysis of the monthly polio counts data set.