Sequential procedures for monltoring the parameters of the autoregressive model relative to unspecified targets

Sequential procedures are developed for monitoring the parameters of a time dependent autoregressive model relative to unspecified targets. Such a problem arises when we need to monitor the parameters for changes from their unknown initial values (the unspecified targets), instead of from specified targets. For this purpose, scores type statistics are proposed which: (1) reflect changes in the parameters from their initial values without requiring any input about these values; and (2) are aimed at detecting arbitrary shifts in the parameters, instead of at restrictive "one point" shift alternatives. The procedures developed are capable of monitoring any one of, or any combination of, the mean, variance or correlation structure of an autoregressive sequence of known finite order. Their false signal rates are controlled, and their performance under local shift     

Seasonal Unit Root Tests Under Structural Breaks*

Abstract. In this paper, several seasonal unit root tests are analysed in the context of structural breaks at known time and a new break corrected test is suggested. We show that the widely used HEGY test, as well as an LM variant thereof, are asymptotically robust to seasonal mean shifts of finite magnitude. In finite samples, however, experiments reveal that such tests suffer from severe size distortions and power reductions when breaks are present. Hence, a new break corrected LM test is proposed to overcome this problem. Importantly, the correction for seasonal mean shifts bears no consequence on the limiting distributions, thereby maintaining the legitimacy of canonical critical values. Moreover, although this test assumes a breakpoint a priori, it is robust in terms of misspecification of the time of the break. This asymptotic property is well reproduced in finite samples. Based on a Monte‐Carlo study, our new test is compared with other procedures suggested in the literature and shown to hold superior finite sample properties.     

A mixed control chart using process capability index

Control charts are considered as a compulsory tool for the monitoring and improvement of the quality of products. The commonly used attribute and the variable control charts are unsatisfactory for process monitoring. To overcome this di?culty, we proposed a monitoring scheme that is an improved technique based on the joint merits of the attribute as well as the variable control charts. The control chart coe?cients have been determined for in-control and out-of-control situations for specified average run length values using simulation. The e?ciency of the proposed control chart has been evaluated using average run length criteria for different values of the process settings. A practical example has been studied for implementation of the proposed technique. It has been observed that the proposed chart performs well for the mixed technique under the process capability index.     

ESTIMATION OF THE PREDICTION ERROR VARIANCE AND AN R2 MEASURE BY AUTOREGRESSIVE MODEL FITTING

Abstract. For predicting the future values of a stationary process { x_t } ( t = 0, pL 1, pL 2,…) on the basis of its past, two key parameters are the variance V ( h ), h ≥ 1, of the h -step prediction error and Z ( h ) ={ R (0) - V ( h )}/ R (0), the corresponding measure, in an R ² sense, of the predictability of the process from its past, where R (0) denotes the process variance. The estimation of V ( h ) and Z ( h ) from a realization of T consecutive observations of { x_t } is considered, without requiring that the process follows a finite parameter model. Three different autoregressive estimators are examined and are shown to be asymptotically equivalent in the sense that as T ∝ they have the same asymptotic normal distribution. The question of bias in estimating these parameters is also examined and a bias correction is proposed. Finite sample behaviour is investigated by a simulation study.     

A partial sequential t-test

Several authors have proposed sequential test procedures for testing one sided hypotheses about the mean μ of a normal distribution with unknown variance σ². Some of these procedures have concerned themselves with tests for units of (μ/σ). I this work, a sequential test procedure is introduced for hypoth-eses concerned with μ itself. In the present procedure the transformed observa-tions follow a central t-distribution as distinct from the noncentral t-distribution used in pnvious tests. Insights into properties of the operating characteristic and the average sample number functions are found for the present test; specifically, approximations to the theoretical operating characteristic function are derived and the sensitivity of the average sample number function to changes in some of the test parameters is investigated.     

Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series

This article proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by non-stationary volatility. The assumed volatility process can accommodate discrete breaks, smooth transition variation as well as trending volatility. We develop wild bootstrap sup-Wald tests of the null hypothesis that the process is either stationary [I(0)] or has a unit root [I(1)] throughout the sample. We also propose a sequential procedure to estimate the number of persistence breaks based on ordering the regime-specific bootstrap p-values. The asymptotic validity of the advocated procedures is established both under the null of stability and a variety of persistence change alternatives. A comparison with existing tests that assume homoskedasticity illustrates the finite sample improvements offered by our methods. An application to OECD inflation rates highlights the empirical relevance of the proposed approach and weakens the case for persistence change relative to existing procedures.     

SBR工艺除磷过程与种群结构在线监测

For efficient energy consumption and control of effluent quality, the cycle duration for a sequencing batch reactor (SBR) needs to be adjusted by real-time control according to the characteristics and loading of wastewater. In this study, an on-line information system for phosphorus removal processes was established. Based on the analysis for four systems with different ecological community structures and two operation modes, anaerobic-aerobic process and anaerobic-anaerobic process, the characteristic patterns of oxidation-reduction potential (ORP) and pH were related to phosphorous dynamics in the anaerobic, anoxic and aerobic phases, for determination of the end of phosphorous removal. In the operation mode of anaerobic-aerobic process, the pH profile in the anaerobic phase was used to estimate the relative amount of phosphorous accumulating organisms (PAOs) and glycogen accumulating organisms (GAOs), which is beneficial to early detection of ecology community shifts. The on-line sensor values of pH and ORP may be used as the parameters to adjust the duration for phosphorous removal and community shifts to cope with influent variations and maintain appropriate operation conditions.     

Maximum Likelihood Estimates of a Class of One-Dimensional Stochastic Differential Equation Models From Discrete Data

The problem of computing the maximum likelihood estimate of the parameters of a specific class of stochastic differential equation (SDE) models with linear drift whose sample paths are observed at discrete time points is considered. This estimate is obtained as in Cleur and Manfredi (1999) by discretizing the explicit expressions for the estimates which maximize the likelihood function in continuous time, by discretizing the likelihood function through a quadrature approximation before maximizing it, and by maximizing the likelihood function of the Euler scheme approximation to the underlying continuous process. Simulation results indicate that, for the constellation of parameter values considered, all three approaches lead to very similar results.     

Testing for Change in Long‐Memory Stochastic Volatility Time Series

In this article, change‐point problems for long‐memory stochastic volatility (LMSV) models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting behavior of CUSUM‐ and Wilcoxon‐type test statistics is derived. In this context, a limit theorem for the two‐parameter empirical process of LMSV time series is proved. In particular, it is shown that the asymptotic distribution of CUSUM test statistics may not be affected by long memory, unlike Wilcoxon test statistics which are typically influenced by long‐range dependence. To avoid the estimation of nuisance parameters in applications, the usage of self‐normalized test statistics is proposed. The theoretical results are accompanied by an analysis of Standard & Poor's 500 daily closing indices with respect to structural changes and by simulation studies which characterize the finite sample behavior of the considered testing procedures when testing for changes in mean and in variance.     

EWMA Charts for Monitoring the Mean and the Autocovariances of Stationary Gaussian Processes

Abstract

In this article simultaneous individual control charts for the mean and the autocovariances of a stationary process are introduced. All control schemes are EWMA (exponentially weighted moving average) charts. A multivariate quality characteristic is considered. It describes the behavior of the mean and the autocovariances. This quantity is transformed to a one-dimensional variable by using the Mahalanobis distance. The control statistic is obtained by exponentially smoothing these variables. Another control procedure is based on a multivariate EWMA recursion applied directly to our multivariate quality characteristic. After that the resulting statistic is transformed to a univariate random variable. Besides modified control charts we consider residual charts. For the residual charts the same procedure is used but the original observations are replaced by the residuals. In an extensive simulation study all control schemes are compared with each other. The target process is assumed to be an ARMA(1, 1) process.     

Minimum risk sequential point estimation of the stress-strength reliability parameter for exponential distribution

Abstract

In this article, using purely and two-stage sequential procedures, the problem of minimum risk point estimation of the reliability parameter (R) under the stress–strength model, in case the loss function is squared error plus sampling cost, is considered when the random stress (X) and the random strength (Y) are independent and both have exponential distributions with different scale parameters. The exact distribution of the total sample size and explicit formulas for the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Using the law of large numbers and Monte Carlo integration, the exact distribution of the stopping rule under the purely sequential procedure is approximated. Moreover, it is shown that both proposed sequential procedures are finite and for special cases the exact distribution of stopping times has a degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally, using a real data set, the procedures are clearly illustrated.     

A 13C n.m.r. study of the sulphonation of novolacs

A parameter scheme has been devised for predicting the ¹³C shifts of atoms in the aromatic rings of phenols substituted with SO^?₃, CH₂Ar and CH₃ in an alkaline medium, from the measured shifts of 30 different substituted benzene rings. The application of the scheme to novolacs is considered before the scheme is used to interpret the changes of chemical shift that occur upon sulphonation of one such sample. In the aromatic carbon region the sites of substitution on the rings are identified. In the upfield region of the spectrum a substantial alteration to the pattern of shifts from the bridging methylene groups was noted: once a ring had been sulphonated the methylene bridge might break to yield methylol groups, which then to a large extent reformed as methylene and dimethylene ether (CH₂OCH₂) links, but with an increased proportion of abutments on sites para with respect to the phenolic group.     

A Novel Data Preprocessing Method for the Modeling and Prediction of Freeze-Drying Behavior of Apples: Multiple Output–Dependent Data Scaling (MODDS)

In the present study, the freeze drying behavior of apples have been modeled and predicted. Because freeze-drying is a very expensive and complex process, modeling of the freeze-drying process is a challenging task. In this study, a novel data scaling method called multiple output–dependent data scaling (MODDS) has been proposed and combined with an adaptive neuro-fuzzy inference system (ANFIS) to forecast the moisture content (MC), moisture ratio (MR), and drying rate (DR) values, which are outputs of freeze-drying behavior of apples. The input parameters of the freeze drying system are the sample thicknesses, drying time, pressure, relative humidity, chamber temperature, and sample temperature. Using the input parameters, the outputs of the freeze-drying process of apples were predicted using a hybrid system based on MODDS and ANFIS. In the first stage, only input parameters were scaled using MODDS. In the second stage, the outputs of freeze drying of apples were predicted with the scaled input parameters using ANFIS algorithm. Ninety-two samples were included in the data set, including 10-, 7-, and 5-mm samples. In order to evaluate the performance of the proposed model, the mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), coefficient of determination (R ²), index of agreement (IA), and mean absolute percentage error (MAPE) were used. Though MSE values of 2.48, 0.035, and 0.011 and IA values of 0.887, 0.887, and 0.466 were obtained for MC, MR, and DR, respectively, using the ANFIS prediction algorithm the hybrid MODDS-ANFIS model achieved MSE values of 0.003, 0.00005, and 0.00007 and IA values of 0.999, 0.999, and 0.993 for the prediction of MC, MR, and DR, respectively. The results obtained demonstrate that the proposed hybrid system is a robust and efficient method for the modeling and prediction of freeze-drying behavior of apples.     

Banded and tapered estimates for autocovariance matrices and the linear process bootstrap

We address the problem of estimating the autocovariance matrix of a stationary process. Under short range dependence assumptions, convergence rates are established for a gradually tapered version of the sample autocovariance matrix and for its inverse. The proposed estimator is formed by leaving the main diagonals of the sample autocovariance matrix intact while gradually down‐weighting off‐diagonal entries towards zero. In addition, we show the same convergence rates hold for a positive definite version of the estimator, and we introduce a new approach for selecting the banding parameter. The new matrix estimator is shown to perform well theoretically and in simulation studies. As an application, we introduce a new resampling scheme for stationary processes termed the linear process bootstrap (LPB). The LPB is shown to be asymptotically valid for the sample mean and related statistics. The effectiveness of the proposed methods are demonstrated in a simulation study.     

现代煤化工设计煤质确定方法的探讨

设计煤质数据是现代煤化工项目中重要的设计基础,直接影响到项目能否稳定运行。本文根据神华煤化工项目的建设经验,提出了原料煤设计煤质确定的程序方法。目前煤化工项目常用的煤气化技术包括:干粉气流床气化技术、水煤浆气化技术、固定床碎煤加压气化技术及流化床气化技术。根据不同气化技术对煤质的不同要求,归纳出了在煤化工项目确定设计煤质过程中所需的煤质分析项目。在煤样的采集与分析工作过程中,采集的煤样具有代表性是保证获得典型煤质数据的前提。文中根据项目配套的煤源矿井所处的生产阶段不同,提出了不同的煤样采集方案包括采样地点、煤样类型、采样质量、煤样粒度及采样方式等。同时对后续煤样制备与分析及最终数据校核工作进行了探讨。     

A Gaussian quadrature analysis of linear sweep voltammetry

The application of Gaussian Quadrature (GQ) procedures to the evaluation of i—E curves in linear sweep voltammetry is advocated. It is shown that a high degree of precision is achieved with these methods and the values obtained through GQ are in good agreement with (and even better than) the values reported in literature by Nicholson-Shain, for example. Another welcome feature with GQ is its ability to be interpreted as an elegant, efficient analytic approximation scheme too. A comparison of the values obtained by this approach and by a recent scheme based on series approximation proposed by Oldham is made and excellent agreement is shown to exist.Three different versions of GQ are described.     

Determination of multiple dependent state repetitive group sampling plan based on the process capability index

Abstract

In this article, we propose a sampling plan called a multiple dependent state repetitive group sampling plan for variable inspection based on the process capability index C_pk. The proposed sampling plan is applicable for the inspection of normally distributed quality characteristics when both mean and variance are assumed to be unknown. This new plan under variable inspection will be very useful particularly in compliance testing. Tables are also constructed for the determination of optimal parameters for easy selection and implementation of the plan. The optimal parameters can be determined by using the approach of two points on the operating characteristic curve. Symmetric and asymmetric cases based on the fraction nonconforming by the lower and the upper specification limits are also considered. Advantages of the proposed plan are also discussed. It is also shown that the proposed plan outperforms other existing sampling plans under variable inspection.     

Multivariate Control Charts for Monitoring the Process Mean and Variability Using Sequential Sampling

Abstract

Traditional control charts for process monitoring are based on taking samples of fixed size at equally spaced sampling points. As an alternative to these traditional fixed sampling rate (FSR) control charts, variable sampling rate (VSR) control charts change the sampling rate as a function of the data from the process. With VSR control charts the sampling rate is increased whenever there is some indication of a problem with the process, and decreased when there is no indication of a problem. This paper investigates a type of VSR control chart based on sequential sampling in which the sample size used at a sampling point is a function of the data from the current and past sampling points. Sequential sampling is investigated in the context of simultaneously monitoring both the mean and variability of a multivariate normal process. Multivariate exponentially weighted moving average (MEWMA) control charts based on sample means and on the sum of the squared deviations from the target are considered. When sequential sampling is used in a combination of the MEWMA charts based on sample means and on squared deviations from the target, the average performance is much better than that of the standard FSR multivariate control charts that have traditionally been used.     

Effects of ultrasonic vibration assisted milling with laser ablation pretreatment on fatigue performance and machining efficiency of SiCf/SiC composites

Due to the poor machinability of SiC_f/SiC parts in machining, many problems are caused, such as low machining efficiency, poor machining quality and high processing cost, which seriously limit its manufacturing and application. A novel process ultrasonic vibration assisted milling with laser ablation pretreatment (UVAMLAP) was proposed to optimize the fatigue performance and machining efficiency of SiC_f/SiC parts. This process was used to fabricate specimens, which were then tested for tensile strength and fatigue performance. The results show that UVAMLAP could enhance surface quality, and increase the tensile strength and residual tensile strength of the sample by 9.4% and 13.5%. This process can avoid damage aggravation in the initial stage of failure, weaken matrix fracture and interface debonding velocity, and reduce fatigue performance degradation caused by machining damage. In addition, comprehensive evaluation based on multi-dimensional indicators such as milling quality, machining efficiency and tool cost for machining strategy was carried out by taking tensile sample machining as an example. The UVAMLAP process can not only improve the machined surface quality, but also reduce the machining time by 31.3% and the tool cost by 75%. Therefore, UVAMLAP provides a feasible process scheme for high-efficiency and low-damage machining of SiC_f/SiC parts.     

Melt index prediction based on fuzzy neural networks and PSO algorithm with online correction strategy

A black‐box modeling scheme to predict melt index (MI) in the industrial propylene polymerization process is presented. MI is one of the most important quality variables determining product specification, and is influenced by a large number of process variables. Considering it is costly and time consuming to measure MI in laboratory, a much cheaper and faster statistical modeling method is presented here to predicting MI online, which involves technologies of fuzzy neural network, particle swarm optimization (PSO) algorithm, and online correction strategy (OCS). The learning efficiency and prediction precision of the proposed model are checked based on real plant history data, and the comparison between different learning algorithms is carried out in detail to reveal the advantage of the proposed best‐neighbor PSO (BNPSO) algorithm with OCS. © 2011 American Institute of Chemical Engineers AIChE J, 2012