Response Surface Models With Random Block Effects

In many experimental situations, a response surface design is divided into several blocks to control an extraneous source of variation. The traditional approach in most response surface applications is to treat the block effect as fixed in the assumed model. There are, however, situations in which it is more appropriate to consider the block effect as random. This article is concerned with inference about a response surface model in the presence of a random block effect. Since this model also contains fixed polynomial effects, it is considered to be a mixed-effects model. The main emphasis of the proposed analysis is on estimation and testing of the fixed effects. A two-stage mixed-model procedure is developed for this purpose. The variance components due to the random block effect and the experimental error are first estimated and then used to obtain the generalized least squares estimator of the fixed effects. This procedure produces the so-called Yates combined intra- and inter-block estimator. By contrast, the Yates intra-block estimator is the one obtained when the block effect is treated as fixed. In particular, if the response surface design blocks orthogonally, then the two estimators are shown to be identical. An experiment on bonding galvanized steel bars is used to motivate the problem and illustrate the results.     

Asymptotic efficiency properties of least squares in an ultrastructural model

This paper considers the estimation of both the intercept term and the slope parameter in a linear ultrastructural model using direct regression and reverse regression methods. Without assuming the errors to be normally distributed, asymptotic expressions for the bias and the variance of the estimators are derived and analyzed. The effect of departure of the errors from normality is also studied.     

Asymptotic efficiency properties of least squares in an ultrastructural model

This paper considers the estimation of both the intercept term and the slope parameter in a linear ultrastructural model using direct regression and reverse regression methods. Without assuming the errors to be normally distributed, asymptotic expressions for the bias and the variance of the estimators are derived and analyzed. The effect of departure of the errors from normality is also studied.     

A Discrete Economic Multiattribute Acceptance Sampling

A mathematical model for multiattribute acceptance sampling is developed. The number of defectives of each attribute in the lot is considered an independent random variable and is properly described by a discrete prior mass function. The concept of distributional reproducibility to hypergeometric sampling is invoked to simplify the expressions normally associated with a discrete model; yet, the model remains exact and may be efficiently optimized. The acceptance sampling situation modeled is identical to one previously published which applied continuous distributions to approximate the lot fraction defective. An extensive example problem is presented in which the two modeling approaches are compared using sensitivity measures. The conclusions drawn from the example are of use to the practitioner who must decide whether to use discrete or continuous modeling of acceptance sampling situations.     

A model‐based approach for attribute gauge analysis

A new method is proposed for the attribute gauge study. A mathematical model based on the Gauge Performance Curve (GPC) is introduced and the connection between the model parameters and gauge characteristics is discussed. The ability of the whole measurement system (the process and the gauge together) is characterized by two key probabilities: the probability of a rejected part being good and the probability of an accepted part being bad. These probabilities can be calculated either with the proposed mathematical model of GPC (GPC‐method) or by using relative frequencies (AIAG‐type method). The performance of the two approaches has been compared, and the proposed GPC‐method is proven to be statistically favourable. Copyright © 2010 John Wiley & Sons, Ltd.     

Gauge capability studies for attribute data

A gauge repeatability and reproducibility (R&R) method is developed to assess the capability of a measurement system. Although gauge capability studies have received substantial attention, few studies have investigated attribute data despite their wide application in industry. The primary aim of this research is to develop a procedure, based on the generalized linear model, to evaluate the R&R of a measurement system for attribute data. To calculate repeatability of a system, the procedure integrates the iterative weighted least squares (IWLS) method and deviance analysis. The proposed procedure is applied to an inclusion measurement system to verify its adequacy to model the process capability. Copyright © 2007 John Wiley & Sons, Ltd.     

Reversibility and Stochastic Networks

The experimental error variance in a response surface model with a block effect has traditionally been assumed to be constant. In some experimental situations, however, this variance may be different for the different blocks that compose the associated design. This article discusses the analysis of a response surface model with a random block effect and heterogeneous error variances among the blocks. The model includes interactions between the fixed polynomial effects and the block effect. Procedures for estimating and testing the fixed effects and the random effects in the model are described. In particular, ANOVA-based procedures for testing equality of the error variances and testing the random effects are introduced.     

Modeling and analysis of dynamic robust design experiments

This paper investigates the response model approach for the dynamic robust design problem. We derive relationships between the effect estimates of the loss model approach and those of the response model approach. We show that the bias problem for the static case solely exists in the estimation of process variance and does not exist in the estimation of the slope and intercept parameters. The two analysis approaches are compared by use of a real example.     

A damage gradient model for fatigue life prediction of notched metallic structures under multiaxial random vibrations

In the present paper, a damage gradient model combing the damage concept with the theory of critical distance (TCD) is established to estimate the fatigue lives of notched metallic structures under multiaxial random vibrations. Firstly, a kind of notched metallic structure is designed, and the biaxial random vibration fatigue tests of the notched metallic structures are carried out under different correlation coefficients and phase differences between two vibration axes. Then, the fatigue lives of the notched metallic structures are evaluated utilizing the proposed model with the numerical simulations. Finally, the proposed model is validated by the experiment results of the biaxial random vibration fatigue tests. The comparison results demonstrate that the proposed model can provide fatigue life estimation with high accuracy.     

A dynamic analysis of motorcycle ownership and usage: A panel data modeling approach

This study aims to develop motorcycle ownership and usage models with consideration of the state dependence and heterogeneity effects based on a large-scale questionnaire panel survey on vehicle owners. To account for the independence among alternatives and heterogeneity among individuals, the modeling structure of motorcycle ownership adopts disaggregate choice models considering the multinomial, nested, and mixed logit formulations. Three types of panel data regression models – ordinary, fixed, and random effects – are developed and compared for motorcycle usage. The estimation results show that motorcycle ownership in the previous year does exercise a significantly positive effect on the number of motorcycles owned by households in the current year, suggesting that the state dependence effect does exist in motorcycle ownership decisions. In addition, the fixed effects model is the preferred specification for modeling motorcycle usage, indicating strong evidence for existence of heterogeneity. Among various management strategies evaluated under different scenarios, increasing gas prices and parking fees will lead to larger reductions in total kilometers traveled.     

Estimation and compensation of ultrasonic wavefront distortion using a blind system identification method

A common random input filter model is described for estimation and correction of wavefront aberration in ultrasonic b-scan imaging. In the model, aberration between the focus and the transducer elements is represented by the response of a linear filter bank to a common random signal. The response of each filter in the bank is found using a two-level extension of an existing subspace method for blind system identification. The receive waveforms are compensated using an inverse filter, and the transmit waveforms are predistorted using time reversal. To test the model, experiments were conducted using a two-dimensional array system to obtain echoes from a point reflector and from a random medium in each case through an aberrator. The aberrator is a phantom that mimics wavefront distortion produced by human abdominal wall, and the random medium is made to mimic ultrasonic characteristics of human liver. The results indicate the method can improve both the transmit and the receive focus and can outperform time-shift estimation and compensation as well as the method of backpropagation followed by time-shift estimation and compensation     

感压膜片预张力对电容薄膜真空规输出特性的影响

电容薄膜真空规中感压膜片在安装时通常须先施加预张力,再固定.为研究感压膜片预张力对电容薄膜真空规输出特性的影响,以现有电容薄膜真空规为对象,基于COMSOL Multiphysics软件,建立有限元模型,得到了不同预张力下输出电容的仿真解,并与理论计算结果进行了比较,分析了预张力对输出电容的影响.同时分析了真空规线性度...     

Stiffness and Reinforcement Effect of Electrical Resistance Strain Gauges

Abstract:  The increasing use of low-modulus materials, on which the reinforcement effect of the electrical resistance strain gauge is not negligible, has re-opened the research interest into this issue. This study deals with the evaluation of stiffness, and of the strain gauge Young's modulus involved in the estimation of both the global and the local reinforcement effect; the relationship between the strain gauge stiffness and the local reinforcement effect is also analysed. In particular, the experimental technique used to determine the stiffness of some commercial strain gauges is described. The results show that the strain gauge stiffness alone does not permit an accurate evaluation of the local reinforcement effect.     

Mixed model estimation methods for the Rasch model

Mixed models take the dependency between observations based on the same person into account by introducing one or more random effects. After introducing the mixed model framework, it is explained, by taking the Rasch model as a generic example, how item response models can be conceptualized as generalized linear and nonlinear mixed models. Common estimation methods for generalized linear and nonlinear models are discussed. In a simulation study, the performance of four estimation methods is assessed for the Rasch model under different conditions regarding the number of items and persons, and the degree of interindividual differences. The estimation methods included in the study are: an approximation of the integral over the random effect by means of Gaussian quadrature; direct maximization with a sixth-order Laplace approximation to the integrand; a linearized approximation of the nonlinear model employing PQL2; and finally a Bayesian MCMC method. It is concluded that the estimation methods perform almost equally well, except for a slightly worse recovery of the variance parameter for PQL2 and MCMC.     

Spectral efficiency evaluation for selection combining diversity (SCD) scheme over slow fading

In this paper we derive closed-form expressions for the single-user capacity of selection combining diversity (SCD) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying spatially independent flat Rayleigh fading channel. The complex channel estimate and the actual channel are modelled as jointly Gaussian random variables with a correlation that depends on the estimation quality. Three adaptive transmission schemes are analysed: 1) optimal power and rate adaptation opra; 2) constant power with optimal rate adaptation ora; and 3) channel inversion with fixed rate cifr. Furthermore, we derive in this paper analytical results for capacity statistics including moment generating function (MGF), complementary cumulative distribution function (CDF) and probability density function (PDF). These statistics are valid for arbitrary number of receive antennas. Our numerical results show the effect of Gaussian channel estimation error on the achievable spectral efficiency.     

Forecasting reliability growth

This paper describes a method for estimating and forecasting reliability from attribute data, using the binomial model, when reliability requirements are very high and test data are limited. Integer data—specifically, numbers of failures — are converted into non-integer data. The rationale is that when engineering corrective action for a failure is implemented, the probability of recurrence of that failure is reduced; therefore, such failures should not be carried as full failures in subsequent reliability estimates. The reduced failure value for each failure mode is the upper limit on the probability of failure based on the number of successes after engineering corrective action has been implemented. Each failure value is less than one and diminishes as test programme successes continue. These numbers replace the integral numbers (of failures) in the binomial estimate. This method of reliability estimation was applied to attribute data from the life history of a previously tested system, and a reliability growth equation was fitted. It was then ‘calibrated’ for a current similar system's ultimate reliability requirements to provide a model for reliability growth over its entire life-cycle. By comparing current estimates of reliability with the expected value computed from the model, the forecast was obtained by extrapolation.     

Postgrouped sampling method of estimation

A postgrouped sampling is considered for estimating the (finite or finite), population mean. Double sampling and an empirical-weighted estimator is used. Unbiasedness, variance and efficiency are considered. Its properties are discussed allowing the simple random sampling with replacement (SRSWR) design in the first phase, and in each stratum for the second phase. It is shown that for a fixed sample size in each postgroup, the variance of the proposed estimator with less prior information is asymptotically equivalent to the usual stratified estimator for fixed allocation. Some examples are provided for natural populations., The method is also extended to simple random sampling without replacement (SRSWOR) design in the first phase, and in each stratum for the second phase. Unbiased variance estimation is provided for both types of sampling designs.     

支撑双层类脂膜电极的温度补偿方法

提出了一种基于支撑双层类脂膜（S-BLM）电导的电极过程温度补偿方法。利用S-BLM电导传感器测试系统,研究了S-BLM电导与温度的关系。在线性假设的前提下,用最小二乘参数估计法,推导了S-BLM电导传感器特性曲线的斜率、截距与温度的线性方程,进而根据传感器曲线特性得到了S-BLM电极过程的温度补偿模型,并给出了LabVIEW平台下的实现方法。通过对线性假设的效果检验及精度分析,以及通过温度补偿模型的实际测试,证实了本文提出方法的有效性和实用性。     

Applicability of Doppler weather radar based rainfall data for runoff estimation in Indian watersheds – A case study of Chennai basin

Traditionally, India has been vulnerable to various hazards such as floods, droughts and cyclones. About 8% of the total Indian landmass is prone to cyclones. A number of Doppler weather radars are installed in India and their products are utilized for weather predictions and detection of cyclones approaching the Indian coast. Radar-based hydrological studies in various countries have proven that computation of runoff using radar rainfall data could outperform rain gauge network measurements. There are no reported studies on their utilization for hydrological modelling and/or flood-related studies in Indian river basins. A comparison study between Doppler weather radar (DWR) derived rainfall data and the conventional rain gauge data was carried out with hourly inputs at one of the watersheds of Chennai basin, Tamil Nadu, India using HEC-HMS model. The model calibration and validation were performed by comparing the simulated outflow with the observed daily outflow data. The calibrated model was used to predict runoff from two post-monsoon cyclonic storm events with hourly inputs. It was noticed that the discrepancy in the runoff volume was small, but the difference in the peak flow was substantial. Additionally, there was a variation at the time to peak flow using daily and hourly inputs. The results show that the use of radar data may be optional for runoff volume estimation for the watersheds with sufficient rain gauge density, but highly desirable for peak flow and time to peak estimation. Therefore, the DWR derived rainfall data is a promising input for runoff estimation, especially in urban flood modelling.     

Reliability modeling for competing failure processes considering degradation rate variation under cumulative shock

Most systems experience both random shocks (hard failure) and performance degradation (soft failure) during service span, and the dependence of the two competing failure processes has become a key issue. In this study, a novel dependent competing failure processes (DCFPs) model with a varying degradation rate is proposed. The comprehensive impact of random shocks, especially the effect of cumulative shock, is reasonably considered. Specifically, a shock will cause an abrupt degradation damage, and when the cumulative shock reaches a predefined threshold, the degradation rate will change. An analytical reliability solution is derived under the concept of first hitting time (FHT). Besides, a one-step maximum likelihood estimation method is established by constructing a comprehensive likelihood function. Finally, the reasonability of the closed form reliability solution and the feasibility and effectiveness of the proposed DCFPs modeling methodology are demonstrated by a comparative simulation study.