基于试验设计的膨胀型钢结构防火涂料配方的多变量分析(英文)

膨胀型防火涂料的配方优化,需要阻燃剂之间有效的协同作用来获得防火效果。以ISO耐火测试标准为依据,对以聚磷酸铵、季戊四醇和三聚氰胺阻燃剂为主要成分的防火涂料,利用D-优化设计原理,借助Design Expert软件进行试验设计,在有限的试验次数基础上,运用MODDE软件对试验结果进行了多变量回归分析,获得了满意的试验结果。     

Sampling Inspection Plans for Discriminating Between Two Weibull Processes

Four procedures—R ₁, R ₂, R ₃ and R ₄, for choosing the better of two processes, the units from which have life times distributed according to the Weibull distribution were formulated in an earlier paper [1]. The calculation in the use of these procedures and some sampling plans based on them are discussed here. The paper also examines the robustness of these procedures.     

Multivariate statistical monitoring of an industrial SBR process. Soft-sensor for production and rubber quality

This work presents a full methodology to build and evaluate a soft sensor capable of monitoring the production of Styrene-Butadiene Rubber (SBR) in an industrial train of 7 continuously-stirred tank reactors. The aim is to develop a device for on-line estimation of production and quality variables using a multivariate statistical technique like partial least squared (PLS). Besides pursuing the soft sensor development, this paper attempts to provide a guide for similar developments by suggesting attention to several specific methodological points. In this regard, the following features are highlighted: i) since a wide range validation space is desired for this sensor and the actual plant cannot be arbitrarily disturbed, an existing complex fundamental model is used to explore different possible operating conditions; ii) the approach used to develop the soft sensor includes a distributed sampling of multivariate steady-state conditions to collect the calibration data set, and the use of a filter for excluding outliers; and iii) it is shown that the analysis of how the explained variability progress when latent variables are included in the model allows the detection of poor predictor variables providing the chance for improving the multivariable regression by eliminating interfering contributions. Few after-modeling techniques are also suggested to confirm the consistency of the calibrating data set and the model precision over the applicability domain.     

The weighted priors approach for combining expert opinions in logistic regression experiments

ABSTRACT

When modeling the reliability of a system or component, it is not uncommon for more than one expert to provide very different prior estimates of the expected reliability as a function of an explanatory variable such as age or temperature. Our goal is to incorporate all information from the experts when choosing a design about which units to test. Bayesian design of experiments has been shown to be very successful for generalized linear models, including logistic regression models. We use this approach to develop methodology for the case where there are several potentially non-overlapping priors under consideration. While multiple priors have been used for analysis in the past, they have never been used in a design context. The Weighted Priors method performs well for a broad range of true underlying model parameter choices and is more robust when compared to other reasonable design choices. We illustrate the method through multiple scenarios and a motivating example. Additional figures for this article are available in the online supplementary information.     

Estimating the error of an effect in unreplicated 2-level fractional factorial designs

Saturated fractional factorial experimental designs and orthogonal main effect plans are extremely valuable tools in quality engineering. However, one problem with these designs is that there are no replicate runs to be used for estimating experimental error. This note develops an estimator of the experimental error based on the hypothesis that not all factor effects will be non-zero. A joint Bayesian prior distribution is presented for the experimental error variance of an effect, σ², and the probability that each effect is non-zero. From this prior distribution a posterior marginal distribution for σ² is derived along with a direct estimate of σ². This method is compared with the traditional methods of estimating σ² in unreplicated designs through a numerical example.     

Concise Experimental Designs

This modest paper contains a much more concise representation of the popular experimental design generators for fractional factorial designs. The information is indexed by the information that the experimenter will start with: the number of factors and the desired resolution for the experiment. Its format facilitates the exploration of the effect of changing the experimental design by using a different number of factors or by changing the experiment resolution.     

Planning of Accelerated Life Tests With Dependent Failure Modes Based on a Gamma Frailty Model

Accelerated life tests (ALT) provide timely information on product reliability. As product complexity increases, ALT often generate multiple dependent failure modes. However, the planning of an ALT with dependent failure modes has not been well studied in the literature. This article investigates the statistical modeling and planning of ALT with multiple dependent failure modes. An ALT model is constructed. Associated with each failure mode there is a latent lifetime described by a log-location-scale distribution, and the statistical dependence between different failure modes is described by a Gamma frailty model. The proposed model incorporates the ALT model with independent failure modes as a special limiting case. We obtain the c-optimal test plans by minimizing the large-sample approximate variance of the maximum likelihood estimator of a certain life quantile at use condition. The method is illustrated by developing ALT plans for field-effect transistors with competing gate oxide breakdown. A sensitivity analysis is performed to investigate the robustness of the optimal ALT plan against misspecification of model parameter values. This article has supplementary materials that are available online.     

A Novel Approach to Simultaneous Robust Design of Product Parameters and Tolerances Using Quality Loss and Multivariate ANOVA Concepts

Design and development of high quality products are of utmost importance to any production plant. Product design consists of parameter design and tolerance design, which affect the product performances and the manufacturing costs, respectively. Most products involve more than one quality feature. Design and development of such products raise multi‐response surface problems in which it is necessary to determine the optimal values of parameters and the tolerances for all responses simultaneously. In this research, an approach for simultaneous robust parameter and tolerance design is proposed to deal with multi‐response problems. The proposed method employs quality loss concept and one‐way multivariate analysis of variance. Two simulation studies are performed to validate the applicability of the proposed method. Research findings show that the proposed method performs better in quality improvement as well as in cost reduction than the existing methods. The variances of the responses are also lower than those of the other methods, that is, the proposed method results in a more robust approach to product design. Copyright © 2016 John Wiley & Sons, Ltd.     

Multivariate Analysis VI

We present graphical and numerical methods for assessing the adequacy of the log-linear model for variances. The proposed methods are derived from the cumulative sum of residuals over the covariate or linear predictor. Under the assumed model, the cumulative residual process converges weakly to a 0-mean Gaussian process whose distribution can be approximated via Monte Carlo simulation. The observed cumulative residual pattern can then be compared both visually and analytically to a number of simulated realizations from the approximate null distribution. These comparisons enable one to examine the functional form of each covariate, the link function as well as the overall model adequacy of the variance model. Simulation studies demonstrate that the proposed methods perform well in practical settings. Illustrations with three datasets are provided.     

An explanation and critique of taguchi's contributions to quality engineering

Recently there has been much interest and some controversy concerning the statistical methods employed by Professor Genichi Taguchi of Japan for improving the quality of products and processes. These methods include the use of fractional factorial designs and other orthogonal arrays, parameter design to minimize sensitivity to environmental factors, parameter design for minimizing transmitted variation, signal-to-noise ratios, loss functions, accumulation analysis, minute analysis and the analysis of life test data. This paper explains some of Taguchi's contributions to quality engineering and also provides a critical evaluation of his statistical methods. Our conclusion is that although on the one hand, Professor Taguchi's quality engineering ideas are of great importance and should become part of the working knowledge of every engineer, on the other hand, many of the techniques of statistical design and analysis he employs to put these ideas into practice are often inefficient and unnecessarily complicated and should be replaced or appropriately modified. In this short article only an overview is attempted, but references are appended where these matters are discussed in greater detail.     

Effect of addition of graphite particulates on the wear behaviour in aluminium–silicon carbide–graphite composites

Aluminium matrix composites with multiple reinforcements (hybrid AMCs) are finding increased applications because of improved mechanical and tribological properties and hence are better substitutes for single reinforced composites. Few investigations have been reported on the tribological behaviour of these composites with % reinforcement above 10%. The present study focuses on the influence of addition of graphite (Gr) particulates as a second reinforcement on the tribological behaviour of aluminium matrix composites reinforced with silicon carbide (SiC) particulates. Dry sliding wear tests have been performed to study the influence of Gr particulates, load, sliding speed and sliding distance on the wear of hybrid composite specimens with combined % reinforcement of 2.5%, 5%, 7.5% and 10% with equal weight % of SiC and Gr particulates. Experiments are also conducted on composites with % reinforcement of SiC similar to hybrid composites for the sake of comparison. Parametric studies based on design of experiments (DOE) techniques indicate that the wear of hybrid composites decreases from 0.0234 g to 0.0221 g as the % reinforcement increases from 3% to 7.5%. But the wear has a tendency to increase beyond % reinforcement of 7.5% as its value is 0.0225 g at.% reinforcement of 10%. This trend is absent in case of composites reinforced with SiC alone. The values of wear of these composites are 0.0323 g, 0.0252 g and 0.0223 g, respectively, at.% reinforcement of 3%, 7.5% and 10% clearly indicating that hybrid composites exhibit better wear characteristics compared to composites reinforced with SiC alone. Load and sliding distance show a positive influence on wear implying increase of wear with increase of either load or sliding distance or both. Whereas speed shows a negative influence on wear indicating decrease of wear with increase of speed. Interactions among load, sliding speed and sliding distance are noticed in hybrid composites and this may be attributed to the addition of Gr particulates. Such interactions are not present in composite reinforced with SiC alone. Mathematical models are formulated to predict the wear of the composites.     

Tutorial: Industrial Split-plot Experiments

Many industrial experiments involve two types of factors: those that are hard-to-change and those that are easy-to-change (ETC). Hard-to-change (HTC) factors have levels that are difficult and/or expensive to change. As a result, the experimenter would prefer to run the experiment in such a manner as to minimize the number of times that he/she must change the levels of these factors. Unfortunately, it is precisely the changing of these levels that provides the information about the effects of the HTC factors. Consequently, when we minimize the number of times we change the levels of these factors, we also minimize the relevant information about their effects.

This paper summarizes the structure and the analysis of industrial split-plot experiments. The purpose of this article is to teach practitioners how to identify split-plot experimental conditions, how to run the experiment efficiently, and then how to analyze the results. The article illustrates both first-order and second-order experiments. The first four sections provide a basic background on experimental design and an introduction to first-order split-plot experiments. The remainder of this article contains more advanced topics dealing with second-order, split-plot experiments.     

Optimum Multiple and Multivariate Poisson Statistical Control Charts

This paper deals with the simultaneous statistical process control of several Poisson variables. The practitioner of this type of monitoring may employ a multiple scheme, i.e. one chart for controlling each variable, or may use a multivariate scheme, based on monitoring all the variables with a single control chart. If the user employs the multivariate schemes, he or she can choose from, for example, three options: (i) a control chart based on the sum of the different Poisson variables; (ii) a control chart on the maximum value of the different Poisson variables; and (iii) in the case of only two variables, a chart that monitors the difference between them. In this paper, the previous control charts are studied when applied to the control of p = 2, 3 and 4 variables. In addition, the optimization of a set of univariate Poisson control charts (multiple scheme) is studied. The main purpose of this paper is to help the practitioner to select the most adequate scheme for her/his production process. Towards this goal, a friendly Windows© computer program has been developed. The program returns the best control limits for each control chart and makes a complete comparison of performance among all the previous schemes. Copyright © 2013 John Wiley & Sons, Ltd.     

Strategies for planning experiments using orthogonal arrays and confounding tables

Genichi Taguchi has popularized a robust design method which employs experimental design techniques to help identify the levels of design factors to improve the quality of products and manufacturing processes. Experimental design techniques are extremely effective for identifying improved factor levels in problems that involve a large number of factors. Taguchi's success in getting engineers to use experimental design techniques is due, at least in large part, to his use of tools and techniques that simplify the experiment planning process. Recognizing the advantages of this approach, this paper proposes a new set of tools, confounding tables, which offer more guidance to experimenters. Confounding tables provide a clear and systematic representation of confounding relationships. They are simple and useful tools for constructing experiment plans, and they enable users easily to evaluate the confounding patterns of a completed plan. We show how confounding tables provide more information than Taguchi's linear graphs, and are useful for a large class of experiment plans.     

A methodology for planning experiments in robust product and process design

Robust design is an important method for improving product manufacturability and life, and for increasing manufacturing process stability and yield. In 1980 Genichi Taguchi introduced his approach to using statistically planned experiments in robust product and process design to U.S. industry. Since then, the robust design problem and Taguchi's approach to solving it has received much attention from product designers, manufacturers, statisticians and quality professionals. Although most agree on the importance of the robust design problem, controversy over some of the specific methods used to solve the problem has made this an active research area. Although the answers are not all in yet, the importance of the problem has led to development of a four-step methodology for implementing robust design. The steps are (1) formulate the problem by stating objectives and then listing and classifying product or process variables, (2) plan an experiment to study these variables, (3) identify improved settings of controllable variables from the experiment's results and (4) confirm the improvement in a small follow-up experiment. This paper presents a methodology for the problem formulation and experiment planning steps. We give practical guidelines for making key decisions in these two steps, including choice of response characteristics, and specification of interactions and test levels for variables. We describe how orthogonal arrays and interaction graphs can be used to simplify the process of planning an experiment. We also compare the experiment planning strategies we are recommending to those of Taguchi and to more traditional approaches.