Effectiveness of a random compound noise strategy for robust parameter design

Robust parameter design has been widely used to improve the quality of products and processes. Although a product array, in which an orthogonal array for control factors is crossed with an orthogonal array for noise factors, is commonly used for parameter design experiments, this may lead to an unacceptably large number of experimental runs. The compound noise strategy proposed by Taguchi [30 G. Taguchi, System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs, UNIPUB/Kraus International, White Plains, New York, 1987. [Google Scholar]] can be used to reduce the number of experimental runs. In this strategy, a compound noise factor is formed based on the directionality of the effects of noise factors. However, the directionality is usually unknown in practice. Recently, Singh et al. [28 J. Singh, D.D. Frey, N. Soderborg, and R. Jugulum, Compound noise: Evaluation as a robust parameter design method, Qual. Reliab. Eng. Int. 23 (2007), 387–398. doi: 10.1002/qre.812[Crossref], [Web of Science ®] , [Google Scholar]] proposed a random compound noise strategy, in which a compound noise factor is formed by randomly selecting a setting of the levels of noise factors. The present paper evaluates the random compound noise strategy in terms of the precision of the estimators of the response mean and the response variance. In addition, the variances of the estimators in the random compound noise strategy are compared with those in the n-replication design. The random compound noise strategy is shown to have smaller variances of the estimators than the 2-replication design, especially when the control-by-noise-interactions are strong.     

Estimation of the correlation coefficient in probability proportional to size with replacement sampling

g of the population correlation coefficient has been suggested in case of probability proportional to size with replacement sampling. The asymptotic bias, variance and the estimate of the variance of the estimator r_g have been obtained. A comparison of this estimator has been made with the estimator r given by Gupta et al (1993) and usual estimator r₁ for PPSWR sampling. The proposed estimator r_g satisfies the condition −1≤r_g≤1 which the estimator r does not satisfy. Received: September 1, 1999; revised version: May 29, 2001     

Analysis of robust design experiments with time-dependent ordinal response characteristics: a quality improvement study from the horticulture industry

An approach to the analysis of time-dependent ordinal quality score data from robust design experiments is developed and applied to an experiment from commercial horticultural research, using concepts of product robustness and longevity that are familiar to analysts in engineering research. A two-stage analysis is used to develop models describing the effects of a number of experimental treatments on the rate of post-sales product quality decline. The first stage uses a polynomial function on a transformed scale to approximate the quality decline for an individual experimental unit using derived coefficients and the second stage uses a joint mean and dispersion model to investigate the effects of the experimental treatments on these derived coefficients. The approach, developed specifically for an application in horticulture, is exemplified with data from a trial testing ornamental plants that are subjected to a range of treatments during production and home-life. The results of the analysis show how a number of control and noise factors affect the rate of post-production quality decline. Although the model is used to analyse quality data from a trial on ornamental plants, the approach developed is expected to be more generally applicable to a wide range of other complex production systems.     

Machine learning and design of experiments with an application to product innovation in the chemical industry

Industrial statistics plays a major role in the areas of both quality management and innovation. However, existing methodologies must be integrated with the latest tools from the field of Artificial Intelligence. To this end, a background on the joint application of Design of Experiments (DOE) and Machine Learning (ML) methodologies in industrial settings is presented here, along with a case study from the chemical industry. A DOE study is used to collect data, and two ML models are applied to predict responses which performance show an advantage over the traditional modeling approach. Emphasis is placed on causal investigation and quantification of prediction uncertainty, as these are crucial for an assessment of the goodness and robustness of the models developed. Within the scope of the case study, the models learned can be implemented in a semi-automatic system that can assist practitioners who are inexperienced in data analysis in the process of new product development.     

The robustness of response surface designs with errors in factor levels

ABSRTACT

Since errors in factor levels affect the traditional statistical properties of response surface designs, an important question to consider is robustness of design to errors. However, when the actual design could be observed in the experimental settings, its optimality and prediction are of interest. Various numerical and graphical methods are useful tools for understanding the behavior of the designs. The D- and G-efficiencies and the fraction of design space plot are adapted to assess second-order response surface designs where the predictor variables are disturbed by a random error. Our study shows that the D-efficiencies of the competing designs are considerably low for big variance of the error, while the G-efficiencies are quite good. Fraction of design space plots display the distribution of the scaled prediction variance through the design space with and without errors in factor levels. The robustness of experimental designs against factor errors is explored through comparative study. The construction and use of the D- and G-efficiencies and the fraction of design space plots are demonstrated with several examples of different designs with errors.     

Some estimation procedures of sensitive character using scrambled response techniques in successive sampling

This paper is an attempt to analyze the effect of scrambled response techniques to estimate the current population mean in two-occasion successive sampling when study and auxiliary variables are sensitive in nature. Using additive and multiplicative scrambled response models on both occasions, some generalized estimation strategies of current population mean have been proposed and their properties are examined. Empirical studies are performed on real data (abortion rate in the states of United States) and simulation studies are also carried out to evaluate the performances of the proposed estimators over other estimators. Results have proved the worthiness of the scrambled response techniques in real-life situations.     

Admissibility of a variance estimator in finite population sampling under Warner's randomized response plan with multiple responses

ABSTRACT

Let P be the proportion of individuals in a finite population possessing a sensitive attribute. We consider the problem of unbiased estimation of (i) the variance of a linear unbiased estimator of P and (ii) the population variance P (1—P) for a given probability sampling design under Warner's (1965 Warner, S.L. (1965). Randomized response - A survey technique for eliminating evasive answer bias. J. Amer. Statist. Assoc. 60:63–69.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) randomized response (RR) plan when independent responses are obtained from each sampled individual as many times as he/she is selected in the sample and prove the admissibility of a quadratic unbiased estimator for each.     

Improved two phase sampling exponential ratio and product type estimators for population mean of study character in the presence of non response

Improved two phase sampling exponential ratio and product type estimators for population mean using known coefficient of variation of study character in the presence of non response have been proposed and their properties are studied under large sample approximation. The proposed estimators are compared with the other existing estimators by using the MSE criterion and the conditions under which the proposed estimators perform better are obtained. An empirical study is also given to judge the performance of the proposed estimators. At the end, simulation studies have been carried out to verify the superiority to the proposed estimators.     

Estimation of mean and variance of stigmatized quantitative variable using distinct units in randomized response sampling

Received: April 6, 1998; revised version: July 12, 1999     

Use of scrambled response model in estimating the finite population mean in presence of non response when coefficient of variation is known

We propose an estimator for the finite population mean utilizing known coefficient of variation of the study character in case of quantitative sensitive variable considering a randomization mechanism on the second call that provides privacy protection to the respondents to get truthful information. We also propose generalized ratio- and regression-type estimators under two-phase sampling scheme. The conditions under which the proposed estimators are more efficient than the relevant estimators under scrambled response model have been obtained. An empirical study is carried out to evaluate performances of the estimators.     

On correlation analysis of many‐to‐many observations: an alternative to Pearson's correlation coefficient and its application to an ecotoxicological study

Correlation studies are an important hypothesis‐generating and testing tool, and have a wide range of applications in many scientific fields. In ecological studies in particular, multiple environmental variables are often measured in an attempt to determine relationships between chemical, physical and biological factors. For example, one may wish to know whether and how soil properties correlate with plant physiology. Although correlation coefficients are widely used, their properties and limitations are often imperfectly understood. This is especially the case when one is interested in correlations between, say, trace element content in sediments and in marine organisms, where no one‐to‐one correspondence exists. We show that evaluating Pearson's correlation coefficient for either site‐specific means or composite samples results in biased estimates, and we propose an alternative estimator. We use simulation studies to demonstrate that our estimator generally has a much smaller bias and mean squared error. We further illustrate its use in a case study of the correlation between trace element content in sediments and in mussels in Lyttelton Harbour, New Zealand.     

On comutativity of design and model expectations in randomized response surveys

Interchangability of the order of design expectation ( E_p ) and model expectation ( E_R ) under randomized response ( RR ) surveys for finding expectation and mean-square error of a linear estimator e found to be permissible for a non-informative sampling design. The non-comutative property established by Chaudhuri & Adhikary ( 1990 ) under probability proportional to size with replacement ( PPSWR ) sampling is disproved.     

A Note on Sufficient Conditions for Valid Unmodified t Testing in Correlation Analysis with Autocorrelated and Heteroscedastic Sample Data

Traditionally, sphericity (i.e., independence and homoscedasticity for raw data) is put forward as the condition to be satisfied by the variance–covariance matrix of at least one of the two observation vectors analyzed for correlation, for the unmodified t test of significance to be valid under the Gaussian and constant population mean assumptions. In this article, the author proves that the sphericity condition is too strong and a weaker (i.e., more general) sufficient condition for valid unmodified t testing in correlation analysis is circularity (i.e., independence and homoscedasticity after linear transformation by orthonormal contrasts), to be satisfied by the variance–covariance matrix of one of the two observation vectors. Two other conditions (i.e., compound symmetry for one of the two observation vectors; absence of correlation between the components of one observation vector, combined with a particular pattern of joint heteroscedasticity in the two observation vectors) are also considered and discussed. When both observation vectors possess the same variance–covariance matrix up to a positive multiplicative constant, the circularity condition is shown to be necessary and sufficient. “Observation vectors” may designate partial realizations of temporal or spatial stochastic processes as well as profile vectors of repeated measures. From the proof, it follows that an effective sample size appropriately defined can measure the discrepancy from the more general sufficient condition for valid unmodified t testing in correlation analysis with autocorrelated and heteroscedastic sample data. The proof is complemented by a simulation study. Finally, the differences between the role of the circularity condition in the correlation analysis and its role in the repeated measures ANOVA (i.e., where it was first introduced) are scrutinized, and the link between the circular variance–covariance structure and the centering of observations with respect to the sample mean is emphasized.