Diego Zappa

Measurement uncertainty with nested mixed effect models

Measurement uncertainty in experiments is receiving increasing interest among practitioners both for quantitative and qualitative evaluations. Applications may be found, for example, to compare experiments run in different laboratories, to certify the precision of gauges used in the masurement process or to measure uncertainty in a classification process, i.e. when objects are qualitatively evaluated by appraisers. In this paper, after having briefly presented how to measure uncertainty using gauge repeatability and reproducibility studies, we focus on a problem quite relevant for practitioners: how to deal with the presence of correlation among ‘replications’. This issue is common to many food/agriculture experiments. By a modification of a nested mixed effect design, we describe the impact of dependencies among replications on measurement capability. Copyright

Measurement Errors and Uncertainty: A Statistical Perspective

Evaluation of measurement systems is necessary in many industrial contexts. The literature on this topic is mainly focused on how to measure uncertainties for systems that yield continuous output. Few references are available for categorical data and they are briefly recalled in this paper. Finally a new proposal to measure uncertainty when the output is bounded ordinal is introduced.

Confidence Regions for Multivariate Calibration: a proposal

Most of the papers on calibration are based on either classic or bayesian parametric context. In addition to the typical problems of the parametric approach (choice of the distribution for the measurement errors, choice of the model that links the sets of variables, etc.), a relevant problem in calibration is the construction of confidence region for the unknown levels of the explanatory variables. In this paper we propose a semiparametric approach, based on simplicial depth, to test the hypothesis of linearity of the link function and then how to find calibration depth confidence regions.

Selecting subgrids from a spatial monitoring network: Proposal and application in semiconductor manufactoring process

The monitoring of spatial production processes typically involves sampling network to gather information about the status of the process. Sampling costs are often not marginal, and once the process has been accurately calibrated, it might be appropriate to reduce the dimension of the sampling grid. This aim is often achieved through the allocation of a brand new network of less dimension. In some cases that is not possible and it might be necessary the selection of a subgrid extracted from the original network. Motivated by a real semiconductor problem, we propose a method to extract a monitoring subgrid from a given one, based upon grid representativeness, accuracy, and spatial coverage of the subgrid and, if available, by expert knowledge of the weights to be assigned to those areas where production may need greater precision. Discussion is mainly focused on circular spatial domain, since, in microelectronics, the basic production support, called wafer, is a circle. Straightforward generalizations to different spatial domains are possible. Furthermore, conditionally upon the availability of experimental data, we check the loss of accuracy by fitting a dual mean-variance response surface on the reduced grid. Joining the latter information and the criteria used to select the subgrid, we provide additional guidelines on how to fine-tune the subgrid selection. Real case studies are used to show the effectiveness of the proposal.

A Novel Approach to Evaluate Repeatability and Reproducibility for Ordinal Data

We propose a novel usage of CUB models in order to evaluate Repeatability and Reproducibility (R&R) for ordinal data in business and industrial experiments. This is a context where there is a small group of appraisers who have to evaluate a sample of objects classifying them according to ordinal categories. By comparing the cumulative distribution functions obtained fitting CUB models to judgments given by appraisers, we give both graphical and analytical instruments to assess R&R for an ordinal measurement system. The approach is applied to the real-life example reported in de Mast and van Wieringen (2010).

Confidence Intervals for Variance Components in Measurement System Capability Studies

In Measurement System Analysis a relevant issue is how to find confidence intervals for the parameters used to evaluate the capability of a gauge. In literature approximate solutions are available but they produce so wide intervals that they are often not effective in the decision process. In this article we introduce a new approach and, with particular reference to the parameter γR, i.e., the ratio of the variance due to the process and the variance due to the instrument, we show that, under quite realistic assumptions, we obtain confidence intervals narrower than other methods. An application to a real microelectronic case study is reported.

Calibration Confidence Regions Using Empirical Likelihood

The literature on multivariate calibration shows an increasing interest in non-parametric or semiparametric methods. Using Empirical Likelihood (EL). we present a semiparametric approach to find multivariate calibration confidence regions and we show how a unique optimum calibration point may be found weighting the EL profile function. In addition, a freeware VBA for Excel© program has been implemented to solve the many relevant computational problems. An example taken from a process of a semiconductor industry is presented.

The role of statistical methodogies in the study or quality design of apparatuses and production systems

Up to the 60s the design criteria of industrial production systems were mainly based on the new findings achieved in that period in technical and physical environments and generally on techniques having deterministic nature. Examples can be typically found in the field of structural project that must support mechanic, dielectric and thermic stress. The functional forms of the relationship between stress (cause), strain and performance changes (effects) were supposed to be known using variables or parameters related to the size of the item under consideration. This kind of design enabled the collection and control of the unknown and random components by using the so-called safety coefficients. As a consequence of this approach, the existence of random effects in industrial work was ignored and a deterministic point of view was accepted.