Tashi P. Erdmann

Measurement System Analysis for Binary Inspection: Continuous Versus Dichotomous Measurands

We review methods for assessing the reliability of binary measurements, such as accept/reject inspection in industry. Our framework introduces two factors that are highly relevant in deciding which method to use: (1) whether a reference value (gold standard) can be obtained and (2) whether the underlying measurand is continuous or truly dichotomous. Artificially dichotomizing a continuous measurand, as is commonly done, creates complications that are underappreciated in the literature and in practice. In particular, it introduces an intrinsic reason for the assumption of conditional i.i.d. to be violated. For most methods, this is not crucial provided the samples are random (or at least representative). But, also for most methods, it is, in general, not clear how one can obtain a random sample from the relevant population. The taxonomy presents methods that are generally known in industry, such as nonparametric estimation of false-acceptance and false-rejection probabilities, AIAGs analytic method (logistic regression), latent class modeling, and latent trait modeling. The methods discussed are applied to an example presented in the measurement-system-analysis manual from the automotive industry.

Quality Quandaries : A Gage R&R Study in a Hospital

In quality improvement projects, the reliability of measurements must be assessed before doing any analysis. This is particularly important in the measurement phase of a Six Sigma project. The precision of a measurement procedure can be determined by a ..

A Measurement System Analysis Approach for Hard-to-Repeat Events

ABSTRACT When measurements are nonreplicable, assessing the measurement system is a difficult task and cannot be done using the conventional gauge repeatability and reproducibility methods. This is due to the fact that the object measured is affected by the measurement and/or changes with time. This article describes an alternative method that can be used to study the repeatability and reproducibility of a measurement system in case the measured quantity varies over time. The essence of the method is that each part is measured simultaneously by multiple gauges.

Quality Quandaries: Improving the Invoicing Process of a Consulting Company

In recent years, lean Six Sigma has been increasingly used for improvement projects in the service sector where the challenge is to structure and quantify the problem. Once made explicit, the solution is often uncomplicated and does not require advanced..

Some common errors of experimental design, interpretation and inference in agreement studies.

We signal and discuss common methodological errors in agreement studies and the use of kappa indices, as found in publications in the medical and behavioural sciences. Our analysis is based on a proposed statistical model that is in line with the typical models employed in metrology and measurement theory. A first cluster of errors is related to nonrandom sampling, which results in a potentially substantial bias in the estimated agreement. Second, when class prevalences are strongly nonuniform, the use of the kappa index becomes precarious, as its large partial derivatives result in typically large standard errors of the estimates. In addition, the index reflects rather one-sidedly in such cases the consistency of the most prevalent class, or the class prevalences themselves. A final cluster of errors concerns interpretation pitfalls, which may lead to incorrect conclusions based on agreement studies. These interpretation issues are clarified on the basis of the proposed statistical modelling. The signalled errors are illustrated from actual studies published in prestigious journals. The analysis results in a number of guidelines and recommendations for agreement studies, including the recommendation to use alternatives to the kappa index in certain situations.

Assessment of binary inspection with a hybrid measurand

This paper addresses issues that arise in measurement system analysis of a binary measurement system if the measurand is a hybrid between a dichotomy and a continuum. A case study is presented, which illustrates methods to assess the error rates of binary measurements with such a hybrid measurand. The case study concerns pass/fail inspection of laptop screens for scratches, where the measurand is the presence or absence of scratches. If a scratch is present, the measurand corresponds with a continuum of scratch sizes, but if no scratch is present, the measurand corresponds with a point. It is argued that if the measurand is a hybrid, a standard logistic regression model is not suitable to estimate the characteristic curve relating the reject probability with the measurand. Several alternative specifications for the characteristic curve are introduced and compared. We conclude that many of the methods currently used for assessment of a binary measurement system with a hybrid measurand are unsuited. This is a remarkable conclusion, given the frequent occurrence in industry of leak tests, inspections for defects, and other binary measurement systems with a hybrid measurand. Copyright

The Statistical Evaluation of Categorical Measurements: “Simple Scales, but Treacherous Complexity Underneath”

ABSTRACT The statistical evaluation of measurements on categorical scales is hampered by hiatuses in insight and conceptualization. Categorical scales have a simple mathematical structure. The underlying empirical reality, however, that they aim to reflect usually has a very complex structure. This complexity induces intricate challenges for the statistical evaluation of the performance of categorical measurement systems. Most current techniques deal ineffectively with these challenges, relying on simplistic conditional independence assumptions and careless sampling strategies. Moreover, they typically evaluate measurement systems in terms of concepts not clearly related to a notion of measurement error. This article proposes an approach for modeling the behavior of categorical measurements based on characteristic curves. The approach is intended to facilitate the development of more effective techniques. It is applied in a case study that illustrates what the authors believe is a realistic degree of complexity.

Quality Quandaries: Reducing Work in Process at an Emergency Assistance Center

This article describes a case study of an improvement in controlling work in progress at an emergency assistance center. Disadvantages of high amounts of WIP include inventory costs, increased throughput times, and other kinds of nuisance.

The Statistical Evaluation of a Binary Test Based on Combined Samples

The statistical evaluation of the reliability of binary tests and inspections is a challenging endeavor. In this paper, we propose an approach for the common situation where the true condition of the inspected items is unobservable (“gold-standard unavailable”), the probabilities of false acceptance and false rejection vary across items, and rejections are relatively rare. Our approach fits a latent-variable model, where the variability in misclassification probabilities is driven by a continuous property of a part. To deal with the low prevalence of rejections, we propose sampling items from multiple sources. The performance and properties of the estimators are assessed using simulation, asymptotic approximations, and a real-life case at a car-parts manufacturer.

Quality quandaries: streamlining the procurement process at a media and entertainment company

In improvement projects, the DMAIC structure and the Pareto principle help to provide focus. As an example, this column presents an improvement project that took place at a large media and entertainment company in The Netherlands in 2012.