Albert W. Jones

On use of Bayesian statistics to make the Guide to the Expression of Uncertainty in Measurement consistent

The International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement is being increasingly recognized as a de facto international standard. The ISO Guide recommends a standardized way of expressing uncertainty in all kinds of measurements and provides a comprehensive approach for combining information to evaluate that uncertainty. The ISO Guide supports uncertainties evaluated from statistical methods, Type A, and uncertainties determined by other means, Type B. The ISO Guide recommends classical (frequentist) statistics for evaluating the Type A components of uncertainty; but it interprets the combined uncertainty from a Bayesian viewpoint. This is inconsistent. In order to overcome this inconsistency, we suggest that all Type A uncertainties should be evaluated through a Bayesian approach. It turns out that the estimates from a classical statistical analysis are either equal or approximately equal to the corresponding estimates from a Bayesian analysis with non-informative prior probability distributions. So the classical (frequentist) estimates may be used provided they are interpreted from the Bayesian viewpoint. The procedure of the ISO Guide for evaluating the combined uncertainty is to propagate the uncertainties associated with the input quantities. This procedure does not yield a complete specification of the distribution represented by the result of measurement and its associated combined standard uncertainty. So the correct coverage factor for a desired coverage probability of an expanded uncertainty interval cannot always be determined. Nonetheless, the ISO Guide suggests that the coverage factor may be computed by assuming that the distribution represented by the result of measurement and its associated standard uncertainty is a normal distribution or a scaled-and-shifted t-distribution with degrees of freedom determined from the Welch–Satterthwaite formula. This assumption may be unjustified and the coverage factor so determined may be incorrect. A popular convention is to set the coverage factor as 2. When the distribution represented by the result of measurement and its associated standard uncertainty is not completely determined, the 2-standard-uncertainty interval may be interpreted in terms of its minimum coverage probability for an applicable class of probability distributions.

Controlling activities in a virtual manufacturing cell

Researchers at the National Institute of Standards and Technology are developing a virtual manufacturing cell. This cell will contain simulation models of a wide range of manufacturing equipment, processes, and systems. It will have commercial and prototype applications software which implement production functions from order release to final inspection. There will be an information base and a collection of interfaces which will provide the integrating infrastructure for these applications. These interfaces will be based on information models and exchange protocols, and will specify what information is shared across those applications and how it is exchanged. This paper describes the current virtual manufacturing cell, with special emphasis on the hierarchy we are developing to control activities within the cell.

Implementing the ISO 15746 Standard for Chemical Process Optimization

This paper proposes an approach to integrating advanced process control solutions with optimization (APC-O) solutions, within any factory, to enable more efficient production processes. Currently, vendors who provide the software applications that implement control solutions are isolated and relatively independent. Each such solution is designed to implement a specific task such as control, simulation, and optimization - and only that task. It is not uncommon for vendors to use different mathematical formalisms and modeling tools that produce different data representations and formats. Moreover, instead of being modeled uniformly only once, the same knowledge is often modeled multiple times - each time using a different, specialized abstraction. As a result, it is extremely difficult to integrate optimization with advanced process control. We believe that a recent standard, International Organization for Standardization (ISO) 15746, describes a data model that can facilitate that integration. In this paper, we demonstrate a novel method of integrating advanced process control using ISO 15746 with numerical optimization. The demonstration is based on a chemical-process-optimization problem, which resides at level 2 of the International Society of Automation (ISA) 95 architecture. The inputs to that optimization problem, which are captured in the ISO 15746 data model, come in two forms: goals from level 3 and feedback from level 1. We map these inputs, using this data model, to a population of a meta-model of the optimization problem for a chemical process. Serialization of the metamodel population provides input to a numerical optimization code of the optimization problem. The results of this integrated process, which is automated, provide the solution to the originally selected, level 2 optimization problem.