Experimentation, Validation, and Uncertainty Analysis for Engineers, 4th Edition

7DETAILED UNCERTAINTY ANALYSIS: COMPREHENSIVE EXAMPLES

In this chapter we present a series of comprehensive examples that illustrate application of the ideas discussed in previous chapters. The procedures, approaches, and engineering judgment illustrated are the point. The numerical values in the examples are definitely not the point and should not be taken as typical or as recommendations.

7-1 TSM COMPREHENSIVE EXAMPLE: SAMPLE-TO-SAMPLE EXPERIMENT

A mining company has retained our laboratory to determine the heating value of some lignite in which they have an interest. Lignite is a brownish coal that is relatively high in ash and moisture content. The most abundant supplies of lignite in the United States are in the Gulf Coast region and in the Northern Great Plains region. The company wants to develop a North Dakota lignite deposit into a boiler fuel.

7-1.1 The Problem

Initially, the company wants to determine the heating value of a small portion of the deposit of lignite. They plan to deliver sealed samples to our laboratory from this section of the deposit. From these they want answers to the following questions:

1. How well can we measure the heating value of a single sample?
2. What is the mean heating value for the particular portion of the deposit, and what is the uncertainty of this mean value?

In question 1 we are essentially considering the uncertainty at a zeroth-order replication level as we are concerned only with the uncertainty caused by the systematic and ...