8.8 A Measurement System Analysis
The ANOVA is a versatile tool that can be used in many situations where several influences could affect a response. In this section we are going to use a variant called two-way ANOVA to analyze a measurement system. It is used when the variation in the samples under study occurs under the influence of two variables, or factors.
An engine laboratory wants to determine the precision of its measurement system for diesel engines. It measures the exhaust emissions of particulates using a so-called smoke meter. These emissions are of interest since the laboratory has found that the smoke value is sensitive to many parameters and, therefore, the repeatability of these measurements is typically poorer than for other emissions.
The laboratory has, wisely, adapted the routine to run a stability check every morning, which consists of taking measurements while operating the engine at a standard condition. If the equipment is working correctly there should be no drift in these measurements from day to day. There should only be the natural variation about a mean value that is always expected and which represents the precision of the measurements. (The accuracy is, of course, taken care of by calibrating the instruments.) Looking in its databases it finds a series of 24 stability checks that were made using the same engine. This sample size should be adequate for determining the measurement precision.
Two potential shortcomings of the data set are found. Firstly, ...