2.1 Introduction

The first model we consider is the balanced one-factor random design. This model describes a gauge R&R study in which a single operator selects a random sample of p parts and measures each part r times using the same measurement gauge.

Table 2.1 presents a subset of data reported by Houf and Berman [32]. In this example, the monitored parts are power modules for a line of motor starters. The response is the thermal performance of the module measured in C per watt. Measurements are taken on the device using a thermal resistance measuring instrument. The data shown in the table represent measurements taken by a single operator. Each response has been multiplied by 100 for convenience of scale. The p = 10 parts were sampled at random from the manufacturing process, and r = 2 replicate measures were made on each part.

We now present the model used to analyze the data in Table 2.1. The completed analysis is reported in Section 2.5.

2.2 The Model

The balanced one-factor random model is

where ? _Y