Design and Analysis of Gauge R&R Studies: Making Decisions with Confidence Intervals in Random and Mixed ANOVA Models

8.4: Three-Factor Crossed Random Designs

8.4 Three-Factor Crossed Random Designs

In Chapters 3 and 5 we presented results for a two-factor crossed random design. We now present some results for a three-factor crossed random design.

Table 8.16 presents a partial listing of data from a gauge R&R study used in the fabrication of magnetic tape for computerized data storage. In this study, o automated test stations (operators) are used to evaluate the quality of p tape heads (parts). To measure characteristics of the heads, t tapes are used in each test station. In this design, all p heads are measured with each of the ot test station tape combinations. There are r = 2 replicates for each treatment condition. The response variable is Forward resolution of a tape head. In the process of writing information to magnetic tape, voltage is measured at two different frequencies. The resolution is a ratio of these two voltages. There is no unit of measurement on the ratio, and it is expressed as a percentage. Ideally, this ratio should be 100%. The specification limits are LSL = 90% and USL = 110%. Forward resolution is measured when the drive writes in the forward direction.

Table 8.16: Example data for a three-factor crossed design.

Part

Operator

Tape

Y

1

1

1

102.8917

1

1

1

103.3077

1

1

2

104.1766

1

1

2

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