5.1 Introduction

As discussed in Chapter 3, interaction terms provide greater flexibility in modeling the covariance structure of the observations. However, in some situations, it is unnecessary to include interaction effects. This is particularly true if a point estimate of an interaction variance component is negative or if H ₀ : = 0 cannot be rejected using the test described in Section 3.8.1. If an investigator omits the interaction from the two-factor model in Equation (3.1), the resulting model is called the two-factor crossed random model with no interaction. This model is the subject of this chapter. We provide confidence intervals for gauge R&R parameters in Section 5.3 and for other parameters in Section 5.6. Both MLS intervals and GCIs are provided.

5.2 The Model

The balanced two-factor crossed random model with no interaction is

where ? _Y is a constant and P _i, O _j, E _ijk are jointly independent normal random variables with means of zero and variances , , and , respectively.

The ANOVA for model (5.1) is shown in Table 5.1, and the definitions for the mean squares and means are shown in Table 5.2. Table 5.3 reports distributional properties based on the assumptions in model (5.1). Table 5.4 reports the gauge R&R parameters and point estimators. The estimators for ? _Y , ? _P, and ? _M are all MVU estimators.