Individual agreement between two measurement systems is determined using the total deviation index (TDI) or the coverage probability (CP) criteria as proposed by Lin (2000) and Lin et al. (2002). We used a variance component model as proposed by Choudhary (2007). Using the bootstrap approach, Choudhary (2007), and generalized confidence intervals, we construct bounds on TDI and CP. A simulation study was conducted to assess whether the bounds maintain the stated type I error probability of the test. We also present a computational example to demonstrate the statistical methods described in the paper.