One of the most pressing technical issues facing BIDs is the need for methodology for estimating appropriate sample sizes. Intertwined with this is the need to assess variability between devices. The sample size methodology that has been derived at present depends on the use of the binomial distribution for making these calculations [ ]. However, it is well known that the binomial distribution is not appropriate for assessing performance of a BID [ ]. In order to develop sample size calculations, it is necessary to understand the sampling distribution and the standard error of the estimated error rate. Some work has been done in this area to derive estimates that are appropriate [1]. This work has largely been non-parametric to avoid assumptions about the distribution of individual error rates, pi’s. However, parametric methods are necessary for ‘inverting’ margins of error to get sample size calculations. One possible approach that Schuckers (to appear) has developed is to use a Beta-binomial distribution to model the overall error rate [ ]. However, it is unclear whether a Beta distribution is appropriate for modeling the pi’s. Therefore, we propose following the extra-variation model of Moore [ ]. That more general model only assumes that the first two moments are known.

     Once the confidence interval work above has been completed, we will turn our attention to sample size calculations. Because of the difficult nature of the problem, we propose a conditional three-step solution to this problem. The first step is to find estimates of the error rate and the intra-individual correlation and to specify the confidence level. As in any sample size calculation it is necessary to estimate the parameters governing the standard error prior to the calculations. The second crucial step is to fix m, the number of tests per individual.
This step is necessary because it is practically impossible to simultaneously solve for both m and n. Then having set a value for m, we solve for n the number of individuals to be tested. In this way we get a conditional solution of how many individuals need to be tested given the number of tests per individual. This procedure allows for a solution to the problem of sample size calculations.

     Another foundational statistical problem is that of assessing performance when zero errors are observed in testing. This is an especially important issue for BID testers since they need to gauge the error rate of extremely accurate systems within a finite time frame. The issue of inference when no errors are observed has been addressed when a binomial sampling distribution is appropriate . This paper and others, e.g. [ ], suggests that an appropriate upper bound for the error rate when no errors are observed in W attempts would be 3/W or 3/(W+1), where W is the number of Bernoulli trials. Bayesian methods are extremely useful and powerful under circumstances such as these. Winkler et al.
(2002) provides guidance regarding accurate specifications of prior distributions for the binomial [ ]. To address this matter, we propose extending the work of Schuckers [ ] by considering various prior distributions, both informative and uninformative, and their impact on inference. Specifically we would like to have a simple function of m and n similar to the 3/(W+1) mentioned above for the binomial model. Beyond zero errors, the eventual goal of this study would be to imbed the zero error methodology into a comprehensive flexible methodology that would be appropriate for collection of data on BID’s.