Reliability and integrity has become increasingly important in ubiquitous positioning systems, and particularly in critical applications. To implement reliability and integrity measures, Fault Detection and Exclusion (FDE) procedures should be used. However, the current FDE procedures in the chi-square test and the outlier test are suboptimal in terms of continuity and availability. This is due to the assumption that the bias always corresponds with the measurement that has the largest Protection Level (PL), and in the setting of the continuity probability to a predefined value rather than being maximised. The FDE procedures assume that the bias always corresponds with the measurement that has the largest PL. However, this is not the case since a bias can occur in any one of the measurements. Consequently, a procedure of averaging the Missed Detection probabilities calculated at the Alert Limit (AL) across all measurements was proposed in the literature. However, simulations demonstrated that only a minor improvement in the availability is achieved. The FDE procedures in the chi-square test and the outlier test are also dependent on the user specifying the instantaneous continuity probability that is required to be met. It is then, once the continuity probability has been specified, that the procedures determine if there is sufficient integrity, via the monitoring of the maximum PL in relation to the AL. However, in general, ubiquitous positioning systems do not have a minimum continuity probability that is required to be met; but simply desire the continuity probability to be maximised. This paper develops an optimised FDE strategy for one or more biases, which assumes that the bias can exist in any one of the measurements and allows varying satellite failure rates. In addition, the procedure also aims to provide a position that has sufficient integrity continuously, via maximising the instantaneous continuity probability.