A method to compute the minimum Horizontal Protection Level (HPL) using the test statistic of normal distribution, which will exploit advances in computational power to meet the requirement of Time to Alert (TTA), is proposed to improve service availability. To obtain the minimum solution, two approximations used in traditional algorithms need exact solutions: the distribution of the horizontal position error and the determination of the worst case to ensure that the resulting HPL is able to accommodate all possible bias. This is validated with results such that the optimal solution is achieved with a pre-defined accuracy and sufficient computational efficiency. Also, the new HPL is used to determine if current approximated methods are conservative, where one of the methods does not meet the integrity requirement with given test statistics, error model and integrity risk definition.
