This paper presents asymptotic formulae, lower and upper bounds for the expected sample size of certain sequential tests of the parameter of an exponential family of distributions. The tests involved are tests of power one based on mixture-type stopping rules and tests for the detecting of change in the underlying distribution. Analysis for incorrect assumptions of the underlying distribution yields asymptotic formulae for such cases, showing robustness of the original formulae. Monte Carlo results indicate the validity of asymptotic formulae for sample sizes one would expect in practical applications.
"Approximations to the Expected Sample Size of Certain Sequential Tests." Ann. Statist. 3 (6) 1267 - 1282, November, 1975. https://doi.org/10.1214/aos/1176343284