$j=1, \ldots, M$. Instead, we only specify the coverage probability for the integrated one, which is a combination of all $M (> 1)$ procedures. Thus, $\tilde a_j$ depends on the total number of procedures $M$, and for each $j$, the coverage of $R_{N_j}$ is less than $1-\alpha$. We show that the integrated one will have the desired coverage probability. This is why we demand few observations in each procedure; it also requires less computation time. ]{}

Combining several sequential estimation procedures
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Suppose we have enough computing capacity available to simultaneously support $M$ sequential estimation procedures. When conducting a sequential procedure, we usually start with a small initial data set; technically, each procedure can have a different size of initial data set. However, to simplify our discussion, we assume that all initial data sets are of the same size ($n_0$), and we let $C_{jn_0}$, $j=1, \ldots, M$ be the initial data set for each of them.

Assume that there are already $k-1$ observations used in the estimation procedure $j$ ($k > n_0$). If the estimates obtained from procedure $j$ based on $C_{j{k-1}}$ cannot fulfil the inequality in , then we will select a new observation from $\mathcal D$; from there, 