  The sequential analysis of series often requires nonparametric procedures,
where the most powerful ones frequently use rank transformations. Re-ranking
the data sequence after each new observation can become too intensive
computationally. This led to the idea of sequential ranks, where only the most
recent observation is ranked. However, difficulties finding, or approximating,
the null distribution of the statistics may have contributed to the lack of
popularity of these methods. In this paper, we propose transforming the
sequential ranks into sequential normal scores which are independent, and
asymptotically standard normal random variables. Thus original methods based on
the normality assumption may be used.
  A novel approach permits the inclusion of a priori information in the form of
quantiles. It is developed as a strategy to increase the sensitivity of the
scoring statistic. The result is a powerful convenient method to analyze
non-normal data sequences. Also, four variations of sequential normal scores
are presented using examples from the literature. Researchers and practitioners
might find this approach useful to develop nonparametric procedures to address
new problems extending the use of parametric procedures when distributional
assumptions are not met. These methods are especially useful with large data
streams where efficient computational methods are required.
