In a multiple stream process (MSP), a same quality variable is measured in several streams in parallel. The first tool proposed for monitoring MSPs was the Group Control Chart (GCC) by Boyd (1950). These schemes are recommended in textbooks and guides as Pyzdek (1992) and Montgomery (until 3rd edition, 1997). Its efficiency is impaired by the presence of cross correlation between streams. A useful model for MSPs (Mortell and Runger, 1995) represents the value of the quality variable in each stream at any time t as the sum of a random variable (or stochastic process) but that is common to all streams, which can be called base level, plus the individual variation of each stream relative to the base level. In the literature, three different Shewhart schemes were developed to control the individual variation of each stream: Mortell e Runger (1995), Runger, Alt and Montgomery (1996) and Barbosa (2008). Only the two first ones were developed both in a Shewhart-type and a EWMA (Exponentially Weighted Moving Average) version. All these schemes were devoted to monitoring the mean of the individual components of the streams; to the best of our knowledge, no previous work considered the case of increases in the variance of a stream. In this thesis four different GCCs for monitoring the inner variability of the individual streams are developed: a GCC of S(2), the sample variance of each stream (which is not the same as Runger, Alt and Montgomery’s statistics); a GCC of EWMA[lnS(2)]; a GCC of the Moving Ranges of the residuals of each stream to the estimated base level, and an EWMA version of it. The last two GCCs cater for the case where, at every sampling time, only individual observations per stream are feasible, which is frequent with a large number of streams. Beyond the mentioned contributions, aiming at more sensitivity to the small shifts in the mean of the individual components, this work proposes a EWMA version of the GCC by Barbosa (2008), the most efficient in the Shewhart version. The ARL performance of every one of these schemes is analyzed, in a variety of situations, including the case of increases in the variance of one stream when the schemes are designed for monitoring the means of individual streams. The results show that the proposed schemes are the fastest in detecting special causes that affect one individual stream.