Since their invention in the 1920s, control charts have been popular tools for use in monitoring processes in fields as varied as manufacturing and healthcare. Most of these charts are designed to monitor a single process parameter, but recently, a number of charts and schemes for jointly monitoring the location and scale of processes which follow two-parameter distributions have been developed. These joint monitoring charts are particularly relevant for processes in which special causes may result in a simultaneous shift in the location parameter and the scale parameter. Among the available schemes for jointly monitoring location and scale parameters, the vast majority are designed for normally distributed processes for which the in-control mean and variance are known rather than estimated from data. When the process data are non-normally distributed or the process parameters are unknown, alternative control charts are needed. This dissertation presents and compares several control schemes for jointly monitoring data from Laplace and shifted exponential distributions with known parameters as well as a pair of charts for monitoring data from normal distributions with unknown mean and variance. The normal theory charts are adaptations of two existing procedures for the known parameter case, Razmy's (2005) Distance chart and Chen and Cheng's (1998) Max chart, while the Laplace and shifted exponential charts are designed using an appropriate statistic for each parameter, such as the maximum likelihood estimators.