In many Industrial applications, censored observations are present and in this cases direct application of the Shewhart mean and np control charts is not adequate. We develop a methodology for constructing a mean control chart based on the conditional expected value of censored observations, assuming that the in-control process follows a Weibull distribution. The performance of the proposed control chart is studied in terms of the false alarm probability. We also compare the proposed chart with the np chart and the Shewhart mean chart.