Summary: In practical applications, the in-control process parameters are often unknown and have to be estimated from an in-control Phase I data set. Therefore, the performance of Phase II control charts depends on the control limits established on the basis of the estimates of the in-control parameters. Different Phase I data sets can result in different parameter estimates, therefore resulting in different control limits and control charts performance. However, mostly one practitioner only has one Phase I data set, so it is necessary and meaningful to study the performance of control charts based on a given Phase I data set, i.e., the conditional performance. Using Monte Carlo simulations, this paper considers the conditional performance of the equal-tailed and unbiased \(R\) control charts with three kinds of parameter estimates, the average sample range, the average sample standard deviation and the pooled sample standard deviation, for monitoring changes in the standard deviation of a normal process. This paper also evaluates the performance of each \(R\) chart in terms of the percentile, mean and standard deviation of conditional in-control ARL distribution. The results show that parameter estimation has a significant effect on the control charts performance, resulting in more frequent false alarms than expected. In order to solve this question, this paper proposes a bootstrap method to adjust the control limits to obtain the control charts with desired conditional in-control performance. Results show that the third estimate of the process standard deviation is better than the first two estimates. In addition, the proposed unbiased \(R\) chart with adjusted limits outperforms than the corresponding equal-tailed chart in terms of the conditional ARL distribution.