An exact method for designing Shewhart and S2 control charts to guarantee in-control performance
针对Shewhart和S²控制图在参数估计后受控性能不足的问题，提出基于正态假设的简单公式来计算控制限，无需使用自举法，且控制图常数不依赖于第一阶段样本数据。
The in-control performance of Shewhart and S2 control charts with estimated in-control parameters has been evaluated by a number of authors. Results indicate that an unrealistically large amount of Phase I data is needed to have the desired in-control average run length (ARL) value in Phase II. To overcome this problem, it has been recommended that the control limits be adjusted based on a bootstrap method to guarantee that the in-control ARL is at least a specified value with a certain specified probability. In this article we present simple formulas using the assumption of normality to compute the control limits and therefore, users do not have to use the bootstrap method. The advantage of our proposed method is in its simplicity for users; additionally, the control chart constants do not depend on the Phase I sample data.