Comparison of the X¯ chart and the t chart when the parameters are estimated

The estimation of the process parameters is an important issue to be fixed before starting a control chart implementation in a manufacturing process: in fact, correctly estimating the in-control mean and standard deviation of the quality parameter to be monitored can prevent from an unwanted deterioriation of the statistical performance of the control chart. Usually, the distribution parameters estimation is performed during the Phase I implementation of the control chart and is based on a finite number m of preliminary samples, each having size n, which is as large as the manufacturing environment can afford. This paper presents a comparison between the statistical properties of the Shewhart X¯ chart and the Shewhart t chart when the process parameters are estimated from a Phase I data set having finite size. Mathematical expressions for the ARL and SDRL are suggested for both the charts. Tables of the design parameters selected for the two charts are provided for different numbers of Phase I samples m and sample sizes n. A comparison between the statistical performances of the two charts with estimated parameters is discussed for process instability conditions shifting the process mean and/or standard deviation during the Phase II implementation of the chart. © ICAQM 2013.