Effect of the Number and Size of the Initial Samples on the Performance of the S Chart

• Activity Number: 599
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Eugenio Epprecht*+ and Lorena Drumond Loureiro
• Companies: PUC-Rio and PUC-Rio
• Keywords: S control chart ; False-alarm probability ; Performance ; Parameter estimation ; Phase I ; Number of samples

Abstract

Most papers on the effect of parameter estimation over control chart performance focus on the marginal distribution of the run length (RL). However, once a process parameter is estimated, the estimation error becomes a constant (albeit unknown), and the RL follows its conditional distribution given the (unknown) value of the error. With this in mind, our focus is rather the conditional distribution of the RL - specifically, of the in-control RL of the S chart, which is geometrically distributed with parameter alfa (false-alarm probability). We obtain the distribution function of alfa as a function of the number and size of the initial samples; resulting probability intervals for alfa; and, for several sample sizes, the minimum number of initial samples that guarantees (with a specified probability) that the actual alfa will not exceed the nominal value by more than a pre-specified percentage. The calculations are straightforward and carried out in spreadsheet software. Some conclusions are drawn in terms of guidance for the user.