Statistical process control (SPC) for short production run with Cauchy distribution, a case study with corrected numbers approach

Abstract

Controlling damages in a short production run is very subtle. Because the samples for each part are small, the control charts for each part can be obscure therefore the deviation of the actual from the nominal size of each part in a unique control chart will be applied. Differences between the control limits of various deviations can generate a heavy-tailed distribution. We will discuss it with an example of Cauchy distribution as a member of this family. From Phase (I) we will propose the Corrected Numbers and these numbers will be applied in Phase (II).

Keywords:

• Dispersion
• Stable distributions
• Symmetric Asymptotically Pareto Property
• Shewhart control charts
• CUSUM chart