Control Charts for Skewed and Left-Censored Data that Approximately Control the Family Type I Error

ABSTRACT

Businesses that have specifications for multiple trace components present challenging issues to the suppliers to these industries. For the electronics industry trace contamination is typically at the part per billion (ppb) level or less. Trace components often have distributions that are skewed to the right and can have varying degrees of censoring imposed by the application of detection limits of the methods required for their analysis. When customers additionally require that the materials they receive be in statistical control, the corresponding control charts need to not only account for these factors but also maintain a fixed type I error at the family level. The high amount of skewness in the measured concentrations of many of the components and the high levels of censoring make traditional multivariate approaches unhelpful. The high level of censoring also seriously compromises standard data transformation and distribution fitting procedures. Also, because the upper control limits are located far into the tails of the distributions, even without censoring competing distributions can give very different results for the control limits. This article describes a nondistribution fitting, non-data-transforming approach that approximately maintains a preset type I error at the family level. The methodology was extensively tested on simulations and real-world data from multiple products from multiple companies and performed well.

KEYWORDS:

• censoring
• control limits
• family type I error
• individual type I error
• multiple characteristics per sample
• nondistribution fitting method
• nontransformation method
• skewed distributions
• specifications

Notes

N = 100.