Process capability indices in normal distribution with the presence of outliers

Abstract

Process capability indices (PCIs) are useful measures to evaluate the performance and capability of a process when it is under control. Assuming the specification variable is distributed from a normal population, several PCIs are derived by the researchers. Also, many scientists have worked on these indices when data are contaminated with outliers as well as in the homogenous case. But, in almost all studies, they evaluated the effect of outliers on the PCIs nonparametrical and used robust methods. Here, the parametric model of outliers is considered and introduced the PCIs based on the outliers model. Therefore, these indices are estimated based on the maximum-likelihood and moment estimator of the unknown parameters of the normal distribution contaminated by outliers. Finally, the performances of these measures as well as their parametric and nonparametric estimators are discussed by using simulation studies and several numerical examples. It has been seen that parametric estimation has better performances than a nonparametric method.

Keywords:

• Normal distribution
• process capability indices
• outliers
• moment estimator
• maximum likelihood estimator
• Robust method

2010 Mathematics Subject Classifications:

• Primary 62F10
• 62F12
• Secondary 62F40
• 62P10

Acknowledgments

The author is thankful to the referees and the editors for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by a grant from Ferdowsi University of Mashhad; No. 2/51303.