Generalized skewness correction structure of X̄ control chart for unknown process parameters and skewed probability distributions

ABSTRACT

In this article, we have highlighted limitations of existing structures of $\overline{X}$ control chart for unknown parameters by considering various circumstances of a process. The circumstances include availability of limited samples for estimating control limits, probability distribution is unknown and collected data are highly skewed. To tackle with the limitations, we have proposed generalized skewness correction structure of $\overline{X}$ chart. For proposing the required structure, we have developed skewness correction based dispersion estimators and corrected control limits multipliers to replace with known probability distribution based dispersion estimator and control limits multipliers. The proposed generalized skewness structure is dependent on the amount of skewness of gathered data from an ongoing process instead of restricted assumptions. Results illustrate that actual false alarm rate of proposed structure remains close to true false alarm rate as compared to existing structures when assumptions are violated. Besides, a real-life example from petrochemical process is presented for explaining the implementation procedure of proposed structure.

KEYWORDS:

• Control chart
• control limits multipliers
• estimators
• estimation effect
• false alarm rate
• parameters estimation
• probability distribution
• skewness

Acknowledgments

I am thankful to my beloved wife for supporting me to accomplish this research work successfully.

Disclosure statement

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

ORCID

Muhammad Hisyam Lee  http://orcid.org/0000-0002-3700-2363

Muhammad Riaz  http://orcid.org/0000-0002-7599-6928