IMPROVED SHEWHART-TYPE X CONTROL SCHEMES UNDER NON-NORMALITY ASSUMPTION: A MARKOV CHAIN APPROACH

Abstract

In statistical process control and monitoring (SPCM), traditional (or classical) X control schemes are designed under the assumption of normally distributed data. However, in real-life applications, the normality assumption could easily fail to hold, and the results would no longer be realistic. Therefore, X control schemes designed under flexible probability distributions are needed. In this paper, we consider to improve the Shewhart-type X control scheme using supplementary 2-of-(h+1) and 1-of-1 or 2-of-(h+1) runs-rules (where ?? 1) for non-normal data. The proposed control schemes are designed using the Burr type XII probability distribution function (pdf) because of its properties and suitability for general industrial applications. The performance of the proposed control schemes is investigated using the Markov chain approach. It was found that the proposed schemes outperform the existing standard and improved X control schemes in many cases. An illustrative real-life example is used to demonstrate the implementation of the proposed schemes.

Keywords

• urr type XII X control scheme
• 2-of-(h+1) scheme
• improved 2-of-(h+1) scheme
• Markov of chain approach
• zero-state mode
• steady-state mode