New Shewhart-type synthetic \bar{X} control schemes for non-normal data

Subject Areas : Mathematical Optimization

Jean‑Claude Malela‑Majika ¹ , Marien Alet Graham ²

1 - Department of Statistics, College of Science, Engineering and Technology, University of South Africa (UNISA), PO Box 392, Pretoria, 0003, South Africa
2 - Department of Science, Mathematics and Technology Education, Faculty of Education, University of Pretoria, Groenkloof Campus, Natural Sciences Building Room 4-18, Corner of George Storrar Drive and Leyds Street, Groenkloof, Pretoria, 0002, South Africa

Received: 2020-10-08 Accepted : 2020-10-08 Published : 2019-09-01

Keywords: Non, side, sensitive synthetic schemes · Side, sensitive synthetic schemes · Zero, state mode · Steady, state mode · Transition probability matrix (TPM),

Abstract :

In this paper, Burr-type XII ̄X synthetic schemes are proposed as an alternative to the classical ̄X synthetic schemes when the assumption of normality fails to hold. First, the basic design of the Burr-type XII ̄X synthetic scheme is developed and its performance investigated using exact formulae. Secondly, the non-side-sensitive and side-sensitive Burr-type XII ̄X synthetic schemes are introduced and their zero-state and steady-state performances, in terms of the average run-length and expected extra quadratic loss values, are investigated using a Markov chain approach. Thirdly, the proposed schemes are compared to the existing classical runs-rules and synthetic ̄X schemes. It is observed that the proposed schemes have very interesting properties and outperform the competing schemes in many cases under symmetric and skewed underlying process distributions. Finally, an illustrative real-life example is given to demonstrate the design and implementation of the proposed Burr-type XII ̄X synthetic schemes.