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


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


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.