New Shewhart-type synthetic X control schemes for non-normal data

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.