new shewhart-type synthetic x bar control schemes for non-normal data

In this paper, burr-type xiix bar synthetic schemes are proposed as an alternative to the classicalx bar synthetic schemes when the assumption of normality fails to hold. first, the basic design of the burr-type xiix bar synthetic scheme is developed and its performance investigated using exact formulae. secondly, the non-side-sensitive and side-sensitive burr-type xiix bar 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 syntheticx bar 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 xiix bar synthetic schemes