Shewhart-Type Q Charts for the Exponential Distribution
Schalk Human1, Subha Chakraborti2
1Statistics, University of Pretoria, Pretoria, Gauteng, South Africa; 2University of Alabama, Tuscaloosa, United States

Shewhart-type Q charts for the exponential distribution are proposed for the three scenarios when the parameter is known, unknown and partially known. The run-length distributions are derived and the in-control and the out-of-control performances of the charts are studied. The proposed charts can be used for individual observations and rational subgroups. These charts have two major advantages: (i) that they can be applied in situations where no historical information is available to estimate the parameters before process monitoring starts, and (ii) the charting statistics are plotted in a standardized normal scale so that different charting statistics can be plotted on the same chart.

Keywords: Shewhart; Control chart; Run length; Exponential

Biography: Dr. SW Human was born in 1981 in Pretoria, South Africa. He completed his high school education in Overkruin High School in 1999 and enrolled at the University of Pretoria where he did his BSc in Financial Mathematics (during 2000-2002) and his BSc(Hons) in Mathematical Statistics (during 2003). Hereafter, he joined the Department of Statistics at the University of Pretoria in 2004 on a full-time basis and completed both his MSc (during 2004-2005) and PhD (during 2007-2009) in Mathematical Statistics; he obtained all his degrees cum laude. Dr. Human received numerous bursaries, a scarce skills scholarship from the Notational Research Foundation (NRF) and research grants from STATOMET, the University of Pretoria and the NRF.