Rational Sampling and Standard Deviations for Random Variables in Phase I Application of Statistical Process Control

"The phased application of statistical process control (SPC) infers that processes are classifiable as pre-SPC (or phase zero), phase I and phase II processes, with different objectives being pursued in the different phases. Phase zero processes, defined as processes affected by assignable causes of variation, are characterised as follows: out-of-control with unknown autocorrelation structure having an unknown statistical distribution not performing consistently on target with minimum variability potentially incapable of conforming to the product specifications. The objectives of phase I SPC is to obtain estimates of the mean (µ), variance (s2), probability density function (f(X)) and the autocorrelation structure, as well as transforming the process into a phase II process (defined as a process conforming to specifications and performing on target with minimum variability). As in any other type of research or pragmatic improvement intervention, sampling is required is to achieve these objectives. The challenge of deciding a phase I sampling plan is multifarious since it has to cope with the aforementioned effects of assignable causes and provide for rigour estimates of the unknown parameters. Furthermore, deciding sampling plans in phase I invariably presents a classical catch-22 situation: appropriate sampling is required to determine the autocorrelation structure of a variable, but knowledge of the autocorrelation structure is required to formulate an appropriate sampling plan. This paper suggests, for random variables, guidelines to formulate sampling plans, and presents a methodology to estimate the inherent process parameters of process variables and an approach to identify assignable causes in phase I. CITATION:Breytenbach, W P, 2014. Rational sampling and standard deviations for random variables in phase i application of statistical process control, in Proceedings Sampling 2014, pp 141–154 (The Australasian Institute of Mining and Metallurgy: Melbourne)."