Control charts and sampling techniques
Ioannis Karakostas, National Technological University Of Athens
Since the introduction of the idea of control charts for monitoring processes by Walter Shewhart, their use has been established in a wide variety of applications, especially in the industrial domain. This is due to their ability to detect shifts in the process mean, by getting information through samples of one or more observations, thus improving its quality. In Chapter 1 of this thesis the simplest form of control charts, namely Shewhart control charts, are presented. Two additional
... s, the CUSUM and the EWMA charts, are subsequently presented in Chapters 2 and 3 respectively, which share a common characteristic, dependence on past observations. In every case, we consider that our data are normally distributed. Moving on, the thesis focuses on EWMA control charts, their properties and their performance measurement. Their evaluation is done through the average run length, which is calculated in R, using either the "spc" library or a markov chain based code. In Chapter 4, techniques that improve the EWMA charts, regarding faster response to mean shifts, are presented, while in Chapter 5, a modified EWMA chart is presented, which can detect shifts ranging from small and gradual to large and sudden shifts. It is towards this direction that the combined control charts were designed, some of which are presented in Chapter 6. In any case, the different versions of EWMA charts derive from modifying either the formula of the statistic or the control limits. Another way of enhancing control charts is by interfering with the sample information. Thus, in Chapter 7, various sampling techniques are presented, with some form of ranking on the observations. The RSS and MRSS techniques are analyzed, as well as the EWMA charts that derive from the relevant ranked data. They are also compared in terms with their ARL performance. Moreover, reference is made to some modifications of the above sampling techniques, namely DRSS, MDRSS, DMRSS and ODRSS, which are compared in terms with their ARL performance as well. Finally, pointing out the issue of autocorrelation of the observations, in Chapter 8 we present a recent alternative category of sampling techniques which faces this problem (sskip, mixed samples) and propose further study of the performance of an EWMA scheme based on such techniques.