R και S διαγράμματα ελέγχου με όρια πιθανότητας
R and S control charts with probability limits
Κοϊμτζόγλου, Αλέξιος Π.
KeywordsR διαγράμματα ελέγχου ; S διαγράμματα ελέγχου ; Διαγράμματα ελέγχου τύπου Shewhart ; Διαγράμματα ελέγχου με όρια πιθανότητας
Shewhart control charts are a significant and powerful tools in an attempt towards a more stable production process. Through these charts, possible deviations on various product parameters can be controlled, which if not identified on time, could possibly lead to an out of control process. Effective use of Shewhart control charts results in the production of optimum quality products and minimize the production of non-conforming ones. Usually, two types of control charts are compiled. One chart for monitoring the process mean and one for monitoring the process variability. The computation method of control limits is of great importance due to the fact that wrong choice of the limits could seriously affect the effectiveness of the chart. Monitoring the process variability with the classical R and S charts with 3σ control limits neither provide an in control average run length of approximately 370 nor guarantee the desired type I error of 0.0027. In this thesis we study R and S control charts with probability limits for normal data which guarantee an in control average run length equal to 370. The non-normal data case is also discussed. The present thesis is divides in three chapters. In the first chapter an extensive analysis of Shewhart control charts structure for monitoring the process mean and variability is given. In addition certain disadvantages of these charts with 3σ control limits are presented. In the second chapter R and S control charts with probability limits are studied. A comparison in the effectiveness of R and S control charts for monitoring process variability for various sample sizes and various shifts in the standard deviation is performed. Finally, in the third chapter a research on how the assumption of non-normality can affect an R control chart is discussed.