Διαγράμματα ελέγχου για την παρακολούθηση εκθετικών δεδομένων
Control charts for monitoring exponential data
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Keywords
Διαγράμματα ελέγχου ; Διεργασίες υψηλής απόδοσης ; Κανόνες ροών ; Μέσο μήκος ροής (ARL) ; ANOSAbstract
The main assumption made for monitoring the defects (or nonconformities) of a process is that the number of defects per inspection unit follows the Poisson distribution and therefore the conventional 𝑐 and 𝑢 control charts are used for their monitoring. In high-yield processes, where the rate of occurrence of defects is quite low, the 𝑐 and 𝑢 control charts are ineffective since the Poisson distribution cannot be approximated accurately by normal distribution, resulting in a much higher probability of type I error than the desired value. Moreover, it is not possible to detect further improvement of the production process since the lower control limit is set to zero. In these cases, the cumulative quantity (time, inspection units etc.) until the occurrence of 𝑟 defects is monitored. For 𝑟 = 1 the cumulative quantity follows the exponential distribution, while for 𝑟 > 1, the cumulative quantity follows the Gamma distribution. In the present dissertation, 79 control charts are presented for monitoring the cumulative quantity until the occurrence of 𝑟 defects, where some of them are studied for first time. In Chapter 1 an introduction in control charts is made and the conventional charts are mentioned. In Chapter 2 the t and tr control charts are presented (unbiased and biased). In Chapter 3 the 𝐴𝑅𝐿-unbiased t and 𝐴𝑅𝐿-unbiased tr control charts with runs rules are studied. In Chapter 4 the exponential control charts with memory CUSUM and EWMA, as well as the exponential CUSUM control chart with the method of fast initial response are presented. Moreover, the average run length (𝐴𝑅𝐿) is calculated for all the control charts which are presented in the dissertation. In Chapter 5 various comparisons are made between the control charts that we presented based on 𝐴𝑁𝑂𝑆 (average number of observations to signal), in order to conclude which control charts are the most efficient for the detection of various shifts in the production process.
Postgraduate Studies Programme
Εφαρμοσμένη ΣτατιστικήDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
174Language
GreekCollections
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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα