{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1157"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1157","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ ΚΑΙ ΠΟΛΥΩΝΥΜΑ ΤΥΠΟΥ-FIBONACCI","abstract":"WE CONSIDER A RANDOM VARIABLE N DENOTING THE LONGEST SUCCESS RUN IN N (N>1) BERNOULLI TRIALS WITH SUCCESS PROBABILITY P (O<P<1). WE DERIVE FORMULAS FOR P (LN=K) AND P (LN<K) (1<K<N). WE ALSO DERIVE THE GENERATING FUNCTION AND FACTORIAL MOMENTS OF LN. OUR FORMULAS ARE IN TERMS OF FIBONACCI-TYPE POLYNOMIALS OF ORDER K. WE INTRODUCE AND STUDY A NEW DISTRIBUTION, THE BINOMIAL DISTRIBUTION OF ORDER K AND DERIVE THE EXACT DISTRIBUTION OF IT. APPLICATIONS OF THE RANDOM VARIABLES WHICH WE STUDY ARE GIVEN IN RELIABILITY OF CONSECUTIVE-K-OUT-OF-N F SYSTEMS.WE ALSO GIVE THE RELIABILITY OF A STRICT-CONSECUTIVE-K-OUT-OF-F SYSTEM.","abstract_html":"WE CONSIDER A RANDOM VARIABLE N DENOTING THE LONGEST SUCCESS RUN IN N (N&gt;1) BERNOULLI TRIALS WITH SUCCESS PROBABILITY P (O&lt;P&lt;1). WE DERIVE FORMULAS FOR P (LN=K) AND P (LN&lt;K) (1&lt;K&lt;N). WE ALSO DERIVE THE GENERATING FUNCTION AND FACTORIAL MOMENTS OF LN. OUR FORMULAS ARE IN TERMS OF FIBONACCI-TYPE POLYNOMIALS OF ORDER K. WE INTRODUCE AND STUDY A NEW DISTRIBUTION, THE BINOMIAL DISTRIBUTION OF ORDER K AND DERIVE THE EXACT DISTRIBUTION OF IT. APPLICATIONS OF THE RANDOM VARIABLES WHICH WE STUDY ARE GIVEN IN RELIABILITY OF CONSECUTIVE-K-OUT-OF-N F SYSTEMS.WE ALSO GIVE THE RELIABILITY OF A STRICT-CONSECUTIVE-K-OUT-OF-F SYSTEM.","abstract_has_math":false,"creators":["Μακρή, Ευφροσύνη"],"institution":"University of Patras","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1989,"date_issued":"1989","date_published":"1989","updated_at":"2026-07-24T02:24:46Z","subjects":["Αξιοπιστία συστημάτων","ΑΥΣΤΗΡΟ-ΣΥΝΕΧΟΜΕΝΟ-Κ-ΑΠΟ-Ν F ΣΥΣΤΗΜΑΤΑ","ΔΙΑΚΡΙΤΕΣ ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ","ΔΙΩΝΥΜΙΚΗ ΚΑΤΑΝΟΜΗ ΤΑΞΕΩΣ Κ","Κ-ΡΟΕΣ ΕΠΙΤΥΧΙΩΝ","ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ","ΠΟΛΥΩΝΥΜΑ-ΤΥΠΟΥ FIBONACCI ΤΑΞΕΩΣ Κ","ΣΥΝΕΧΟΜΕΝΑ Κ-ΑΠΟ-N FΣΥΣΤΗΜΑΤΑ","BINOMIAL DISTRIBUTION OF ORDER K","CONSECUTIVE-K-OUT-OF-N F SYSTEMS","DISCRETE DISTRIBUTIONS OF ORDER K","FIBONACCI-TYPE POLYNOMIALS OF ORDER K","K-SUCCESS RUNS","LONGESTSUCCESS RUN","RELIABILITY OF CONSECUTIVE-K-OUT-OF N F SYSTEMS","STRICT-CONSECUTIVE-K-OUT-OF N F SYSTEMS","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1157"],"render_values":[{"text":"10.12681/eadd/1157","href":"https://doi.org/10.12681/eadd/1157","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1157","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Μακρή, Ευφροσύνη"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1989"]},{"key":"dc:publisher","label":"Institution","values":["University of Patras","Πανεπιστήμιο Πατρών"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Αξιοπιστία συστημάτων","ΑΥΣΤΗΡΟ-ΣΥΝΕΧΟΜΕΝΟ-Κ-ΑΠΟ-Ν F ΣΥΣΤΗΜΑΤΑ","ΔΙΑΚΡΙΤΕΣ ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ","ΔΙΩΝΥΜΙΚΗ ΚΑΤΑΝΟΜΗ ΤΑΞΕΩΣ Κ","Κ-ΡΟΕΣ ΕΠΙΤΥΧΙΩΝ","ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ","ΠΟΛΥΩΝΥΜΑ-ΤΥΠΟΥ FIBONACCI ΤΑΞΕΩΣ Κ","ΣΥΝΕΧΟΜΕΝΑ Κ-ΑΠΟ-N FΣΥΣΤΗΜΑΤΑ","BINOMIAL DISTRIBUTION OF ORDER K","CONSECUTIVE-K-OUT-OF-N F SYSTEMS","DISCRETE DISTRIBUTIONS OF ORDER K","FIBONACCI-TYPE POLYNOMIALS OF ORDER K","K-SUCCESS RUNS","LONGESTSUCCESS RUN","RELIABILITY OF CONSECUTIVE-K-OUT-OF N F SYSTEMS","STRICT-CONSECUTIVE-K-OUT-OF N F SYSTEMS","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1157","http://hdl.handle.net/10442/hedi/1157"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["WE CONSIDER A RANDOM VARIABLE N DENOTING THE LONGEST SUCCESS RUN IN N (N>1) BERNOULLI TRIALS WITH SUCCESS PROBABILITY P (O<P<1). WE DERIVE FORMULAS FOR P (LN=K) AND P (LN<K) (1<K<N). WE ALSO DERIVE THE GENERATING FUNCTION AND FACTORIAL MOMENTS OF LN. OUR FORMULAS ARE IN TERMS OF FIBONACCI-TYPE POLYNOMIALS OF ORDER K. WE INTRODUCE AND STUDY A NEW DISTRIBUTION, THE BINOMIAL DISTRIBUTION OF ORDER K AND DERIVE THE EXACT DISTRIBUTION OF IT. APPLICATIONS OF THE RANDOM VARIABLES WHICH WE STUDY ARE GIVEN IN RELIABILITY OF CONSECUTIVE-K-OUT-OF-N F SYSTEMS.WE ALSO GIVE THE RELIABILITY OF A STRICT-CONSECUTIVE-K-OUT-OF-F SYSTEM.","ΜΕΛΕΤΑΤΑΙ Η ΤΥΧΑΙΑ ΜΕΤΑΒΛΗΤΗ LN Η ΟΠΟΙΑ ΠΑΡΙΣΤΑΝΕΙ ΤΟ ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ ΣΕ N ΠΕΙΡΑΜΑΤΑ BERNOULLI. ΔΙΝΟΝΤΑΙ Η ΠΥΚΝΟΤΗΤΑ ΠΙΘΑΝΟΤΗΤΑΣ Η ΣΥΝΑΡΤΗΣΗ ΚΑΤΑΝΟΜΗΣ, Η ΓΕΝΝΗΤΡΙΑ ΣΥΝΑΡΤΗΣΗ ΚΑΙ ΤΑ ΑΡΙΘΜΗΤΙΚΑ ΧΑΡΑΚΤΗΡΙΣΤΙΚΑ ΤΗΣ ΤΥΧΑΙΑΣ ΜΕΤΑΒΛΗΤΗΣ . Η ΠΑΡΟΥΣΙΑΣΗ ΤΩΝ ΑΠΟΤΕΛΕΣΜΑΤΩΝ ΑΥΤΩΝ ΓΙΝΕΤΑΙ ΣΥΝΑΡΤΗΣΕΙ ΠΟΛΥΩΝΥΜΩΝ ΤΥΠΟΥ-FIBONACCI ΩΣΤΕ ΟΙ ΕΚΦΡΑΣΕΙΣ ΝΑ ΕΙΝΑΙ ΑΠΛΕΣ ΚΑΙ ΥΠΟΛΟΓΙΣΙΜΕΣ ΑΝΑΔΡΟΜΙΚΑ. ΓΙΝΕΤΑΙ ΕΠΙΣΗΣ ΜΕΛΕΤΗ ΤΗΣ ΑΝΤΙΣΤΟΙΧΗΣ Τ. Μ ΣΕ ΚΥΚΛΟ. ΕΙΣΑΓΕΤΑΙ ΚΑΙ ΜΕΛΕΤΑΤΑΙ ΜΙΑ ΝΕΑΚΑΤΑΝΟΜΗ, Η ΔΙΩΝΥΜΙΚΗ ΤΑΞΕΩΣ Κ ΓΙΑ ΤΗΝ ΟΠΟΙΑ ΔΙΝΕΤΑΙ ΑΚΡΙΒΗΣ ΕΚΦΡΑΣΗ ΤΗΣ ΠΥΚΝΟΤΗΤΑΣ ΠΙΘΑΝΟΤΗΤΑΣ ΤΗΣ. ΕΦΑΡΜΟΓΕΣ ΤΩΝ ΤΥΧΑΙΩΝ ΜΕΤΑΒΛΗΤΩΝ ΠΟΥ ΜΕΛΕΤΩΝΤΑΙ ΔΙΝΟΝΤΑΙΣΤΗΝ ΑΞΙΟΠΙΣΤΙΑ ΣΥΝΕΧΟΜΕΝΩΝ-Κ ΑΠΟ-Ν F ΣΥΣΤΗΜΑΤΩΝ. ΔΙΝΕΤΑΙ ΤΕΛΟΣ Η ΑΞΙΟΠΙΣΤΙΑ ΕΝΟΣ ΑΥΣΤΗΡΟΥ-ΣΥΝΕΧΟΜΕΝΟΥ ΣΥΝΕΧΟΜΕΝΟΥ-Κ-ΑΠΟ-Ν F ΣΥΣΤΗΜΑΤΟΣ."]},{"key":"dc:title","label":"Title","values":["ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ ΚΑΙ ΠΟΛΥΩΝΥΜΑ ΤΥΠΟΥ-FIBONACCI","LONGEST SUCCESS RUN AND FIBONACCI-TYPE POLYNOMIALS"]}]}],"canonical_facts":{"dc:creator":["Μακρή, Ευφροσύνη"],"dc:date":["1989"],"dc:description":["WE CONSIDER A RANDOM VARIABLE N DENOTING THE LONGEST SUCCESS RUN IN N (N>1) BERNOULLI TRIALS WITH SUCCESS PROBABILITY P (O<P<1). WE DERIVE FORMULAS FOR P (LN=K) AND P (LN<K) (1<K<N). WE ALSO DERIVE THE GENERATING FUNCTION AND FACTORIAL MOMENTS OF LN. OUR FORMULAS ARE IN TERMS OF FIBONACCI-TYPE POLYNOMIALS OF ORDER K. WE INTRODUCE AND STUDY A NEW DISTRIBUTION, THE BINOMIAL DISTRIBUTION OF ORDER K AND DERIVE THE EXACT DISTRIBUTION OF IT. APPLICATIONS OF THE RANDOM VARIABLES WHICH WE STUDY ARE GIVEN IN RELIABILITY OF CONSECUTIVE-K-OUT-OF-N F SYSTEMS.WE ALSO GIVE THE RELIABILITY OF A STRICT-CONSECUTIVE-K-OUT-OF-F SYSTEM.","ΜΕΛΕΤΑΤΑΙ Η ΤΥΧΑΙΑ ΜΕΤΑΒΛΗΤΗ LN Η ΟΠΟΙΑ ΠΑΡΙΣΤΑΝΕΙ ΤΟ ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ ΣΕ N ΠΕΙΡΑΜΑΤΑ BERNOULLI. ΔΙΝΟΝΤΑΙ Η ΠΥΚΝΟΤΗΤΑ ΠΙΘΑΝΟΤΗΤΑΣ Η ΣΥΝΑΡΤΗΣΗ ΚΑΤΑΝΟΜΗΣ, Η ΓΕΝΝΗΤΡΙΑ ΣΥΝΑΡΤΗΣΗ ΚΑΙ ΤΑ ΑΡΙΘΜΗΤΙΚΑ ΧΑΡΑΚΤΗΡΙΣΤΙΚΑ ΤΗΣ ΤΥΧΑΙΑΣ ΜΕΤΑΒΛΗΤΗΣ . Η ΠΑΡΟΥΣΙΑΣΗ ΤΩΝ ΑΠΟΤΕΛΕΣΜΑΤΩΝ ΑΥΤΩΝ ΓΙΝΕΤΑΙ ΣΥΝΑΡΤΗΣΕΙ ΠΟΛΥΩΝΥΜΩΝ ΤΥΠΟΥ-FIBONACCI ΩΣΤΕ ΟΙ ΕΚΦΡΑΣΕΙΣ ΝΑ ΕΙΝΑΙ ΑΠΛΕΣ ΚΑΙ ΥΠΟΛΟΓΙΣΙΜΕΣ ΑΝΑΔΡΟΜΙΚΑ. ΓΙΝΕΤΑΙ ΕΠΙΣΗΣ ΜΕΛΕΤΗ ΤΗΣ ΑΝΤΙΣΤΟΙΧΗΣ Τ. Μ ΣΕ ΚΥΚΛΟ. ΕΙΣΑΓΕΤΑΙ ΚΑΙ ΜΕΛΕΤΑΤΑΙ ΜΙΑ ΝΕΑΚΑΤΑΝΟΜΗ, Η ΔΙΩΝΥΜΙΚΗ ΤΑΞΕΩΣ Κ ΓΙΑ ΤΗΝ ΟΠΟΙΑ ΔΙΝΕΤΑΙ ΑΚΡΙΒΗΣ ΕΚΦΡΑΣΗ ΤΗΣ ΠΥΚΝΟΤΗΤΑΣ ΠΙΘΑΝΟΤΗΤΑΣ ΤΗΣ. ΕΦΑΡΜΟΓΕΣ ΤΩΝ ΤΥΧΑΙΩΝ ΜΕΤΑΒΛΗΤΩΝ ΠΟΥ ΜΕΛΕΤΩΝΤΑΙ ΔΙΝΟΝΤΑΙΣΤΗΝ ΑΞΙΟΠΙΣΤΙΑ ΣΥΝΕΧΟΜΕΝΩΝ-Κ ΑΠΟ-Ν F ΣΥΣΤΗΜΑΤΩΝ. ΔΙΝΕΤΑΙ ΤΕΛΟΣ Η ΑΞΙΟΠΙΣΤΙΑ ΕΝΟΣ ΑΥΣΤΗΡΟΥ-ΣΥΝΕΧΟΜΕΝΟΥ ΣΥΝΕΧΟΜΕΝΟΥ-Κ-ΑΠΟ-Ν F ΣΥΣΤΗΜΑΤΟΣ."],"dc:identifier":["10.12681/eadd/1157","http://hdl.handle.net/10442/hedi/1157"],"dc:language":["gre"],"dc:publisher":["University of Patras","Πανεπιστήμιο Πατρών"],"dc:subject":["Αξιοπιστία συστημάτων","ΑΥΣΤΗΡΟ-ΣΥΝΕΧΟΜΕΝΟ-Κ-ΑΠΟ-Ν F ΣΥΣΤΗΜΑΤΑ","ΔΙΑΚΡΙΤΕΣ ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ","ΔΙΩΝΥΜΙΚΗ ΚΑΤΑΝΟΜΗ ΤΑΞΕΩΣ Κ","Κ-ΡΟΕΣ ΕΠΙΤΥΧΙΩΝ","ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ","ΠΟΛΥΩΝΥΜΑ-ΤΥΠΟΥ FIBONACCI ΤΑΞΕΩΣ Κ","ΣΥΝΕΧΟΜΕΝΑ Κ-ΑΠΟ-N FΣΥΣΤΗΜΑΤΑ","BINOMIAL DISTRIBUTION OF ORDER K","CONSECUTIVE-K-OUT-OF-N F SYSTEMS","DISCRETE DISTRIBUTIONS OF ORDER K","FIBONACCI-TYPE POLYNOMIALS OF ORDER K","K-SUCCESS RUNS","LONGESTSUCCESS RUN","RELIABILITY OF CONSECUTIVE-K-OUT-OF N F SYSTEMS","STRICT-CONSECUTIVE-K-OUT-OF N F SYSTEMS","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"dc:title":["ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ ΚΑΙ ΠΟΛΥΩΝΥΜΑ ΤΥΠΟΥ-FIBONACCI","LONGEST SUCCESS RUN AND FIBONACCI-TYPE POLYNOMIALS"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:46Z"}