❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦
❡♠ ❊st❛tíst✐❝❛
Modelos robustos para degradação linear
e tempo de falha
Rívert Paulo Braga Oliveira lamabarista@gmail.com
Orientadora: Profa. Dra. Rosângela Helena Loschi loschi@est.ufmg.br
Co-orientadora: Profa. Dra. Marta Afonso Freitas marta@dep.ufmg.br
Rívert Paulo Braga Oliveira
Modelos robustos para degradação linear
e tempo de falha
Tese apresentada ao Departamento de Pós-Graduação em Estatística da Universidade Federal de Minas Gerais, para a obtenção do Título de Doutor em Estatística
Orientadora: Rosângela Helena Loschi Co-orientadora: Marta Afonso Freitas
Agradecimentos
❆❣r❛❞❡ç♦ ❛ t♦❞♦s q✉❡ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡ ♠❡ ❛♣♦✐❛r❛♠ ♥❡st❡ tr❛❜❛❧❤♦✳
❆ ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛✱ ❉r➟✳ ❘♦sâ♥❣❡❧❛ ❍❡❧❡♥❛ ▲♦s❝❤✐ ♣❡❧❛ ♦r✐❡♥t❛çã♦✱ ♣❛❝✐ê♥❝✐❛ ❡ ❞❡❞✐❝❛çã♦ à ❡❧❛❜♦r❛çã♦ ❞❛ t❡s❡✱ ♣❡❧♦ ❡s♠❡r♦ ❝♦♠ ❛ ❡①❝❡❧ê♥❝✐❛ ❞♦ tr❛❜❛❧❤♦ s❡♠♣r❡ ♠❡ ❡♥s✐♥❛♥❞♦ ❛ s❡r ✉♠ ♠❡❧❤♦r ♣❡sq✉✐s❛❞♦r✳
❆ ♠✐♥❤❛ ❝♦✲♦r✐❡♥t❛❞♦r❛✱ ❉r➟✳ ▼❛rt❛ ❆❢♦♥s♦ ❋r❡✐t❛s ♣❡❧❛ ♦r✐❡♥t❛çã♦ ❡ ✐♥✐❝✐❛çã♦ ♥❛ ♠✐♥❤❛ ❧✐♥❤❛ ❞❡ ♣❡sq✉✐s❛ ❢❛✈♦r✐t❛✳
❆ ❛♠❜❛s ♣♦r ❛❝r❡❞✐t❛r❡♠ ♥❛ ♠✐♥❤❛ ❝❛♣❛❝✐❞❛❞❡✳ ❚❡rã♦ s❡♠♣r❡ ♠✐♥❤❛ ❡t❡r♥❛ ❣r❛t✐✲ ❞ã♦✱ ❛❞♠✐r❛çã♦✱ r❡s♣❡✐t♦ ❡ ❝❛r✐♥❤♦✳
❆♦s ♠❡✉s ♣❛✐s✱ ❏♦sé ❆♥tô♥✐♦ ❡ ❱❛❧❞❡❧✐❝❡❀ ♠❡✉s s♦❣r♦s✱ ❉❡✉s❞❡❞✐t ❡ ▼❛r✐❛ ❆✉①✐❧✐❛✲ ❞♦r❛❀ ♠❡✉s ✐r♠ã♦s✱ ❘♦❞r✐❣♦ ❡ ❘♦♥②❀ ♠✐♥❤❛s ❝✉♥❤❛❞❛s ▼❛r✐♥❛❧✈❛ ❡ ❨❛r❛❀ ♠❡✉s ❝✉♥❤❛❞♦s ▲✉ís ❡ ❲✐❧❧❀ ♣❡❧❛ ❢♦rç❛✱ ❞❡❞✐❝❛çã♦✱ ❛♣♦✐♦ ❡ ❝❛r✐♥❤♦✳
❆ ♠✐♥❤❛ ❡s♣♦s❛ ❈❛r♦❧✐♥❛✱ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦✱ ❢♦rç❛✱ ✐♥❝❡♥t✐✈♦✱ ❞❡❞✐❝❛çã♦✱ ❝❛r✐♥❤♦ ❡ ❝♦♠♣r❡❡♥sã♦✳
❆♦s ❛♠✐❣♦s ❞♦ ❖❜❥❡t✐✈♦✱ ❞♦ ❈❊❋❊❚✲▼●✱ ❞❛ ❊st❛tíst✐❝❛✲❯❋▼●✱ ❞♦ ♠❡str❛❞♦ ❞♦ PP●❊P✲❯❋▼●✱ ❞♦ ❞♦✉t♦r❛❞♦ ❞♦ ❉❊❙❚✲❯❋▼●✱ ❞❛ ♠✐♥❤❛ ✐♥❢â♥❝✐❛ ❡ ❞❡♠❛✐s ❛♠✐❣♦s q✉❡ ✜③ ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s✳
❆♦s ♣r♦❢❡ss♦r❡s ❞♦ ♣r♦❣r❛♠❛ ❞❡ Pós ●r❛❞✉❛çã♦ ❡♠ ❊st❛tíst✐❝❛✱ ♣❡❧♦ ❝♦♥❤❡❝✐♠❡♥t♦ tr❛♥s♠✐t✐❞♦✳
❆ ❘♦❣ér✐❛✱ ❘♦s❡✱ ▼❛ís❛✱ ❲✐❧t♦♥✱ ♣❡❧♦ ❝❛r✐♥❤♦ ❡ ót✐♠♦ tr❛❜❛❧❤♦ q✉❡ ❞❡s❡♠♣❡♥❤❛♠ ♣❛r❛ ♦ ❞❡♣❛rt❛♠❡♥t♦✱ ❡ ❛♦s ❞❡♠❛✐s ❢✉♥❝✐♦♥ár✐♦s ❞❛ ❯❋▼●✳
❆ ❯❋▼● ♣❡❧♦ s✉♣♦rt❡ ❡ ❡str✉t✉r❛✳
❆♦ ❈❡♥tr♦ ❯♥✐✈❡rs✐tár✐♦ ▼❡t♦❞✐st❛ ■③❛❜❡❧❛ ❍❡♥❞r✐① q✉❡ ♠❡ ♣❡r♠✐t✐✉ ❞❡s❝♦❜r✐r ❛ ❜❡❧❡③❛ ❡ ♦ ♣r❛③❡r ❞❛ ❛t✐✈✐❞❛❞❡ ❞❡ ❞♦❝ê♥❝✐❛✱ ❡ t❛♠❜é♠ ♣❡❧♦ ❛♣♦✐♦ ❞❛ ❡q✉✐♣❡ ❞❡ ♣r♦❢❡ss♦r❡s ❡ ❝♦♦r❞❡♥❛çã♦ ❞♦s ❝✉rs♦s✳
Resumo
❊♠ ❡st❛tíst✐❝❛ ❛ ❝♦♥✜❛❜✐❧✐❞❛❞❡ é ✉♠ r❛♠♦ q✉❡ ✈✐s❛ ❞❡s❝r❡✈❡r ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ❞❡ ♦❜❥❡t♦s ❞❡ ✐♥t❡r❡ss❡✳
P❛r❛ ❞❡t❡r♠✐♥❛❞❛s s✐t✉❛çõ❡s✱ ♥❛s q✉❛✐s ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❢❛❧❤❛s é ♣❡q✉❡♥❛ ♦✉ q✉❛s❡ ♥✉❧❛✱ ❛ ❡st✐♠❛çã♦ ❞❛s q✉❛♥t✐❞❛❞❡s q✉❡ ❞❡s❝r❡✈❡♠ ♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✜❝❛ ❝♦♠♣r♦♠❡t✐❞❛✳ ❉❡ss❛ ❢♦r♠❛ ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ♦s ♠♦❞❡❧♦s ❣❡r❛✐s ❞❡ ❞❡❣r❛❞❛çã♦✱ q✉❡ ♣♦ss✉❡♠ ❝♦♠♦ ❞❛❞♦ ❡①♣❡r✐♠❡♥t❛❧ ♥ã♦ ❛ ❢❛❧❤❛✱ ♠❛s s✐♠ ❛❧❣✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ♠❡♥s✉rá✈❡❧ ❛ ❡❧❛ ❛tr❡❧❛❞❛✳ ◗✉❛♥❞♦ t❛❧ ❝❛r❛❝t❡ríst✐❝❛ é ♠♦♥✐t♦r❛❞❛ t♦r♥❛♠✲s❡ ♣♦ssí✈❡✐s ♠❡❧❤♦r✐❛s s✐❣♥✐✜❝❛t✐✈❛s ♥❛s ❡st✐♠❛t✐✈❛s ❞❛s q✉❛♥t✐❞❛❞❡s ❞❡ ✐♥t❡r❡ss❡✳
◆❡st❡ t❡①t♦ ✐♥tr♦❞✉③✐♠♦s ❝❧❛ss❡s ✢❡①í✈❡✐s ❞❡ ♠♦❞❡❧♦s ❞❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ❡ ❞❡❣r❛❞❛çã♦ ❝❛♣❛③❡s ❞❡ ❛❝♦♠♦❞❛r ❝♦♠♣♦rt❛♠❡♥t♦s ❛ss✐♠étr✐❝♦s ❡ ❝❛✉❞❛s ♣❡s❛❞❛s✳
P❛r❛ ♦s ♠♦❞❡❧♦s ❞❡ ❞❡❣r❛❞❛çã♦ ❛ss✉♠✐♠♦s q✉❡ ❛ t❛①❛ ❡ ❛ t❛①❛ r❡❝í♣r♦❝❛ ❞❡ ❞❡❣r❛❞❛✲ çã♦ s❡❣✉❡♠ ❞✐str✐❜✉✐çõ❡s ❡♠ ❛♠❜❛s ❛s ❝❧❛ss❡s ❞❡ ❞✐str✐❜✉✐çã♦✱ ❛s ❞❡ ❢❛♠í❧✐❛s ❞❡ ♠✐st✉r❛ ❞❡ ❡s❝❛❧❛ ❞❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ❡ ❧♦❣ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛✳ ◆♦ q✉❡ ❝♦♥❝❡r♥❡ ❛♦s ♠♦❞❡❧♦s ❞❡ ❛♥á❧✐s❡ ❝♦♥✈❡♥❝✐♦♥❛❧ ❞❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛ t❛♠❜é♠ ❝♦♥s✐❞❡r❛♠♦s ❛s ♠❡s✲ ♠❛s ❢❛♠í❧✐❛s✳ P❛r❛ ❛♠❜❛s ❛s ♠♦❞❡❧❛❣❡♥s ✐♥tr♦❞✉③✐♠♦s ❛❧❣♦r✐t♠♦s ❝♦♠ ❜❛s❡ ♥❛ té❝♥✐❝❛ ❞❡ ❛✉♠❡♥t♦ ❞❡ ❞❛❞♦s ♣❛r❛ ❛♠♦str❛r ❞❛s ❞✐str✐❜✉✐çõ❡s a posteriori ❞♦s ♣❛râ♠❡tr♦s✳
❖ tr❛❜❛❧❤♦ ❝♦♥t❛ ❛✐♥❞❛ ❝♦♠ ✉♠❛ r✐❝❛ ❞✐s❝✉ssã♦ s♦❜r❡ ♠♦❞❡❧♦s ❣❡r❛✐s ❞❡ ❞❡❣r❛❞❛çã♦ ❡ ♠♦❞❡❧♦s ❝♦♥✈❡♥❝✐♦♥❛✐s ❞❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ❡♠ t❡r♠♦s ❞♦ ♣❛r❛❞✐❣♠❛ ❜❛②❡s✐❛♥♦✳ ❆❧❣✉♠❛s ♣r♦✈❛s ❢♦r♠❛✐s ❡ ♣r♦♣♦s✐çõ❡s t❛♠❜é♠ ❢♦r♥❡❝❡♠ r❡s✉❧t❛❞♦s t❡ór✐❝♦s ✐♥t❡r❡ss❛♥t❡s ❛✐♥❞❛ ♥ã♦ ❡①♣❧♦r❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✳
P♦r ✜♠✱ ❛ ♠♦❞❡❧❛❣❡♠ ❞❡s❡♥✈♦❧✈✐❞❛ ❞❡✐①❛ ✈ár✐♦s ♣r♦❜❧❡♠❛s ❛❜❡rt♦s ❡ r❡s✉❧t❛❞♦s ♣❛r❛ ❢♦♠❡♥t❛r ♣❡sq✉✐s❛s ❢✉t✉r❛s✳
Abstract
■♥ st❛t✐st✐❝s t❤❡ r❡❧✐❛❜✐❧✐t② ✐s ❛ ❜r❛♥❝❤ t❤❛t s❡❡❦s t♦ ❞❡s❝r✐❜❡ t❤❡ t✐♠❡ t♦ ❢❛✐❧✉r❡ ❞✐str✐✲ ❜✉t✐♦♥ ♦❢ ♦❜❥❡❝ts ♦❢ ✐♥t❡r❡st✳
❋♦r ❝❡rt❛✐♥ s✐t✉❛t✐♦♥s ✇❤❡r❡ ❢❛✐❧✉r❡s ❛r❡ ♥♦t ❢r❡q✉❡♥t ♦r ✈✐rt✉❛❧❧② ♥♦♥❡①✐st❡♥t✱ t❤❡ ❡st✐♠❛t✐♦♥ ♦❢ q✉❛♥t✐t✐❡s ❞❡s❝r✐❜✐♥❣ t❤❡ ❢❛✐❧✉r❡ t✐♠❡s ✐s ❝♦♠♣r♦♠✐s❡❞✳ ❚❤❡ ❣❡♥❡r❛❧ ❞❡❣r❛✲ ❞❛t✐♦♥ ♠♦❞❡❧s ❤❛✈❡ ❜❡❡♥ ❞❡✈❡❧♦♣❡❞ t♦ ♦✈❡r❝♦♠❡ t❤✐s ♣r♦❜❧❡♠ ❜② ♠❡❛s✉r✐♥❣ ❛ ❢❡❛t✉r❡ ❧✐♥❦❡❞ t♦ ❢❛✐❧✉r❡✱ ♥♦t t❤❡ ❢❛✐❧✉r❡ ✐ts❡❧❢✳ ❲❤❡♥ t❤✐s ❢❡❛t✉r❡ ✐s ♠♦♥✐t♦r❡❞ ✐t ❜❡❝♦♠❡s ♣♦ss✐❜❧❡ t♦ ✐♠♣r♦✈❡ t❤❡ ❡st✐♠❛t❡s ♦❢ t❤❡ t✐♠❡ t♦ ❢❛✐❧✉r❡ q✉❛♥t✐t✐❡s ♦❢ ✐♥t❡r❡st✳
■♥ t❤✐s ♣❛♣❡r ✇❡ ✐♥tr♦❞✉❝❡ ✢❡①✐❜❧❡ ❝❧❛ss❡s ♦❢ ❢❛✐❧✉r❡ t✐♠❡ ♠♦❞❡❧s ❛♥❞ ❞❡❣r❛❞❛t✐♦♥ t❤❛t ❛r❡ ❛❜❧❡ t♦ ❛❝❝♦♠♠♦❞❛t❡ ❛s②♠♠❡tr✐❝ ❜❡❤❛✈✐♦r ❛♥❞ ❤❡❛✈② t❛✐❧s✳
❋♦r t❤❡ ❞❡❣r❛❞❛t✐♦♥ ♣❛t❤ ♠♦❞❡❧s t❤✐s ❣♦❛❧ ✐s ❛❝❤✐❡✈❡❞ ❜② ❛ss✉♠✐♥❣ t❤❡ ❞❡❣r❛❞❛t✐♦♥ ❛♥❞ r❡❝✐♣r♦❝❛❧ ❞❡❣r❛❞❛t✐♦♥ r❛t❡s ❤❛✈❡ ❞✐str✐❜✉t✐♦♥s ✐♥ ❜♦t❤ ❝❧❛ss❡s ♦❢ ❞✐str✐❜✉t✐♦♥s✱ t❤❡ s❝❛❧❡ ♠✐①t✉r❡ ♦❢ s❦❡✇✲♥♦r♠❛❧ ❛♥❞ s❝❛❧❡ ♠✐①t✉r❡ ♦❢ ❧♦❣ s❦❡✇ ♥♦r♠❛❧ ❢❛♠✐❧✐❡s ♦❢ ❞✐str✐❜✉t✐♦♥s✳ ❲❡ ❛❧s♦ ❝♦♥s✐❞❡r t❤❡ s❛♠❡ ❢❛♠✐❧✐❡s t♦ ♣❡r❢♦r♠ ❝♦♥✈❡♥t✐♦♥❛❧ t✐♠❡ t♦ ❢❛✐❧✉r❡ ❛♥❛❧②s✐s✳ ❋♦r ❜♦t❤ ♠♦❞❡❧s ✇❡ ❜✉✐❧❞ ✉♣ ❛❧❣♦r✐t❤♠s ❜❛s❡❞ ♦♥ t❤❡ ❞❛t❛ ❛✉❣♠❡♥t❛t✐♦♥ t❡❝❤♥✐q✉❡ ✐♥ ♦r❞❡r t♦ s❛♠♣❧❡ ♣❛r❛♠❡t❡rs ❢r♦♠ t❤❡ ♣♦st❡r✐♦r ❞✐str✐❜✉t✐♦♥✳
❚❤❡ ♥❡✇ ♠❡t❤♦❞♦❧♦❣✐❡s ❛r❡ ❛♣♣❧✐❡❞ t♦ s✐♠✉❧❛t❡❞ ❞❛t❛❜❛s❡s ✇✐t❤ ❞✐✛❡r❡♥t ❝❤❛r❛❝✲ t❡r✐st✐❝s✱ ❝♦♥s✐❞❡r✐♥❣ t❤❡ ♣r❡s❡♥❝❡ ♦r ❛❜s❡♥❝❡ ❛s②♠♠❡tr②✱ ❤❡❛✈② t❛✐❧s ❛♥❞ ❧✐❣❤t t❛✐❧s✳ ❚❤❡ ♠♦❞❡❧✐♥❣ ♦❢ ❦♥♦✇♥ ❧✐t❡r❛t✉r❡ ♣r❛❝t✐❝❛❧ s✐t✉❛t✐♦♥s ✐s ❛❧s♦ ❡①♣❧♦r❡❞✱ ♥❛♠❡❧② t❤❡ tr❛✐♥ ✇❤❡❡❧s ❛♥❞ ❧❛s❡rs ❞❡❣r❛❞❛t✐♦♥ ❞❛t❛✱ ❛♥❞ t❤❡ ❧✉♥❣ ❝❛♥❝❡r ❧✐❢❡t✐♠❡ ❞❛t❛✳ ❚❤❡ r❡s✉❧ts ♦❢ t❤❡ ♥❡✇ ♠♦❞❡❧✐♥❣ ❛r❡ ❝♦♠♣❛r❡❞ ✇✐t❤ ❝✉rr❡♥t ❛♣♣r♦❛❝❤❡s t♦ ♠♦❞❡❧ ❞❡❣r❛❞❛t✐♦♥ ❛♥❞ ❝♦♥✈❡♥t✐♦♥❛❧ ❢❛✐❧✉r❡ t✐♠❡s✳ ❉✉❡ t♦ ✐ts ✢❡①✐❜✐❧✐t② ❝❤❛r❛❝t❡r✐st✐❝s✱ t❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞s s❤♦✇ ♣r♦♠✐s❡ ❡✈❡♥ ✐♥ ❝❛s❡s ♦❢ ♠✐ss♣❡❝✐✜❝❛t✐♦♥✳
❛♥❞ ♣r♦♣♦s✐t✐♦♥s ❛❧s♦ ♣r♦✈✐❞❡ ✐♥t❡r❡st✐♥❣ t❤❡♦r❡t✐❝❛❧ r❡s✉❧ts ♥♦t ②❡t ❡①♣❧♦r❡❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✳
❋✐♥❛❧❧②✱ t❤❡ ❞❡✈❡❧♦♣❡❞ ♠❡t❤♦❞♦❧♦❣② ❧❡❛✈❡s s❡✈❡r❛❧ ♦♣❡♥ ✐ss✉❡s ❛♥❞ r❡s✉❧ts t♦ ❡♥❝♦✉✲ r❛❣❡ ❢✉rt❤❡r r❡s❡❛r❝❤✳
Lista de Figuras
✶✳✶ ❆❧❣✉♥s ♣❡r✜s ❞❡ ❞❡s❣❛st❡ ❞❡ r♦❞❛s ❞❡ tr❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✷✳✶ ❉❡♥s✐❞❛❞❡s ❞❛ ❞✐str✐❜✉✐çã♦ s❦❡✇ ♥♦r♠❛❧ ♣❛❞rã♦ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ 𝛼 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✷✳✷ ❉❡♥s✐❞❛❞❡s ❞❛ ❞✐str✐❜✉✐çã♦ ❧♦❣ s❦❡✇ ♥♦r♠❛❧ ♣❛❞rã♦ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦✲ r❡s ❞❡𝛼 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✸✳✶ ❊st✐♠❛t✐✈❛ ♣r♦♣♦st❛ ♣♦r ❍❛♠❛❞❛ ✭✷✵✵✺✮ versus ❡st✐♠❛t✐✈❛ ✈✐❛ ❞✐str✐❜✉✐✲ çã♦ ♣r❡❞✐t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✹✳✶ ❋✉♥çõ❡s ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ s❦❡✇ ♥♦r♠❛❧ ❝♦♠
𝜇𝛽 = 5 ❡ 𝜔𝛽2 = 4 ♣❛r❛ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ❝♦♠ ❧✐♠✐❛r ❞❡
❢❛❧❤❛ ♣❛r❛ ❛ ❞❡❣r❛❞❛çã♦𝐷𝑓 = 20✱ ❛ss✉♠✐♥❞♦✲s❡ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡𝛼𝛽
✲ ♠♦❞❡❧♦𝑦𝑖𝑗 =𝛽𝑖/𝑡𝑖𝑗 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✹✳✷ ❋✉♥çõ❡s ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ s❦❡✇✲t ❝♦♠𝜇𝛽 = 40✱
𝜔𝛽2 = 4 ❡ 𝛼𝛽 =±3 ♣❛r❛ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ❝♦♠ ❧✐♠✐❛r ❞❡
❢❛❧❤❛ ♣❛r❛ ❛ ❞❡❣r❛❞❛çã♦ 𝐷𝑓 = 20✱ ❛ss✉♠✐♥❞♦✲s❡ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ 𝜈𝛽
✹✳✸ ❋✉♥çõ❡s ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❧♦❣ s❦❡✇ ♥♦r♠❛❧ ❝♦♠
𝜇𝛽 = 5 ❡ 𝜔𝛽2 = 4 ♣❛r❛ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ❝♦♠ ❧✐♠✐❛r ❞❡
❢❛❧❤❛ ♣❛r❛ ❛ ❞❡❣r❛❞❛çã♦𝐷𝑓 = 20✱ ❛ss✉♠✐♥❞♦✲s❡ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡𝛼𝛽
✲ ♠♦❞❡❧♦𝑦𝑖𝑗 =𝛽𝑖/𝑡𝑖𝑗 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✹✳✹ ❋✉♥çõ❡s ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❧♦❣ s❦❡✇✲t ❝♦♠𝜇𝛽 = 4✱
𝜔𝛽2 = 4 ❡ 𝛼𝛽 =±100♣❛r❛ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ❝♦♠ ❧✐♠✐❛r
❞❡ ❢❛❧❤❛ ♣❛r❛ ❛ ❞❡❣r❛❞❛çã♦𝐷𝑓 = 20✱ ❛ss✉♠✐♥❞♦✲s❡ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡
𝜈𝛽 ✲ ♠♦❞❡❧♦𝑦𝑖𝑗 =𝛽𝑖/𝑡𝑖𝑗 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✹✳✺ ❋✉♥çõ❡s ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❧♦❣ s❦❡✇ ♥♦r♠❛❧ ❝♦♠
𝜇𝛽 = 5 ❡ 𝜔𝛽2 = 4 ♣❛r❛ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ❝♦♠ ❧✐♠✐❛r ❞❡
❢❛❧❤❛ ♣❛r❛ ❛ ❞❡❣r❛❞❛çã♦𝐷𝑓 = 20✱ ❛ss✉♠✐♥❞♦✲s❡ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡𝛼𝛽
✲ ♠♦❞❡❧♦𝑦𝑖𝑗 =𝛽𝑖𝑡𝑖𝑗 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✹✳✻ ❋✉♥çõ❡s ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❧♦❣ s❦❡✇✲t ❝♦♠𝜇𝛽 = 3✱
𝜔𝛽2 = 0.04 ❡ 𝛼𝛽 =±3 ♣❛r❛ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ❝♦♠ ❧✐♠✐❛r
❞❡ ❢❛❧❤❛ ♣❛r❛ ❛ ❞❡❣r❛❞❛çã♦𝐷𝑓 = 10✱ ❛ss✉♠✐♥❞♦✲s❡ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡
𝜈𝛽 ✲ ♠♦❞❡❧♦𝑦𝑖𝑗 =𝛽𝑖𝑡𝑖𝑗 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✹✳✼ ❋✉♥çõ❡s ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❧♦❣ s❦❡✇ ♥♦r♠❛❧ ❝♦♠ 𝜇𝛽 = 5 ❡ 𝜔𝛽2 = 2✱ ❝♦♠ ❧✐♠✐❛r ❞❡ ❢❛❧❤❛ ♣❛r❛ ❛ ❞❡❣r❛❞❛çã♦ 𝐷𝑓 = 20✱
❛ss✉♠✐♥❞♦✲s❡ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ 𝛼𝛽 ✲ ♠♦❞❡❧♦𝑦𝑖𝑗 =𝛽𝑖𝑡𝑖𝑗 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✹✳✽ ❋✉♥çõ❡s ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❧♦❣ s❦❡✇✲t ❝♦♠𝜇𝛽 = 3✱
𝜔2
𝛽 = 0.04 ❡ 𝛼𝛽 =±3 ♣❛r❛ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ❝♦♠ ❧✐♠✐❛r
❞❡ ❢❛❧❤❛ ♣❛r❛ ❛ ❞❡❣r❛❞❛çã♦𝐷𝑓 = 10✱ ❛ss✉♠✐♥❞♦✲s❡ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡
𝜈𝛽 ✲ ♠♦❞❡❧♦𝑦𝑖𝑗 =𝛽𝑖𝑡𝑖𝑗 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
✹✳✾ P❡r✜s ❞❡ ❞❡❣r❛❞❛çã♦ ❞♦s ❞❛❞♦s ❛rt✐✜❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✹✳✶✵ ❈♦♠♣❛r❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s ♣❛râ♠❡tr♦s ❝♦♠ ♦s ✈❛❧♦r❡s
✹✳✶✶ ❈♦♠♣❛r❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s ♣❛râ♠❡tr♦s ❝♦♠ ♦s ✈❛❧♦r❡s r❡❛✐s ♥♦ ❛❥✉st❡ ❙❚✿ ❞❛❞♦s ❛rt✐✜❝✐❛✐s ❝♦♠ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❙❦❡✇ ❚ ✳ ✳ ✳ ✳ ✳ ✾✷ ✹✳✶✷ ❈♦♠♣❛r❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s ♣❛râ♠❡tr♦s ❝♦♠ ♦s ✈❛❧♦r❡s
r❡❛✐s ♥♦ ❛❥✉st❡ ▲❙❚✿ ❞❛❞♦s ❛rt✐✜❝✐❛✐s ❝♦♠ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ▲♦❣ ❙❦❡✇ ❚ ✳ ✳ ✾✸ ✹✳✶✸ ❈♦♠♣❛r❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s ♣❛râ♠❡tr♦s ❝♦♠ ♦s ✈❛❧♦r❡s
r❡❛✐s ♥♦ ❛❥✉st❡ ❲✿ ❞❛❞♦s ❛rt✐✜❝✐❛✐s ❝♦♠ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❲❡✐❜✉❧❧ ✳ ✳ ✳ ✳ ✳ ✾✹ ✹✳✶✹ ❋✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛
✉♠❛ ✉♥✐❞❛❞❡ ❢✉t✉r❛✱ ♣❡❧♦s ♠ét♦❞♦s ❞❡ ❍❛♠❛❞❛ ✭✷✵✵✺✮ ✭❡sq✉❡r❞❛✮ ❡ ♣r♦✲ ♣♦st❛ ♣❡❧❛ ♣r❡❞✐t✐✈❛ ❛ ♣♦st❡r✐♦r✐ ✭❞✐r❡✐t❛✮✱ ♣❛r❛ t♦❞♦s ♦s ♠♦❞❡❧♦s ❛❥✉s✲ t❛❞♦s ❛♦s ❞❛❞♦s ❇✲❙◆ ✭♣r✐♠❡✐r❛ ❧✐♥❤❛✮✱ ❇✲❙❚ ✭s❡❣✉♥❞❛ ❧✐♥❤❛✮✱ ❇✲▲❙❚ ✭t❡r❝❡✐r❛ ❧✐♥❤❛✮ ❡ ❇✲❲ ✭q✉❛rt❛ ❧✐♥❤❛✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✹✳✶✺ ❋✉♥çã♦ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛
✉♠❛ ✉♥✐❞❛❞❡ ❢✉t✉r❛✱ ♣❡❧♦s ♠ét♦❞♦s ❞❡ ❍❛♠❛❞❛ ✭✷✵✵✺✮ ✭❡sq✉❡r❞❛✮ ❡ ♣r♦✲ ♣♦st❛ ♣❡❧❛ ♣r❡❞✐t✐✈❛ ❛ ♣♦st❡r✐♦r✐ ✭❞✐r❡✐t❛✮✱ ♣❛r❛ t♦❞♦s ♦s ♠♦❞❡❧♦s ❛❥✉s✲ t❛❞♦s ❛♦s ❞❛❞♦s ❇✲❙◆ ✭♣r✐♠❡✐r❛ ❧✐♥❤❛✮✱ ❇✲❙❚ ✭s❡❣✉♥❞❛ ❧✐♥❤❛✮✱ ❇✲▲❙❚ ✭t❡r❝❡✐r❛ ❧✐♥❤❛✮ ❡ ❇✲❲ ✭q✉❛rt❛ ❧✐♥❤❛✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✹✳✶✻ ❋✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛ ✉♠❛ ✉♥✐✲
❞❛❞❡ ❢✉t✉r❛ ♣❡❧♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ✈✐❛ ♣r❡❞✐t✐✈❛ ❛ ♣♦st❡r✐♦r✐ ❞♦ ♠♦❞❡❧♦ ❛❥✉st❛❞♦ ❚✱ ❞❛❞♦s ❇✲❙❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✹✳✶✼ 𝐶𝑃 𝑂𝑖 ♣♦r ❞❡❣r❛❞❛çã♦ 𝑦𝑖𝑗 ✭❡sq✉❡r❞❛✮ ❡ ♣❡r✜❧ 𝑦𝑖 ✭❞✐r❡✐t❛✮✱ ♥♦s ❝❡♥ár✐♦s
❇✲❙◆ ✭♣r✐♠❡✐r❛ ❧✐♥❤❛✮✱ ❇✲❙❚ ✭s❡❣✉♥❞❛ ❧✐♥❤❛✮✱ ❇✲▲❙❚ ✭t❡r❝❡✐r❛ ❧✐♥❤❛✮ ❡ ❇✲❲ ✭q✉❛rt❛ ❧✐♥❤❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺ ✹✳✶✽ 𝐶𝑃 𝑂𝑖 ♣♦r t❡♠♣♦ ❞❡ ❢❛❧❤❛ ✭❡sq✉❡r❞❛✮ ❡ ♣s❡✉❞♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ✭❞✐r❡✐t❛✮✱
✹✳✶✾ 𝐾𝐿𝑖 ♣♦r ❞❡❣r❛❞❛çã♦𝑦𝑖𝑗 ✭❡sq✉❡r❞❛✮ ❡ ♣♦r ♣❡r✜❧𝑦i ✭❞✐r❡✐t❛✮✱ ♥♦s ❝❡♥ár✐♦s
❇✲❙◆ ✭♣r✐♠❡✐r❛ ❧✐♥❤❛✮✱ ❇✲❙❚ ✭s❡❣✉♥❞❛ ❧✐♥❤❛✮✱ ❇✲▲❙❚ ✭t❡r❝❡✐r❛ ❧✐♥❤❛✮ ❡ ❇✲❲ ✭q✉❛rt❛ ❧✐♥❤❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✹✳✷✵ 𝑝𝑖 ♣♦r ❞❡❣r❛❞❛çã♦ 𝑦𝑖𝑗 ✭❡sq✉❡r❞❛✮ ❡ ♣♦r ♣❡r✜❧ 𝑦i ✭❞✐r❡✐t❛✮✱ ♥♦s ❝❡♥ár✐♦s
❇✲❙◆ ✭♣r✐♠❡✐r❛ ❧✐♥❤❛✮✱ ❇✲❙❚ ✭s❡❣✉♥❞❛ ❧✐♥❤❛✮✱ ❇✲▲❙❚ ✭t❡r❝❡✐r❛ ❧✐♥❤❛✮ ❡ ❇✲❲ ✭q✉❛rt❛ ❧✐♥❤❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✹✳✷✶ 𝐾𝐿𝑖 ♣♦r t❡♠♣♦ ❞❡ ❢❛❧❤❛ 𝑡𝑖 ✭❡sq✉❡r❞❛✮ ❡ ♣♦r ♣s❡✉❞♦t❡♠♣♦ ❞❡ ❢❛❧❤❛ ˆ𝑡𝑖
✭❞✐r❡✐t❛✮✱ ♥♦s ❝❡♥ár✐♦s ❇✲❙◆ ✭♣r✐♠❡✐r❛ ❧✐♥❤❛✮✱ ❇✲❙❚ ✭s❡❣✉♥❞❛ ❧✐♥❤❛✮✱ ❇✲ ▲❙❚ ✭t❡r❝❡✐r❛ ❧✐♥❤❛✮ ❡ ❇✲❲ ✭q✉❛rt❛ ❧✐♥❤❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✹✳✷✷ 𝑝𝑖 ♣♦r t❡♠♣♦ ❞❡ ❢❛❧❤❛ 𝑡𝑖 ✭❡sq✉❡r❞❛✮ ❡ ♣♦r ♣s❡✉❞♦t❡♠♣♦ ❞❡ ❢❛❧❤❛ ˆ𝑡𝑖 ✭❞✐✲
r❡✐t❛✮✱ ♥♦s ❝❡♥ár✐♦s ❇✲❙◆ ✭♣r✐♠❡✐r❛ ❧✐♥❤❛✮✱ ❇✲❙❚ ✭s❡❣✉♥❞❛ ❧✐♥❤❛✮✱ ❇✲▲❙❚ ✭t❡r❝❡✐r❛ ❧✐♥❤❛✮ ❡ ❇✲❲ ✭q✉❛rt❛ ❧✐♥❤❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✹✳✷✸ ❉✐str✐❜✉✐çã♦ a posteriori 𝛽𝑖|𝑦 s♦❜ t♦❞♦s ♦s ♠♦❞❡❧♦s✱ ❝❡♥ár✐♦ ❇✲❙◆✳ ❆s
❧✐♥❤❛s ♣r❡t❛s ❤♦r✐③♦♥t❛✐s ✐♥❞✐❝❛♠ ♦s ✈❛❧♦r❡s r❡❛✐s𝛽𝑖 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺
✹✳✷✹ ❉✐str✐❜✉✐çã♦ a posteriori 𝛽𝑖|𝑦 s♦❜ t♦❞♦s ♦s ♠♦❞❡❧♦s✱ ❝❡♥ár✐♦ ❇✲❙❚✳ ❆s
❧✐♥❤❛s ♣r❡t❛s ❤♦r✐③♦♥t❛✐s ✐♥❞✐❝❛♠ ♦s ✈❛❧♦r❡s r❡❛✐s𝛽𝑖 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻
✹✳✷✺ ❉✐str✐❜✉✐çã♦ a posteriori 𝛽𝑖|𝑦 s♦❜ t♦❞♦s ♦s ♠♦❞❡❧♦s✱ ❝❡♥ár✐♦ ❇✲▲❙❚✳ ❆s
❧✐♥❤❛s ♣r❡t❛s ❤♦r✐③♦♥t❛✐s ✐♥❞✐❝❛♠ ♦s ✈❛❧♦r❡s r❡❛✐s𝛽𝑖 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼
✹✳✷✻ ❉✐str✐❜✉✐çã♦ a posteriori 𝛽𝑖|𝑦 s♦❜ t♦❞♦s ♦s ♠♦❞❡❧♦s✱ ❝❡♥ár✐♦ ❇✲❲✳ ❆s
❧✐♥❤❛s ♣r❡t❛s ❤♦r✐③♦♥t❛✐s ✐♥❞✐❝❛♠ ♦s ✈❛❧♦r❡s r❡❛✐s𝛽𝑖 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽
✹✳✷✼ ❈r♦q✉✐ ✲ ✈✐st❛ ♣r✐♥❝✐♣❛❧ ✐♥❢❡r✐♦r ❞❡ ✉♠ ✈❛❣ã♦ ♠♦t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶ ✹✳✷✽ P❡r✜s ❞❡ ❞❡s❣❛st❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷ ✹✳✷✾ ❋✉♥çã♦ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ✭❡sq✉❡r❞❛✮ ❡ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡
✹✳✸✵ ❋✉♥çã♦ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ✭❡sq✉❡r❞❛✮ ❡ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ✭❞✐r❡✐t❛✮ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛ ✉♠❛ ✉♥✐❞❛❞❡ ❢✉t✉r❛✱ ♣❡❧♦s ♠ét♦❞♦s ❞❡ ❍❛♠❛❞❛ ✭✷✵✵✺✮ ✭❛❝✐♠❛✮ ❡ ♣r♦♣♦st❛ ♣❡❧❛ ♣r❡❞✐t✐✈❛ ❛ ♣♦st❡r✐♦r✐ ✭❡♠❜❛✐①♦✮✱ ♣❛r❛ t♦❞♦s ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ❛♦s ❞❛❞♦s ❞❛ r♦❞❛ ❞❡ tr❡♠ ▼❆✶✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺ ✹✳✸✶ ❋✉♥çã♦ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ✭❡sq✉❡r❞❛✮ ❡ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡
✭❞✐r❡✐t❛✮ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛ ✉♠❛ ✉♥✐❞❛❞❡ ❢✉t✉r❛✱ ♣❡❧♦s ♠ét♦❞♦s ❞❡ ❍❛♠❛❞❛ ✭✷✵✵✺✮ ✭❛❝✐♠❛✮ ❡ ♣r♦♣♦st❛ ♣❡❧❛ ♣r❡❞✐t✐✈❛ ❛ ♣♦st❡r✐♦r✐ ✭❡♠❜❛✐①♦✮✱ ♣❛r❛ t♦❞♦s ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ❛♦s ❞❛❞♦s ❞❛ r♦❞❛ ❞❡ tr❡♠ ▼❆✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ✹✳✸✷ P❡r✜❧ ❞❡ ❞❡❣r❛❞❛çã♦ ❞❛s ✉♥✐❞❛❞❡s ❡♠✐ss♦r❛s ❧❛s❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✺ ✹✳✸✸ ❋✉♥çã♦ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ✭❡sq✉❡r❞❛✮ ❡ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡
✭❞✐r❡✐t❛✮ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛ ✉♠❛ ✉♥✐❞❛❞❡ ❢✉t✉r❛✱ ♣❡❧♦s ♠ét♦❞♦s ❞❡ ❍❛♠❛❞❛ ✭✷✵✵✺✮ ✭❛❝✐♠❛✮ ❡ ♣r♦♣♦st❛ ♣❡❧❛ ♣r❡❞✐t✐✈❛ ❛ ♣♦st❡r✐♦r✐ ✭❡♠❜❛✐①♦✮✱ ♣❛r❛ t♦❞♦s ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ❛♦s ❞❛❞♦s ❞❡ ❧❛s❡r ✳ ✳ ✳ ✳ ✳ ✶✹✻
✺✳✶ ❉✐str✐❜✉✐çõ❡s a posteriori ❞♦s ♣❛râ♠❡tr♦s s♦❜ ♦s ♠♦❞❡❧♦s ❙◆ ❝❡♥tr❛❞♦ ✭❡sq✉❡r❞❛✮ ❡ ❙◆ ♥ã♦ ❝❡♥tr❛❞♦ ✭❞✐r❡✐t❛✮✱ ❞❛❞♦s ❇❚✲❙◆✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✺ ✺✳✷ ❉✐str✐❜✉✐çõ❡s a posteriori ❞♦s ♣❛râ♠❡tr♦s s♦❜ ♦s ♠♦❞❡❧♦s ❙◆ ❝❡♥tr❛❞♦
✭❡sq✉❡r❞❛✮ ❡ ❙◆ ♥ã♦ ❝❡♥tr❛❞♦ ✭❞✐r❡✐t❛✮✱ ❞❛❞♦s ❇❚✲❙◆✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✼ ✺✳✸ ❈♦♠♣❛r❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s ♣❛râ♠❡tr♦s ❝♦♠ ♦s ✈❛❧♦r❡s
r❡❛✐s ♥♦ ❛❥✉st❡ ▲❙❚✿ ❞❛❞♦s s✐♠✉❧❛❞♦s ❧♦❣ s❦❡✇✲t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✽ ✺✳✹ ❈♦♥✜❛❜✐❧✐❞❛❞❡ ❡♠♣ír✐❝❛ ✈✐❛ ❑❛♣♣❧❛♥✲▼❡②❡r ✭❛❜s❝✐ss❛✮ ✈❡rs✉s ♠♦❞❡❧♦s
✺✳✺ ❈♦♥✜❛❜✐❧✐❞❛❞❡ ❡♠♣ír✐❝❛ ✈✐❛ ❑❛♣♣❧❛♥✲▼❡②❡r ✭❛❜s❝✐ss❛✮ ✈❡rs✉s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ♣❡❧❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ a posteriori ✭♦r❞❡♥❛❞❛✮ ♣❛r❛ ♦s t❡♠✲ ♣♦s ❞❡ ❢❛❧❤❛✳ ◆✱ ▲◆ ❡ ❚ ✭t♦♣♦✮✳ ❚❡♠♣♦s ▲❙❚✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✶ ✺✳✻ ❈♦♥✜❛❜✐❧✐❞❛❞❡ ❘❡❛❧✱ ❡♠♣ír✐❝❛ ✈✐❛ ❑❛♣♣❧❛♥✲▼❡②❡r✱ ❡ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐✲
t✐✈❛ a posteriori s♦❜ ♦s ♠♦❞❡❧♦s ▲❙◆✱ ❙❚✱ ▲❙❚ ❡ ❲ ♣❛r❛ ♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ❞❡ ✉♠❛ ✉♥✐❞❛❞❡ ❢✉t✉r❛ ❞❛ ♣♦♣✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✷ ✺✳✼ ❙♦❜r❡✈✐✈ê♥❝✐❛ ❡♠♣ír✐❝❛ ✈✐❛ ❑❛♣♣❧❛♥✲▼❡②❡r ✭❛❜s❝✐ss❛✮ ✈❡rs✉s ♠♦❞❡❧♦s
❛❥✉st❛❞♦s ♣❡❧❛ ♠é❞✐❛ a posteriori ✭♦r❞❡♥❛❞❛✮ ♣❛r❛ ♦s t❡♠♣♦s ❞❡ ✈✐❞❛✳ ❉❛❞♦s ❞❡ ❝â♥❝❡r ❞❡ ♣✉❧♠ã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✺ ✺✳✽ ❙♦❜r❡✈✐✈ê♥❝✐❛ ❡♠♣ír✐❝❛ ✈✐❛ ❑❛♣♣❧❛♥✲▼❡②❡r ✭❛❜s❝✐ss❛✮ ✈❡rs✉s ♠♦❞❡❧♦s
❛❥✉st❛❞♦s ♣❡❧❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ a posteriori ✭♦r❞❡♥❛❞❛✮ ♣❛r❛ ♦s t❡♠✲ ♣♦s ❞❡ ✈✐❞❛✳ ❉❛❞♦s ❞❡ ❝â♥❝❡r ❞❡ ♣✉❧♠ã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✻ ✺✳✾ ❙♦❜r❡✈✐✈ê♥❝✐❛ ❡♠♣ír✐❝❛ ✈✐❛ ❑❛♣♣❧❛♥✲▼❡②❡r✱ ❡ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ a
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✸✳✶ ❖❜t❡♥çã♦ ❞❛ ❛♠♦str❛ ❞❡𝑄𝐼𝑃 𝑂𝑆𝑇 ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ a posteriori
❞❡ ❚ ✈✐❛ ❍❛♠❛❞❛ ✭✷✵✵✺✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✷ ❆♠♦str❛ ❞❡𝐹𝑇n+1|𝛽n+1,𝜎2
ε(∙)♣❡❧♦ ♠ét♦❞♦ ❞❡ ❘♦❜✐♥s♦♥ ❡ ❈r♦✇❞❡r ✭✷✵✵✵✮ ✹✽ ✹✳✶ ❋♦rç❛ ❞❛ ❡✈✐❞ê♥❝✐❛ s♦❜r❡𝐹 𝐵(ℳ1,ℳ2)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
✹✳✷ ❘❡s✉♠♦s a posteriori ♥♦s ❛❥✉st❡s ❞❡ ♠❡s♠❛ ❞✐str✐❜✉✐çã♦ ❞❛s ❞❡❣r❛❞❛çõ❡s ❣❡r❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✹✳✸ P❡r❝❡♥t✐s ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✉s❛♥❞♦ ❛ ❉✐s✲
tr✐❜✉✐çã♦ Pr❡❞✐t✐✈❛ a posteriori ❡ ♦ ♠ét♦❞♦ ❞❡ ❍❛♠❛❞❛ ✭✷✵✵✺✮ ❡♠ t♦❞♦s ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ♣❛r❛ ♦ ❝❡♥ár✐♦ ❇✲❙◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✹✳✹ P❡r❝❡♥t✐s ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✉s❛♥❞♦ ❛ ❉✐s✲
tr✐❜✉✐çã♦ Pr❡❞✐t✐✈❛ a posteriori ❡ ♦ ♠ét♦❞♦ ❞❡ ❍❛♠❛❞❛ ✭✷✵✵✺✮ ❡♠ t♦❞♦s ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ♣❛r❛ ♦ ❝❡♥ár✐♦ ❇✲❙❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✹✳✺ P❡r❝❡♥t✐s ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✉s❛♥❞♦ ❛ ❉✐s✲
tr✐❜✉✐çã♦ Pr❡❞✐t✐✈❛ a posteriori ❡ ♦ ♠ét♦❞♦ ❞❡ ❍❛♠❛❞❛ ✭✷✵✵✺✮ ❡♠ t♦❞♦s ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ♣❛r❛ ♦ ❝❡♥ár✐♦ ❇✲▲❙❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✹✳✻ P❡r❝❡♥t✐s ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✉s❛♥❞♦ ❛ ❉✐s✲
✹✳✼ ▼❡❧❤♦r❡s ✭t♦♣♦✮ ❡ ♣✐♦r❡s ✭♣é✮ ♠♦❞❡❧♦s s❡❣✉♥❞♦ ♦s ❝r✐tér✐♦s ▲P▼▲✱ ❉■❈✱ ❲❆■❈✱ ❋❇✱ ❜❛s❡❛❞♦s ♥❛ ❞❡❣r❛❞❛çã♦ ✭❉❡❣✮✱ t❡♠♣♦s r❡❛✐s ✭❚✮ ❡ ♣s❡✉❞♦ t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✭P❚❋✮❀ ❡ t❡st❡ ❑❙ ❡♠ r❡❧❛çã♦ à ❢❞❛ ❡♠♣ír✐❝❛ ✭❑❙✲❋❉❆ ❊▼P✮✱ ❢❞❛ r❡❛❧ ✭❑❙✲❋❉❆ ❘❊❆▲✮✱ ❢❞❛ r❡❛❧ ❝♦♠ ❣r❛❞❡❛♠❡♥t♦ ❞♦ ❡✐①♦ ❞♦ t❡♠♣♦ ✭❑❙●✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✹✳✽ ▼♦❞❡❧♦s ♦r❞❡♥❛❞♦s ❞♦ ♠❡❧❤♦r ✭t♦♣♦✮ ♣❛r❛ ♦ ♣✐♦r ✭♣é✮ s❡❣✉♥❞♦ ▲P▼▲✱
❉■❈✱ ❲❆■❈✱ ❋❛t♦r ❞❡ ❇❛②❡s ✭❋❇✮✱ ❚❡st❡ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ✭❑❙✮✱ ❜❛s❡❛❞♦s ♥❛ ❞❡❣r❛❞❛çã♦ ✭❉❡❣✮ ❡ ♣s❡✉❞♦ t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✭P❚❋✮✱ ❘♦❞❛s ❞❡ ❚r❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾ ✹✳✾ P❡r❝❡♥t✐s ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛ ❛ ❘♦❞❛
▼❆✸✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶ ✹✳✶✵ P❡r❝❡♥t✐s ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛ ❛ ❘♦❞❛
▼❆✶✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷ ✹✳✶✶ P❡r❝❡♥t✐s ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛ ❛ ❘♦❞❛
▼❆✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✹ ✹✳✶✷ ▼♦❞❡❧♦s ♦r❞❡♥❛❞♦s ❞♦ ♠❡❧❤♦r ✭t♦♣♦✮ ♣❛r❛ ♦ ♣✐♦r ✭♣é✮ s❡❣✉♥❞♦ ▲P▼▲✱
❉■❈✱ ❲❆■❈✱ ❋❛t♦r ❞❡ ❇❛②❡s ✭❋❇✮✱ ❚❡st❡ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ✭❑❙✮✱ ❜❛s❡❛❞♦s ♥❛ ❞❡❣r❛❞❛çã♦ ✭❉❡❣✮ ❡ ♣s❡✉❞♦ t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✭P❚❋✮✱ ❉❛❞♦s ❞❡ ▲❛s❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼ ✹✳✶✸ P❡r❝❡♥t✐s ❞❛ ❞✐str✐❜✉✐çã♦ a posteriori ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛ ♦s ❡♠✐s✲
s♦r❡s ❞❡ ❧❛s❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✽
✺✳✷ P❡r❝❡♥t✐s ❞❡ ♦r❞❡♠ ✺✪✱ ✶✵✪✱ ✷✺✪✱ ✺✵✪✱ ✼✺✪✱ ✾✵✪ ♣❛r❛ ♦s ♣❛❝✐❡♥t❡s ❞❡ ❝â♥❝❡r ❞❡ ♣✉❧♠ã♦ ✐♥♦♣❡rá✈❡❧✱ s❡❣✉♥❞♦ ♦ ❡st✐♠❛❞♦r ❞❡ ❑❛♣♣❧❛♥✲▼❡②❡r✱ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ a posteriori ❡ ♠é❞✐❛ a posteriori ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✽
❈✳✶ ▼❡❞✐❞❛s ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ ❛❥✉st❡ ❞❡ ♠♦❞❡❧♦s ❜❛s❡❛❞❛s ♥❛s ❞❡❣r❛❞❛çõ❡s
𝑦𝑖𝑗 ❡ ♥♦s ♣❡r✜s 𝑦𝑖✱ ❞❛❞♦s ❛rt✐✜❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✽
❈✳✷ ▼❡❞✐❞❛s ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ ❛❥✉st❡ ❞❡ ♠♦❞❡❧♦s ❜❛s❡❛❞❛s ♥♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✭P❚❋✮ r❡❛✐s✱ ❞❛❞♦s ❛rt✐✜❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✾ ❈✳✸ ▼❡❞✐❞❛s ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ ❛❥✉st❡ ❞❡ ♠♦❞❡❧♦s ❜❛s❡❛❞❛s ♥♦s ♣s❡✉❞♦t❡♠♣♦s
❞❡ ❢❛❧❤❛ ˆ𝑡𝑖✱ ❞❛❞♦s ❛rt✐✜❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✵ ❈✳✹ ❋❛t♦r ❞❡ ❇❛②❡s ❜❛s❡❛❞♦ ♥❛s ❞❡❣r❛❞❛çõ❡s𝑦𝑖𝑗 ❡ ♥♦s ♣❡r✜s𝑦𝑖✱ ❞❛❞♦s ❛rt✐✜❝✐❛✐s✷✷✶
❈✳✺ ❋❛t♦r ❞❡ ❇❛②❡s ❜❛s❡❛❞♦ ♥♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛𝑡𝑖✱ ❞❛❞♦s ❛rt✐✜❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✷✷✷
❈✳✻ ❋❛t♦r ❞❡ ❇❛②❡s ❜❛s❡❛❞♦ ♥♦s ♣s❡✉❞♦ t❡♠♣♦s ❞❡ ❢❛❧❤❛𝑡ˆ𝑖✱ ❞❛❞♦s ❛rt✐✜❝✐❛✐s ✳ ✷✷✸ ❈✳✼ ❚❡st❡ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ❜❛s❡❛❞♦ ♥♦s t❡♠♣♦s𝑡𝑖❡ ♣s❡✉❞♦t❡♠♣♦s ❞❡
❢❛❧❤❛𝑡ˆ𝑖✿ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❡♠♣ír✐❝❛ ♥♦ ❝❡♥ár✐♦ ❇✲❙◆ ✳ ✳ ✳ ✷✷✹ ❈✳✽ ❚❡st❡ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ❜❛s❡❛❞♦ ♥♦s t❡♠♣♦s𝑡𝑖❡ ♣s❡✉❞♦t❡♠♣♦s ❞❡
❢❛❧❤❛𝑡ˆ𝑖✿ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❡♠♣ír✐❝❛ ♥♦ ❝❡♥ár✐♦ ❇✲❙❚ ✳ ✳ ✳ ✳ ✷✷✹ ❈✳✾ ❚❡st❡ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ❜❛s❡❛❞♦ ♥♦s t❡♠♣♦s𝑡𝑖❡ ♣s❡✉❞♦t❡♠♣♦s ❞❡
❢❛❧❤❛𝑡ˆ𝑖✿ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❡♠♣ír✐❝❛ ♥♦ ❝❡♥ár✐♦ ❇✲▲❙❚ ✳ ✳ ✳ ✷✷✺ ❈✳✶✵ ❚❡st❡ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ❜❛s❡❛❞♦ ♥♦s t❡♠♣♦s𝑡𝑖❡ ♣s❡✉❞♦t❡♠♣♦s ❞❡
❢❛❧❤❛𝑡ˆ𝑖✿ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❡♠♣ír✐❝❛ ♥♦ ❝❡♥ár✐♦ ❇✲❲ ✳ ✳ ✳ ✳ ✷✷✺ ❈✳✶✶ ❚❡st❡ ❞❡ ❑✲❙ ❝♦♠♣❛r❛♥❞♦ ❛s ❞✐str✐❜✉✐çõ❡s ❡st✐♠❛❞❛s ❡ ❛ r❡❛❧ ❜❛s❡❛❞♦ ♥♦s
t❡♠♣♦s ❞❡ ❢❛❧❤❛ ❡ ♣s❡✉❞♦t❡♠♣♦s ❞❡ ❢❛❧❤❛✱ t♦❞♦s ♦s ❝❡♥ár✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✻ ❈✳✶✷ ❉✐stâ♥❝✐❛ ❑❙ ❝♦♠ ♣❛rt✐❝✐♦♥❛♠❡♥t♦ ❞♦s ❡s♣❛ç♦ ❛♠♦str❛❧ ❞♦s t❡♠♣♦s ❞❡
❈✳✶✸ ◗✉❛❧✐❞❛❞❡ ❞❡ ❛❥✉st❡ ❜❛s❡❛❞♦ ♥❛ ❞❡❣r❛❞❛çã♦ ✭❉❡❣✮ ❡ ♣s❡✉❞♦t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✭P❚❋✮✱ ❘♦❞❛s ❞❡ ❚r❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✼ ❈✳✶✹ ❋❛t♦r ❞❡ ❇❛②❡s ❜❛s❡❛❞♦ ♥❛ ❞❡❣r❛❞❛çã♦ ✭❉❡❣✮ ❡ ♣s❡✉❞♦ t❡♠♣♦s ❞❡ ❢❛❧❤❛
✭P❚❋✮✱ ❘♦❞❛ ▼❆✸✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✽ ❈✳✶✺ ❋❛t♦r ❞❡ ❇❛②❡s ❜❛s❡❛❞♦ ♥❛ ❞❡❣r❛❞❛çã♦ ✭❉❡❣✮ ❡ ♣s❡✉❞♦ t❡♠♣♦s ❞❡ ❢❛❧❤❛
✭P❚❋✮✱ ❘♦❞❛ ▼❆✶✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✽ ❈✳✶✻ ❋❛t♦r ❞❡ ❇❛②❡s ❜❛s❡❛❞♦ ♥❛ ❞❡❣r❛❞❛çã♦ ✭❉❡❣✮ ❡ ♣s❡✉❞♦ t❡♠♣♦s ❞❡ ❢❛❧❤❛
✭P❚❋✮✱ ❘♦❞❛ ▼❆✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✾ ❈✳✶✼ ❚❡st❡ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ❜❛s❡❛❞♦ ♥♦s ♣s❡✉❞♦t❡♠♣♦s ❞❡ ❢❛❧❤❛ˆ𝑡𝑖♣❛r❛
❛s ❘♦❞❛s ▼❆✸✶✱ ▼❆✶✷ ❡ ▼❆✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✾ ❈✳✶✽ ◗✉❛❧✐❞❛❞❡ ❞❡ ❛❥✉st❡ ❜❛s❡❛❞♦ ♥❛ ❞❡❣r❛❞❛çã♦ ✭❉❡❣✮ ❡ ♣s❡✉❞♦ t❡♠♣♦s ❞❡
❢❛❧❤❛ ✭P❚❋✮✱ ❉❛❞♦s ❞❡ ▲❛s❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸✵ ❈✳✶✾ ❋❛t♦r ❞❡ ❇❛②❡s ❜❛s❡❛❞♦ ♥❛ ❞❡❣r❛❞❛çã♦ ✭❉❡❣✮ ❡ ♣s❡✉❞♦ t❡♠♣♦s ❞❡ ❢❛❧❤❛
✭P❚❋✮✱ ❉❛❞♦s ❞❡ ▲❛s❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸✵ ❈✳✷✵ ❚❡st❡ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ❜❛s❡❛❞♦ ♥♦s ♣s❡✉❞♦ t❡♠♣♦s ❞❡ ❢❛❧❤❛ ˆ𝑡𝑖
Lista de Quadros
Sumário
1 Introdução 1
✶✳✶ ▲✐t❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❖ ♠♦❞❡❧♦ ❣❡r❛❧ ❞❡ ❞❡❣r❛❞❛çã♦ ❡ ❛ ❡st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
2 Algumas famílias de distribuições assimétricas 21
✷✳✶ ❆❧❣✉♠❛s ❞✐str✐❜✉✐çõ❡s ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✶✳✶ ❆ ❢❛♠í❧✐❛ ❞❡ ❞✐str✐❜✉✐çõ❡s s❦❡✇ ♥♦r♠❛❧ ✉♥✐✈❛r✐❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✶✳✷ ❆ ❢❛♠í❧✐❛ ❞❡ ❞✐str✐❜✉✐çõ❡s ❧♦❣ s❦❡✇ ♥♦r♠❛❧ ✉♥✐✈❛r✐❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✶✳✸ ❋❛♠í❧✐❛s ❞❡ ❞✐str✐❜✉✐çõ❡s ❞❡ ♠✐st✉r❛ ♥❛ ❡s❝❛❧❛ ❞❛ s❦❡✇ ♥♦r♠❛❧
✉♥✐✈❛r✐❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✶✳✹ ❋❛♠í❧✐❛s ❞❡ ❞✐str✐❜✉✐çõ❡s ❞❡ ♠✐st✉r❛ ♥❛ ❡s❝❛❧❛ ❞❛ ❧♦❣ s❦❡✇ ♥♦r♠❛❧
✉♥✐✈❛r✐❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
3 Modelos gerais de degradação: inferência sobre a distribuição dos
tempos de falha 30
✸✳✷ ■♥❢❡rê♥❝✐❛ ❜❛②❡s✐❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✷✳✶ ▼ét♦❞♦ ♣r♦♣♦st♦ ♣♦r ❍❛♠❛❞❛ ✭✷✵✵✺✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✷✳✷ ▼ét♦❞♦ ❞❡ ❘♦❜✐♥s♦♥ ❡ ❈r♦✇❞❡r ✭✷✵✵✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✷✳✸ ❉✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ a posteriori ❞❡ 𝑇𝑛+1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✸✳✷✳✹ ◆♦✈❛ ✉♥✐❞❛❞❡ ♥❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✈✐❛ ❛✉♠❡♥t♦ ❞❡ ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✺✶ ✸✳✷✳✺ ■♥t❡r♣r❡t❛çã♦ ♥❛s ❛❜♦r❞❛❣❡♥s ❜❛②❡s✐❛♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
4 Modelos de degradação robustos 55
✹✳✶ ▼ét♦❞♦ ❛♥❛❧ít✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✶✳✶ ▼♦❞❡❧♦ ❧✐♥❡❛r ❝♦♠ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❙▼❙◆ ❡ ❙▼▲❙◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✶✳✷ ❖✉tr♦ ♠♦❞❡❧♦ r♦❜✉st♦ ❞❡ ❞❡❣r❛❞❛çã♦ ❧✐♥❡❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✷ ■♥❢❡rê♥❝✐❛ s♦❜r❡ ♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❧✐♥❡❛r ❞❡ ❞❡❣r❛❞❛çã♦ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✸ ❈r✐tér✐♦s ❡ ♠❡❞✐❞❛s✿ s❡❧❡çã♦ ❞❡ ♠♦❞❡❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✸✳✶ ❖r❞❡♥❛❞❛ ♣r❡❞✐t✐✈❛ ❝♦♥❞✐❝✐♦♥❛❧ ✭❈P❖✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✸✳✷ ❉❡✈✐❛♥❝❡ ✐♥❢♦r♠❛t✐♦♥ ❝r✐t❡r✐♦♥ ✭❉■❈✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✸✳✸ ❲❛t❛♥❛❜❡✲❆❦❛✐❦❡ ✐♥❢♦r♠❛t✐♦♥ ❝r✐t❡r✐♦♥ ✭❲❆■❈✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✹✳✸✳✹ ❋❛t♦r ❞❡ ❜❛②❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✹✳✸✳✺ ❚❡st❡ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ✭❑❙✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✹✳✸✳✻ ❉✐❛❣♥óst✐❝♦ ❞❡ ✐♥✢✉ê♥❝✐❛ ✈✐❛ ❞✐✈❡r❣ê♥❝✐❛ ❞❡ ❑✉❧❧❜❛❝❦✲▲❡✐❜❧❡r ✭❑▲✮ ✽✸ ✹✳✸✳✼ ❙❡❧❡çã♦ ❞❡ ♠♦❞❡❧♦s ❡♠ ♠♦❞❡❧♦s ❞❡ ❞❡❣r❛❞❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✹✳✹ ❆♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦ ❛rt✐✜❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✹✳✺✳✷ ❊st✉❞♦ ❞❡ ❝❛s♦ ✷✿ ❝♦rr❡♥t❡ ❞❡ ♦♣❡r❛çã♦ ❞❡ ❡♠✐ss♦r❡s ❞❡ ❧❛s❡r ✳ ✳ ✶✹✸
5 Modelagem robusta para análise convencional de tempo de falha 149 ✺✳✶ ▼♦❞❡❧♦ ♣❛r❛ t❡♠♣♦s ❞❡ ❢❛❧❤❛ ❡ té❝♥✐❝❛ ❞❡ ❛✉♠❡♥t♦ ❞❡ ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✶ ✺✳✷ ▼♦❞❡❧♦s r♦❜✉st♦s ♣❛r❛ t❡♠♣♦ ❛té ❛ ❢❛❧❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✸ ✺✳✷✳✶ ❆♠♦str❛❣❡♠ ✈✐❛ ▼❈▼❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✻ ✺✳✷✳✷ ▼♦❞❡❧♦ ❙◆ ❝❡♥tr❛❞♦ ♣❛r❛ ♦ t❡♠♣♦ ❛té ❛ ❢❛❧❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✵ ✺✳✸ ❆♥á❧✐s❡ ❞❡ ❞❛❞♦s ❛rt✐✜❝✐❛✐s ❞❡ t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✸
✺✳✸✳✶ ❉❛❞♦s ❛rt✐✜❝✐❛✐s✿ s❦❡✇ ♥♦r♠❛❧ ❝❡♥tr❛❞❛ versus s❦❡✇ ♥♦r♠❛❧ ♥ã♦ ❝❡♥tr❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✹ ✺✳✸✳✷ ❉❛❞♦s ❛rt✐✜❝✐❛✐s ❧♦❣ s❦❡✇✲t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✻ ✺✳✹ ❉❛❞♦s ❞❡ ❝â♥❝❡r✿ ❛♥á❧✐s❡ ❞❡ t❡♠♣♦ ❞❡ ✈✐❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✷
6 Conclusões 179
Referências Bibliográficas 184
Anexos 194
Anexo A Provas de Proposições 195
Anexo B Códigos no R/WinBUGS 206
❇✳✶ ▼♦❞❡❧♦ ▲❙❚ ♣❛r❛ ❞❡❣r❛❞❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✻ ❇✳✷ ▼♦❞❡❧♦ ▲❙❚ ♣❛r❛ t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✷ ❇✳✷✳✶ ▼♦❞❡❧♦ ❙◆ ❈❡♥tr❛❞♦ ♥♦ ❲✐♥❇❯●❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✻
Capítulo 1
Introdução
1.1 Literatura
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✷
P♦r ❡st❛ r❛③ã♦✱ ❛ ❧✐t❡r❛t✉r❛ ❡s♣❡❝í✜❝❛ ♥❛ ár❡❛ ❞❡ ❝♦♥✜❛❜✐❧✐❞❛❞❡ t❡♠ ❞❛❞♦ ♠❛✐♦r ê♥❢❛s❡ à ✉t✐❧✐③❛çã♦ ❞❡ ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦ ❝♦♠♦ ✉♠❛ ❛❧t❡r♥❛t✐✈❛ ❛♦s ❞❛❞♦s ❞❡ t❡♠♣♦ ❛té ❛ ❢❛❧❤❛✳ ❆❧❣✉♥s ❡①❡♠♣❧♦s ✐♠♣♦rt❛♥t❡s sã♦ ♦s tr❛❜❛❧❤♦s ❞❡ ✭▲✉ ❡ ▼❡❡❦❡r✱ ✶✾✾✸❀ ❚s❡♥❣ et al.✱ ✶✾✾✺❀ ▲✉ et al.✱ ✶✾✾✻❀ ❈❤✐❛♦ ❡ ❍❛♠❛❞❛✱ ✶✾✾✻✱ ✷✵✵✵❀ ❘♦❜✐♥s♦♥ ❡ ❈r♦✇❞❡r✱ ✷✵✵✵❀ ❞❡ ❖❧✐✈❡✐r❛ ❡ ❈♦❧♦s✐♠♦✱ ✷✵✵✹❀ ❍❛♠❛❞❛✱ ✷✵✵✺❀ ❍♦♥❣ et al.✱ ✷✵✶✺✮✳ ◆♦s t❡st❡s ❞❡ ❞❡❣r❛❞❛✲ çã♦✱ ❛ ✈❛r✐á✈❡❧ ♦❜s❡r✈❛❞❛ ♥ã♦ é ♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ♠❛s ✉♠❛ ♠❡❞✐❞❛ ❞❡ ❞❡❣r❛❞❛çã♦ ❞❡ ❛❧❣✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ q✉❛❧✐❞❛❞❡ ❞♦ ♣r♦❞✉t♦ ❞❡ ✐♥t❡r❡ss❡ t♦♠❛❞❛ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✳ ❊st❛ ♠❡❞✐❞❛ ❞❡✈❡ ❡st❛r ❞✐r❡t❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞❛ à ❢❛❧❤❛✳ ❆❧é♠ ❞✐st♦✱ ❛ ♣ró♣r✐❛ ❞❡✜♥✐çã♦ ❞❛ ❢❛❧❤❛ ❞❡✈❡ ❡st❛r ❛ss♦❝✐❛❞❛ ❛ ❛❧❣✉♠ ♥í✈❡❧ ❝rít✐❝♦ ♣ré✲❡s♣❡❝✐✜❝❛❞♦ ❞❛ ♠❡❞✐❞❛ ❞❡ ❞❡❣r❛❞❛çã♦✳ ❊st❡ ♥í✈❡❧ ❝rít✐❝♦ é ❞❡♥♦♠✐♥❛❞♦ ❧✐♠✐❛r ❞❡ ❢❛❧❤❛ ♦✉ ✏failure threshold✑✳ ❆ ❥✉st✐✜❝❛t✐✈❛ ♣❛r❛ ❛ ✉t✐❧✐③❛çã♦ ❞❡ss❡ t✐♣♦ ❞❡ ❛❜♦r❞❛❣❡♠ r❡s✐❞❡ ♥♦ ❢❛t♦ ❞❡ q✉❡ ♠✉✐t❛s ❢❛❧❤❛s sã♦ ♦ r❡s✉❧t❛❞♦ ❞❡ ✉♠ ♠❡❝❛♥✐s♠♦ ❞❡ ❞❡❣r❛❞❛çã♦ ❡♠ ❛t✉❛çã♦ ♣❛r❛ ♦ q✉❛❧ ❡①✐st❡♠ ❝❛r❛❝t❡ríst✐❝❛s q✉❡ s❡ ❞❡❣r❛❞❛♠ ❝♦♠ ♦ t❡♠♣♦✳ ❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❛ ❡♥❣❡♥❤❛r✐❛✱ ❛❧❣✉♥s ♠❡❝❛♥✐s♠♦s ❞❡ ❞❡❣r❛❞❛çã♦ ❝♦♠✉♥s ✐♥❝❧✉❡♠ ❢❛❞✐❣❛✱ tr✐♥❝❛s✱ ❝♦rr♦sã♦ ❡ ♦①✐❞❛çã♦✳ P❛r❛ ❝♦♥❞✉③✐r ✉♠ t❡st❡ ✭❡♥s❛✐♦✮ ❞❡ ❞❡❣r❛❞❛çã♦✱ é ♥❡❝❡ssár✐♦ ♣ré✲❡s♣❡❝✐✜❝❛r ✉♠ ❧✐♠✐❛r ❝rít✐❝♦ ❞❡ ❞❡❣r❛❞❛çã♦ ♦✉ ❧✐♠✐❛r ❞❡ ❢❛❧❤❛✱ ♦❜t❡r ♠❡❞✐❞❛s ❞❛ ❞❡❣r❛❞❛çã♦ ❡♠ t❡♠♣♦s ♣ré✲✜①❛❞♦s ❡ ❞✐st✐♥t♦s ❡ ❞❡✜♥✐r q✉❡ ❛ ❢❛❧❤❛ ♦❝♦rr❡ q✉❛♥❞♦ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❡❣r❛❞❛çã♦ ♣❛r❛ ✉♠❛ ✉♥✐❞❛❞❡ s♦❜ t❡st❡ ❡①❝❡❞❡ àq✉❡❧❡ ♥í✈❡❧ ❝rít✐❝♦✳ ❆ ♣r✐♥❝✐♣❛❧ ✈❛♥t❛❣❡♠ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦ s♦❜r❡ ♦s ❞❛❞♦s ❞❡ t❡♠♣♦s ❞❡ ❢❛❧❤❛✱ ♦r✐✉♥❞♦s ❞❡ t❡st❡s ❞❡ ✈✐❞❛✱ é q✉❡ ❛ ❛♥á❧✐s❡ ♣♦❞❡ s❡r ❢❡✐t❛ ❞❡ ♠❛♥❡✐r❛ s❛t✐s❢❛tór✐❛✱ ❛✐♥❞❛ q✉❡ ♥❡♥❤✉♠❛ ❢❛❧❤❛ t❡♥❤❛ ♦❝♦rr✐❞♦✱ ✐st♦ é✱ ♠❡s♠♦ q✉❡ ♥❡♥❤✉♠ ❞♦s ♣❡r✜s ❞❛s ✉♥✐❞❛❞❡s s♦❜ ♦❜s❡r✈❛çã♦ t❡♥❤❛ ❛t✐♥❣✐❞♦ ♦ ❧✐♠✐❛r ❝♦♥s✐❞❡r❛❞♦ ♣❛r❛ ❞❡✜♥✐r ✉♠❛ ✏❢❛❧❤❛✑✳
❆ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦✱ ❛ss✐♠ ❝♦♠♦ ❞♦s ❞❛❞♦s ❞❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❡st✐♠❛r ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❛té ❛ ❢❛❧❤❛ ♦✉ ❝❛r❛❝t❡ríst✐❝❛s ❞❛ ♠❡s♠❛✱ t❛✐s ❝♦♠♦ ♦𝑝✲és✐♠♦ q✉❛♥t✐❧(𝑡𝑝)✱ ♦ t❡♠♣♦ ♠é❞✐♦ ❛té ❛ ❢❛❧❤❛✱ ♦✉ ❛ ❢✉♥çã♦ ❞❡ ❝♦♥✜❛❜✐❧✐❞❛❞❡
✸
♦ ♣r♦❜❧❡♠❛ ❞❡ ❞❡❣r❛❞❛çã♦ s♦❜ ♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❛ ❡♥❣❡♥❤❛r✐❛✳ ❖s ❛✉t♦r❡s ❛♣r❡s❡♥t❛♠ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❇❡r♥st❡✐♥✱ ❛ q✉❛❧ ❞❡s❝r❡✈❡ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❛té ❛ ❢❛❧❤❛ ♣❛r❛ ✉♠ ♠♦❞❡❧♦ ❧✐♥❡❛r s✐♠♣❧❡s ❝♦♠ ✐♥t❡r❝❡♣t♦ ❡ ✐♥❝❧✐♥❛çã♦ ❛♠❜♦s ❛❧❡❛tór✐♦s✳ ◆❡❧s♦♥ ✭✶✾✽✶✮ ❞✐s❝✉t❡ ✉♠❛ s✐t✉❛çã♦ ❡s♣❡❝✐❛❧ ♥❛ q✉❛❧ ❛ ♠❡❞✐❞❛ ❞❡ ❞❡❣r❛❞❛çã♦ é ❞❡str✉t✐✈❛✱ ❡♠ q✉❡ s♦♠❡♥t❡ ✉♠❛ ♠❡❞✐❞❛ ♣♦❞❡ s❡r ❢❡✐t❛ ❡♠ ❝❛❞❛ ✐t❡♠✳ ❯♠❛ r❡✈✐sã♦ ❞❡t❛❧❤❛❞❛ s♦❜r❡ ❡st❡ t❡♠❛ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ❡♠ ✭◆❡❧s♦♥✱ ✶✾✾✵✱ ❈❛♣ít✉❧♦ ✶✶✮✱ ♦♥❞❡ t❛♠❜é♠ s❡ ❡♥❝♦♥tr❛♠ ❡①❡♠♣❧♦s ✐♠♣♦rt❛♥t❡s ❞❡ ❛♣❧✐❝❛çõ❡s ❡ ❛ ❞❡s❝r✐çã♦ ❞❡ ✐❞é✐❛s ❜ás✐❝❛s ❞❡ ❝♦♠♦ s❡ ❛♥❛❧✐s❛r ❝❡rt♦ t✐♣♦ ❞❡ ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦✳
❉✉❛s ❛❜♦r❞❛❣❡♥s ❜ás✐❝❛s ♣❛r❛ ♠♦❞❡❧❛❣❡♠ ❡ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦ ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛✳ ◆✉♠❛ ❞❡❧❛s ❛ss✉♠❡✲s❡ q✉❡ ❛ ❞❡❣r❛❞❛çã♦ é ✉♠ ♣r♦❝❡ss♦ ❛❧❡❛tór✐♦ ♥♦ t❡♠♣♦✳ ❉❡♥tr♦ ❞❡st❛ ❧✐♥❤❛✱ ❉♦❦s✉♠ ✭✶✾✾✶✮ ✉t✐❧✐③❛ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❲✐❡♥❡r ♣❛r❛ ❛♥❛❧✐s❛r ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦✳ ❚❛♥❣ ❡ ❈❤❛♥❣ ✭✶✾✾✺✮ ♠♦❞❡❧❛♠ ❞❛❞♦s ♦r✐✉♥❞♦s ❞❡ ❡♥s❛✐♦s ❞❡ ❞❡❣r❛❞❛çã♦ ❛❝❡❧❡r❛❞♦s ♥ã♦ ❞❡str✉t✐✈♦s ❝♦♠♦ ✉♠❛ ❝♦❧❡çã♦ ❞❡ ♣r♦❝❡ss♦s ❡s✲ t♦❝ást✐❝♦s✳ ❲❤✐t♠♦r❡ ❡ ❙❝❤❡♥❦❡❧❜❡r❣ ✭✶✾✾✼✮ ♠♦❞❡❧❛♠ ♦ ♣r♦❝❡ss♦ ❞❡ ❞❡❣r❛❞❛çã♦ ❝♦♠♦ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❞✐❢✉sã♦ ❞❡ ❲✐❡♥❡r✳ P❡tt✐t ❡ ❨♦✉♥❣ ✭✶✾✾✾✮ r❡❧❛❝✐♦♥❛♠ ❛ ❞❡❣r❛❞❛çã♦✱ ♠♦❞❡❧❛❞❛ ♣♦r ✉♠ ♣r♦❝❡ss♦ ❲✐❡♥❡r✱ ❝♦♠ ✉♠ ❧✐♠✐❛r ❞❡ ❢❛❧❤❛✱ ❡♠ q✉❡ ♦s r❡s✉❧t❛❞♦s ❞❛s ❡st✐♠❛t✐✈❛s s♦❜r❡ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ❢♦r❛♠ s✉♣❡r✐♦r❡s ❛ ♠♦❞❡❧♦s q✉❡ ♥ã♦ ❝♦♥s✐❞❡r❛♠ ❛ ❞❡❣r❛❞❛çã♦✳ ❇❛❣❞♦♥❛✈✐❝✐✉s ❡ ◆✐❦✉❧✐♥ ✭✷✵✵✶✮ ❡ ❇❛❣❞♦♥❛✈✐❝✐✉s et al. ✭✷✵✶✵✮ ♠♦❞❡❧❛♠ ❛ ❞❡❣r❛❞❛çã♦ ♣♦r ✉♠ ♣r♦❝❡ss♦ ❣❛♠❛ ❡ ✐♥❝❧✉❡♠ ♣♦ssí✈❡✐s ❝♦✈❛r✐á✈❡✐s ❞❡♣❡♥❞❡♥t❡s ❞♦ t❡♠♣♦✳ ▲❛✇❧❡ss ❡ ❈r♦✇❞❡r ✭✷✵✵✹✮ ✐♥s❡r❡♠ ❝♦✈❛r✐á✈❡✐s ❡ ❡❢❡✐t♦s ❛❧❡❛tó✲ r✐♦s ♥✉♠ ♣r♦❝❡ss♦ ❣❛♠❛ ❝♦♠ ❛♣❧✐❝❛çã♦ ♣❛r❛ ❞❡❣r❛❞❛çã♦ ❡ ❢❛❧❤❛✳ P❡♥❣ ❡ ❚s❡♥❣ ✭✷✵✶✸✮ ❝♦♥s✐❞❡r❛♠ q✉❡ ❛ ✈❛r✐❛❜✐❧✐❞❛❞❡ ❡♥tr❡ ✉♥✐❞❛❞❡s✱ ❝♦♠ ❡str✉t✉r❛ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ t❡♠♣♦r❛❧✱ ❞❡ ✉♠ ♠♦❞❡❧♦ ❧✐♥❡❛r ❞❡ ♣r♦❝❡ss♦ ❡st♦❝ást✐❝♦ ♣❛r❛ ❛ ❞❡❣r❛❞❛çã♦ ♣♦❞❡ s❡r ❞❡s❝r✐t❛ ♣❡❧❛ ❞✐str✐❜✉✐çã♦ s❦❡✇✲♥♦r♠❛❧✱ ♦ q✉❡ ❝♦♥❢❡r❡ ♠❛✐♦r ✢❡①✐❜✐❧✐❞❛❞❡ ❛♦ ♠♦❞❡❧♦ ❡ r❡❞✉③ ♣r♦❜❧❡✲ ♠❛s r❡❧❛❝✐♦♥❛❞♦s à ♠á ❡s♣❡❝✐✜❝❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❞♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ♥❛ ♣r❡s❡♥ç❛ ❞❡ ❛ss✐♠❡tr✐❛✳
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✹
♠♦❞❡❧♦s ❡st❛tíst✐❝♦s ❡♠ q✉❡ ❛ ❞❡❣r❛❞❛çã♦ é ❞❡s❝r✐t❛ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ❡✱ ♣♦ss✐✈❡❧♠❡♥t❡✱ ❛❧❣✉♠❛s ♦✉tr❛s ✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ✭♣♦r ❡①❡♠♣❧♦✱ ❢❛❜r✐❝❛♥t❡s ❡ ♠❛t❡r✐❛✐s ❞✐✈❡rs♦s✮✳ ❚r❛t❛♠✲s❡ ❞♦s ♠♦❞❡❧♦s ❣❡r❛✐s ❞❡ ♣❡r✜s ❞❡ ❞❡❣r❛❞❛çã♦ ✭✏general degradation path models✑✮✳ ❆ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦ ♣♦r ❡st❛ ❛❜♦r❞❛❣❡♠ é ✐♠♣❧❡♠❡♥t❛❞❛ ❡♠ ❞✉❛s ❡t❛♣❛s✳ ❆ ♣r✐♠❡✐r❛ ❝♦♥s✐st❡ ♥❛ ❝♦♥str✉çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ♠✐st♦✱ q✉❡ ♣♦❞❡ s❡r ❧✐♥❡❛r ♦✉ ♥ã♦ ❧✐♥❡❛r✱ q✉❡ ❞❡s❝r❡✈❛ ♦ ♣❡r✜❧ ❞❡ ❞❡❣r❛❞❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✱ s❡❣✉✐❞❛ ❞❛ ❡st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ❞❡s❝♦♥❤❡❝✐❞♦s ❞♦ ♠❡s♠♦✳ ❆ s❡❣✉♥❞❛ ❡t❛♣❛ ❝♦♥s✐st❡ ❡♠ ✉t✐❧✐③❛r ❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ❡st✐♠❛r ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❛té ❛ ❢❛❧❤❛✱ ❜❡♠ ❝♦♠♦ ♦✉tr❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ✐♥t❡r❡ss❡ ❛ ❡❧❛ ❛ss♦❝✐❛❞❛s✳
❊♠ ❣❡r❛❧✱ ❛ ❛♥á❧✐s❡ é ✐♠♣❧❡♠❡♥t❛❞❛ ❡♠ ❞✉❛s ❡t❛♣❛s✳ ➱ ✐♠♣♦rt❛♥t❡ r❡ss❛❧t❛r q✉❡ ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦ ♣♦ss✉❡♠ ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❞❛❞♦s ❧♦♥❣✐t✉❞✐♥❛✐s ✭❋✐t③♠❛✉r✐❝❡ et al.✱ ✷✵✵✹✮✳ P♦rt❛♥t♦✱ ❛ ♣r✐♠❡✐r❛ ❡t❛♣❛ ❞❛ ❛♥á❧✐s❡ é ♥❛ r❡❛❧✐❞❛❞❡ ✉♠❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❧♦♥✲ ❣✐t✉❞✐♥❛✐s ❝♦♠ r❡s♣♦st❛ ❝♦♥tí♥✉❛✱ ✐♠♣❧❡♠❡♥t❛❞❛ ❛tr❛✈és ❞❡ ✉♠ ♠♦❞❡❧♦ ♥ã♦ ❧✐♥❡❛r ♦✉ ❧✐♥❡❛r ♠✐st♦✳ ❆ ✉t✐❧✐③❛çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ♠✐st♦✱ ✐st♦ é✱ q✉❡ ✐♥❝♦r♣♦r❛ ❡♠ s✉❛ ❢♦r♠❛ ❢✉♥❝✐♦♥❛❧ t❛♥t♦ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s q✉❛♥t♦ ✜①♦s✱ ♣♦❞❡✱ ♣♦r s✉❛ ✈❡③✱ s❡r ✈✐st❛ ❝♦♠♦ ✉♠❛ ♠♦❞❡❧❛❣❡♠ ❡♠ ❞♦✐s ❡stá❣✐♦s✱ ♥❛ q✉❛❧ ♣r✐♠❡✐r❛♠❡♥t❡ ♦s ♣❛râ♠❡tr♦s ♥ã♦ ♦❜s❡r✈á✈❡✐s ✭♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✮ sã♦ ❛♠♦str❛❞♦s ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ q✉❡ ♣♦r s✐ só✱ ♣♦ss✉✐ ♣❛râ♠❡tr♦s ✭✜①♦s✮ ❞❡s❝♦♥❤❡❝✐❞♦s✳ ❊♠ s❡❣✉✐❞❛ ✭✷➸✳ ❊stá❣✐♦✮ ♦s ❞❛❞♦s ♦❜s❡r✈❛❞♦s ♥♦ ❡♥s❛✐♦ sã♦ ❝♦♥✲ s✐❞❡r❛❞♦s ❝♦♠♦ s❡♥❞♦ ❛♠♦str❛s ✭r❡❛❧✐③❛çõ❡s✮ ❞❡ ❞✐str✐❜✉✐çõ❡s ♥♦r♠❛✐s ✐♥❞❡♣❡♥❞❡♥t❡s✱ ❝✉❥❛s ♠é❞✐❛s sã♦ ❢✉♥çõ❡s ❧✐♥❡❛r❡s ✭♦✉ ♥ã♦ ❧✐♥❡❛r❡s✮ ❞❡st❡s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❡✱ ♣♦ss✐✈❡❧✲ ♠❡♥t❡✱ ❞❡ ♦✉tr♦s ♣❛râ♠❡tr♦s ♣♦♣✉❧❛❝✐♦♥❛✐s ✭❡❢❡✐t♦s ✜①♦s✮✳ ❯♠❛ ✈❡③ q✉❡ ✉♠❛ ❢❛♠í❧✐❛ ♣❛r❛♠étr✐❝❛ ♣❛r❛ ♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s é ❡s❝♦❧❤✐❞❛✱ é ♣r❡❝✐s♦ ❡st✐♠❛r ♦s ♣❛râ♠❡tr♦s ✜①♦s ❞♦ ♠♦❞❡❧♦✱ q✉❛✐s s❡❥❛♠ ♦s ♣❛râ♠❡tr♦s q✉❡ ✐♥❞❡①❛♠ ❛ ❞✐str✐❜✉✐çã♦ ❞♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❡ ♦✉tr♦s ♣❛râ♠❡tr♦s ✜①♦s q✉❡ ❢❛③❡♠ ♣❛rt❡ ❞❛ ❢♦r♠❛ ❢✉♥❝✐♦♥❛❧ ❞♦ ♣❡r✜❧ ❞❡ ❞❡❣r❛❞❛çã♦✳ ❉❡ ♣♦ss❡ ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦✱ ❛ s❡❣✉♥❞❛ ❡t❛♣❛ ❞❛ ❛♥á❧✐s❡ ❞♦s ❞❛❞♦s ❞❡ ❞❡❣r❛❞❛çã♦ ❝♦♥s✐st❡ ❡♠ ❡st✐♠❛r ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❛té ❛ ❢❛❧❤❛𝐹𝑇(𝑡)✳ ❙❡
✺
❢❡❝❤❛❞❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ✉♠❛ ❡st✐♠❛t✐✈❛ ♣♦❞❡ s❡r ♦❜t✐❞❛ ❛tr❛✈és ❞❡ s✐♠✉❧❛çã♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦ ♦✉ ❛❧❣✉♠ ♦✉tr♦ ♣r♦❝❡❞✐♠❡♥t♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳ ❯♠ ❜♦♠ ❡①❡♠♣❧♦ é ♦ ❛rt✐❣♦ r❡❝❡♥t❡ ❞❡ ❍♦♥❣ et al. ✭✷✵✶✺✮✱ ❡♠ q✉❡ ♦s ❛✉t♦r❡s ❝♦♥str♦❡♠ ✉♠ ♠♦❞❡❧♦ ❞❡ ❞❡❣r❛❞❛çã♦ ❝♦♠ ❝♦✈❛r✐á✈❡✐s ❞✐♥â♠✐❝❛s ♥♦ t❡♠♣♦ ❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡st❛s ❝♦✈❛r✐á✈❡✐s é ♠♦❞❡❧❛❞❛ ❛tr❛✈és ❞❡ s♣❧✐♥❡s ❞❡ ❢♦r♠❛ r❡str✐t❛✳ ❆ ❞✐str✐❜✉✐çã♦ ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ é ♦❜t✐❞❛ ✈✐❛ s✐♠✉❧❛çã♦ ❛ss✉♠✐♥❞♦ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ♣❛r❛ ♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✳
▼ét♦❞♦s ❞❡ ❡st✐♠❛çã♦ ❜❛s❡❛❞♦s ❡♠ ✐♥❢❡rê♥❝✐❛ ❝❧áss✐❝❛ ♦✉ ❜❛②❡s✐❛♥❛ ♣♦❞❡♠ s❡r ❡♠✲ ♣r❡❣❛❞♦s ♣❛r❛ ♦❜t❡r ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ❞❡s❝♦♥❤❡❝✐❞♦s ♥♦s ♠♦❞❡❧♦s ❞❡ ❞❡❣r❛✲ ❞❛çã♦ ❡✱ ❛ ♣❛rt✐r ❞❡❧❛s✱ ❡st✐♠❛r ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛✳ ❯♠ ❜♦♠ ❡①❡♠♣❧♦ ❞❡ ❡st✐♠❛çã♦ ♥♦ ❝♦♥t❡①t♦ ❜❛②❡s✐❛♥♦ é ♦ ❛rt✐❣♦ ❞❡ ❘♦❜✐♥s♦♥ ❡ ❈r♦✇❞❡r ✭✷✵✵✵✮✳
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✻
❡st✉❞❛♠ ❛s ♣r♦♣r✐❡❞❛❞❡s ❛ss✐♥tót✐❝❛s ❞♦s ❡st✐♠❛❞♦r❡s ❞❡ ♠í♥✐♠♦s q✉❛❞r❛❞♦s ✭♣♦♥❞❡r❛✲ ❞♦s✮ ❞♦ ♠♦❞❡❧♦ ◆▲▼❊✳ ❖s ❛✉t♦r❡s ✉t✐❧✐③❛♠ ❡st❛s ♣r♦♣r✐❡❞❛❞❡s ♣❛r❛ ♦❜t❡r ❡st✐♠❛t✐✈❛s ♣♦♥t✉❛✐s ❡ ✐♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ❛♣r♦①✐♠❛❞♦s ♣❛r❛ ♣❡r❝❡♥t✐s ❞❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛✳ ❖s ♠ét♦❞♦s ♣r♦♣♦st♦s sã♦ ✐❧✉str❛❞♦s ❝♦♠ ❞❛❞♦s ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡ tr✐♥❝❛s ❡♠ ♠❡t❛✐s s✉❜♠❡t✐❞♦s ❛ ❡♥s❛✐♦s ❞❡ ❢❛❞✐❣❛✳ ❯♠❛ ❜♦❛ r❡❢❡rê♥❝✐❛ ❡♠ ♠♦❞❡❧♦s ❣❡r❛✐s ❞❡ ♣❡r✜s ❞❡ ❞❡❣r❛❞❛çã♦ é ▼❡❡❦❡r ❡ ❊s❝♦❜❛r ✭✶✾✾✽✮✳ ❲✉ ❡ ❙❤❛♦ ✭✷✵✵✵✮ ❛♣r❡s❡♥t❛♠ ✉♠ ♠ét♦❞♦ ❞❡ ❡st✐♠❛çã♦ ♣♦♥❞❡r❛❞♦ ❝♦♠ ❜❛s❡ ❡♠ ❛❣r✉♣❛♠❡♥t♦ ❞✐❢✉s♦ ✭fuzzy clustering✮ ♣❛r❛ ♠♦❞✐✜❝❛r ♦ ♣r♦❝❡❞✐♠❡♥t♦ ❡♠ ❞♦✐s ❡stá❣✐♦s ♣r♦♣♦st♦ ♣♦r ▲✉ ❡ ▼❡❡❦❡r ✭✶✾✾✸✮✳ ❖ ♠ét♦❞♦ ♣r♦♣♦st♦ ❡ ♦ ❞❡ ❞♦✐s ❡stá❣✐♦s ❞❡ ▲✉ ❡ ▼❡❡❦❡r ✭✶✾✾✸✮ sã♦ ❛♠❜♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛♥❛❧✐s❛r ♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❛♣r❡s❡♥t❛❞♦ ♥♦ tr❛❜❛❧❤♦ ❞❡ ❲✉ ❡ ❙❤❛♦ ✭✶✾✾✾✮✳
❖✉tr♦s tr❛❜❛❧❤♦s ✐♠♣♦rt❛♥t❡s ♥♦ ❡st✉❞♦ ❞❡ ❞❡❣r❛❞❛çã♦ sã♦ ♦s tr❛❜❛❧❤♦s ❞❡ ❈r❦ ✭✷✵✵✵✮✱ ❏✐❛♥❣ ❡ ❩❤❛♥❣ ✭✷✵✵✷✮ ❡ ❞❡ ❖❧✐✈❡✐r❛ ❡ ❈♦❧♦s✐♠♦ ✭✷✵✵✹✮✳ ◆❡st❡ ú❧t✐♠♦✱ ♦s ❛✉t♦r❡s ❝♦♠♣❛r❛r❛♠ ♦s três ♠ét♦❞♦s ♣r♦♣♦st♦s ♣♦r ▼❡❡❦❡r ❡ ❊s❝♦❜❛r ✭✶✾✾✽✮ ✭❛♥❛❧ít✐❝♦✱ ❛♣r♦✲ ①✐♠❛❞♦ ❡ ♥✉♠ér✐❝♦✮ ❛♥❛❧✐s❛♥❞♦ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❞❡ ❞❡s❣❛st❡ ❞❡ ❜❛♥❞❛s ❞❡ r♦❞❛❣❡♠ ❞❡ ♣♥❡✉s ❛✉t♦♠♦t✐✈♦s✳
