athijeevana pravartthanam

oru rogio upakaranamo thaalpparyamulla mattu vasthukkalo oru nischitha samayathinu sesham athijeevikkaan saadhyatha nalkunna oru pravarthanamaanu athijeevana pravartthanam.
athijeevana pravartthanatthe athijeevana pravartthanam allengil vishwaasyatha pravartthanam ennum vilikkunnu.
reliability function" enna padam enchineeyaringil saadhaaranamaanu, athesamayam "survival function" enna padam manushyamardham ulppedeyulla vishalamaaya aaplikkeshanukalil upayogikkunnu. athijeevana pravartthanam jeevithakaalathinte pooraka sanjitha vitharana pravarthanamaanu. chilappol paripooraka sanjitha vitharana pravartthanangale pothuve athijeevana pravartthanangal ennu vilikkunnu.
nirvachanam.
tii" enna ayuss, [0, φ] enna edavelayil cumulative density function "eph" ("tii") umm probability density function "eph" ("tii") umm ulla oru thudarchayaaya kramarahithamaya veriyabilaayirikkatte. athinte "athijeevana pravartthanam" allengil "vishwaasyatha pravartthanam" ithaanu
athijeevana pravartthanangalude udaaharanagal.
chuvadeyulla graafukal saangalppika athijeevana pravartthanangalude udaaharanagal kaanikkunnu. x-axis samayamaan. athijeevicha vishayangalude anupaathamaan vaii-axis. oru vishayam samayathinu appuram nilanilkkanulla saadhyatha graafukal kaanikkunnu.
udaaharanathinu, athijeevana pravartthanam 1-nuu, t = 2 maasathil kooduthal kaalam nilanilkkanulla saadhyatha 0.37 aanu. athaayath, 37 sathamaanam vishayangalum 2 maasathil kooduthal athijeevikkunnu.
athijeevana pravartthanam 2-ll, t = 2 maasathil kooduthal kaalam nilanilkkanulla saadhyatha 0.97 aanu. athaayath, 97 sathamaanam vishayangalum 2 maasathil kooduthal athijeevikkunnu.
athijeevana pravartthanatthil ninnu sharashari athijeevanam nirnnayikkaam. udaaharanathinu, athijeevana pravarthanatthinu 2, vishayangalil 50 sathamaanam 3.72 maasam athijeevikkunnu. athinaal sharashari athijeevanam 3.72 maasamaan.
chila sandarbhangalil, graafiloode sharashari athijeevanam nirnnayikkaan kazhiyilla. udaaharanathinu, athijeevana pravartthanam 4-ll, 50 sathamaanathiladhikam vishayangal 10 maasathe nireekshana kaalayalavinekkaal kooduthal kaalam nilanilkkunnu.
athijeevana daatta vivarikkunnathinum pradarshippikkunnathinnum niravadhi maargangalilonnaan athijeevana pravartthanam. daatta pradarshippikkunnathinulla mattoru upayogapradamaaya maarggam vishayangalude athijeevana samayathinte vitharanam kaanikkunna oru graafaanu. oolkin, peju 426, athijeevana daattayude inipparayunna udaaharanam nalkunnu. oru eyar contitioning samvidaanathinte thudarchayaaya paraajayangalkkidayilulla manikkoorukalude ennam rekhappeduthiyittundu. thudarchayaaya paraajayangalkkidayilulla samayam 1,33,5,7,11,11,11,12,14,14,14,16,16,20,21,23,42,47,52,62,71,71,87,90,95,120,120,225,256,261 manikkoorukalaan. paraajayangalkkidayilulla sharashari samayam 59.6 aanu. eee sharashari moolyam daattayumaayi oru saidhaanthika vakram poruthappedutthaan udan upayogikkum. thaazhe koduthirikkunna chithram paraajayangalkkidayilulla samayathinte vitharanam kaanikkunnu. graphinu thaazheyulla neela tick adayaalangal thudarchayaaya paraajayangalkkidayilulla yadhaartha manikkoorukalaan.
parajaya samayangalude vitharanam oru exponential vitharanathe prathinidheekarikkunna oru vakram upayogichu ovar-lade cheiyunnu. eee udaaharanathinu, exponential distribution parajaya samayangalude vitharanathe ekadeshamaayi kanakkakkunnu. yadhaartha parajaya samayangalumayi poruthappedunna oru saidhaanthika vitharanamaanu exponential karvu. eee prathyeka exponential karvu nirddishta paraameettar lamdayanu, λ = 1/(paraajayangalkkidayilulla sharashari samayam) = 1/59.6 = 0.0168. samayathinu enthengilum positteev moolyam edukkaan kazhiyumenkil parajaya samayangalude vitharanathe probability density function (pdf) ennu vilikkunnu. samavakyangalil, pdf f (t) aayi vyakthamaakkunnu. samayathinu vyathirikthamaya moolyangal (1 divasam, 2 divasam muthalaayava) maathrame edukkaan kazhiyoovenkil, parajaya samayangalude vitharanathe probability maas function (pii. emm. eph) ennu vilikkunnu. mikka athijeevana vishakalana reethikalum samayathinu eathu positteev moolyavum edukkaamennu anumaanikkunnu, f (t) aanu pdf. nireekshicha airconditioner paraajayangalkkidayilulla samayam exponential function upayogichu ekadeshamaayi kanakkaakkukayaanenkil, exponential karvu airconditioner parajaya samayangalkk probability density function, f (t) nalkunnu.
athijeevana daatta pradarshippikkunnathinulla mattoru upayogapradamaaya maarggam oro samaya pooyintilekkum sanjitha parajayangal kaanikkunna oru graafaanu. eee daatta oro thavanayum paraajayangalude sanjitha samkhyayaayo sanjitha anupaathamaayo pradarshippikkaam. eyar contitioning samvidaanathinte oro thavanayum paraajayappedaanulla sanjitha saadhyatha (allengil anupatham) chuvadeyulla graph kaanikkunnu. karupp niratthilulla staarstepp line paraajayangalude sanjitha anupatham kaanikkunnu. oro ghattathinum graafinte chuvade oru neela tick undu, athu oru nireekshicha parajaya samayathe soochippikkunnu. minusamarnna chuvanna rekha nireekshicha daattayil gadippicha exponential vakrathe prathinidheekarikkunnu.
oro samaya pooyintum vareyulla paraajayangalude sanjitha saadhyathayude graphine sanjitha vitharana pravartthanam allengil sii. dii. eph ennu vilikkunnu. athijeevana vishakalanathil, sanjitha vitharana pravartthanam athijeevana samayam oru nirddishta samayathekkaal kuravo thulyamo aayirikkanulla saadhyatha nalkunnu.
athijeevana samayam ayirikkatte, athu eathenkilum positteev samkhyayaanu. oru prathyeka samayam nirnnayikkunnath cheria aksharamaaya tii aanu. t" yude sanjitha vitharana pravarthanamaanu function
ivide valathuvashath kramarahithamaya variable "t" "t" nekkaal kuravo thulyamo aayirikkanulla saadhyathaye prathinidheekarikkunnu. samayathinu eathenkilum positteev moolyam edukkaan kazhiyumenkil, cumulative distribution function f (t) probability density function f (t)-nte avibhaajya gadakamaanu.
eyar contitioning udaaharanathinu, daattaykk anuyojyamaaya exponential karvu upayogichu kanakkaakkunnathupole, paraajayappedaanulla samayam 100 manikkooril kuravo thulyamo aakanulla saadhyatha 0.81 aanennu chuvadeyulla sii. dii. ephinte graph vyakthamaakkunnu.
parajaya samayam 100 manikkooril kuravo thulyamo aanenna saadhyatha graafukal varaykkunnathinulla oru badal, parajaya samayam 100 manikkooril kooduthalo aanenna saadhyatha graafukal varaykkuka ennathaanu. parajaya samayam 100 manikkooril kooduthalaayirikkaanulla saadhyatha 1 mainus parajaya samayam 100 manikkooril kuravo thulyamo aayirikkanulla saadhyatha aayirikkanam, kaaranam motham saadhyatha 1 aayirikkanam.
ithu nalkunnu
p (parajaya samayam> 100 manikkoor) = 1-p (parajaya samayam <100 manikkoor) = 1-0.81 = 0.19.
eee bandham ellah parajaya samayangalilekkum saamaanyavalkkarikkunnu
p (t> t) = 1-p (t <t) = 1-cumulative distribution function.
eee bandham chuvadeyulla graafukalil kaanichirikkunnu. idathuvashathulla graph cumulative distribution functionaanu, athu p (t <t) aanu. valathuvashathulla graph p (t> t) = 1-p (t <t) aanu. valathuvashathulla graph athijeevana pravarthanamaanu, s (t). s (t) = 1-cdf aanu survival functionte mattoru peru complimentary cumulative distribution function ennathinulla kaaranam.
paaraameettar athijeevana pravartthanangal.
airconditioner udaaharanam polulla chila sandarbhangalil, athijeevana samayathinte vitharanam exponential distribution polulla oru function vazhi nannayi kanakkakkaam. exponential, weibul, gaama, normal, logue-normal, logue-logistic ennivayulppede niravadhi vitharanangal athijeevana vishakalanathil saadhaaranayaayi upayogikkunnu. eee vitharanangal nirvachikkunnath paaraamettarukal anusarichaanu. udaaharanathinu, saadhaarana (gausiyan) vitharanam nirvachikkunnath sharashari, staanderd deviation ennee rund paaraamettarukalaanu. paaraamettarukal nirvachichirikkunna athijeevana pravartthanangal paaraameettar aanennu parayappedunnu.
mukalil kaanichirikkunna naalu survival function graafukalil, survival functionte aakruthi nirvachikkunnath oru prathyeka probability distributionaanu survival function 1 oru exponential distribution nirvachikkunnu, 2 oru weibul distribution nirvachikkunnu, 3 oru logue-logistic distribution nirvachikkunnu, 4 mattoru weibul distribution nirvachikkunnu.
exponential athijeevana pravartthanam.
exponential athijeevana vitharanathinu, vyakthiyudeyo upakaranathinteyo praayam pariganikkathe, oro samaya edavelayilum paraajayappedaanulla saadhyatha thulyamaanu. eee vastutha exponential athijeevana vitharanathinte "oormmayillaatha" gunathilekku nayikkunnu oru vishayathinte praayam adutha edavelayil paraajayappedaanulla saadhyathaye baadikkilla. bhagangal paraajayappedumbol maattisthaapikkunna oru sisttathinte jeevithakaalathe oru nalla maathrkayaayirikkaam exponential. churungiya samayathinullil jeevajaalangalude athijeevanathe maathrkayaakkunnathinum ithu upayogapradamaakum. oru jeevajaalathinte samboornna aayussinte nalla maathrkayaayirikkaan ithu saadhyathayilla. ephran aandu haashti 
(pii. 134) shradhikkuka, "manushyante jeevithakalam ghaathaamkamaayirunnenkil praayamaayavaro cheruppakkaaro undakumaayirunnilla, bhaagyamullavaro nirbhaagyamullavaro mathramaayirunnu".
weibul athijeevana pravartthanam.
apakadanirakku sthiramaanennathaanu exponential survival functionte oru pradhana anumaanam. mukalil nalkia oru udaaharanathil, oro varshavum marikkunna purushanmaarude anupatham 10 shathamaanamaayirunnu, athaayath apakada nirakk sthiramaayirunnu. nirantharamaaya apakadasaadhyathayude anumaanam uchithamallayirikkaam. udaaharanathinu, mikka jeevajaalangalilum, maranasadhyatha madhyavayassinekkaal vaardhakyathil kooduthalaanu-athaayath, apakada nirakk kaalakramena vardhikkunnu. stanarbudam polulla chila rogangalil, 5 varshathinu sesham aavarthanathinulla saadhyatha kuravaanu-athaayath, apakada nirakk kaalakramena kurayunnu. apakada nirakkukal sthiramaayi vardhippikkunnathino kuraykkunnathino anuvadikkunnathinu weibul vitharanam exponential vitharanam vipuleekarikkunnu.
mattu paaraameettar athijeevana pravartthanangal.
saadhaarana, lognormal, logue-logistic, gaama ennivayulppede oru prathyeka daatta settinu mikacha phitt nalkunna niravadhi parametric survival functionukal undu. oru prathyeka aaplikkeshanaayi paaraameettar vitharanathinte thiranjeduppu graaphikkal reethikal upayogicho fittinte aupachaarika parisodhanakal upayogicho nadatthaam.
eee vitharanangalum parishodhanakalum athijeevana vishakalanathekurichulla paatapusthakangalil vivarichittundu. niyamaviruddham 
parametric modalukalude vipulamaaya kavarej undu.
nireekshana kaalayalavinu purathulla athijeevana pravartthanatthe kanakkakkaan avaa praapthamaakkunnathinaal nirmmaana aaplikkeshanukalil parametric athijeevana pravartthanangal saadhaaranayaayi upayogikkunnu. ennirunnaalum, parametric functionukalude uchithamaaya upayogathinu daatta thiranjeduttha vitharanathaal nannayi maathrkayaakkendathundu. uchithamaaya vitharanam labhyamallengilo oru klinikkal trialinteo pareekshanatthinteyo munbu vyakthamakkaan kazhiyunnillengil, noonn-parametric survival functionukal upayogapradamaaya oru badal vaagdaanam cheiyunnu.
noonn-parametric athijeevana pravartthanangal.
athijeevanathinte oru parametric model saadhyamo abhikaamyamo aayirikkilla. eee saahacharyangalil, athijeevana pravartthanatthe maathrkayaakkunnathinulla ettavum saadhaaranamaaya reethi noonn-parametric cuplan-mayer esttimettaanu.
swathukkal.
angane aaa soothravaakyam _ 13
oru kramarahithamaya variable formula _ 15-nte prathekshikkunna moolyam ingane nirvachikkappedunnu
ivide formula _ 9 probability density functionaanu. relation formula _ 18 upayogichu, prathekshikkunna moolya formula parishkkarikkam
bhagangal upayogichu samyojanam upayogikkunnathiloode ithu kooduthal lalithamakkaam
nirvachanam anusarichu, formula _ 21, athaayath athirthi padangal poojyathinu thulyamaanu. athinaal, prathekshikkunna moolyam athijeevana pravartthanatthinte avibhaajyaghadakamaanennu namukk nigamanam cheyyaam

