Regression and degradation models in reliability theory and survival analysis ; Regresiniai ir degradaciniai modeliai patikimumo teorijoje ir išgyvenamumo analizėje

VILNIUS UNIVERSITYInga Masiulaityte˙REGRESSION AND DEGRADATION MODELS IN RELIABILITYTHEORY AND SURVIVAL ANALYSISDoctoral dissertationPhysical sciences, mathematics (01P)Vilnius, 2010The scientific work was carried out in 2005–2009 at Vilnius University.Scientific supervisor:Prof. Dr. Vilijandas Bagdonaviˇcius (Vilnius University, Physical sciences, Mathe-matics - 01P)NotationF(t) Cumulative distribution function;f(t) Probability density function;S(t) Survival function;n Sample size;T Failure timeix Explanatory variable;λ(t) Hazard rate function;Λ(t) Cumulative hazard rate functionT ,...,T Failuretimesofn unitstestedin”hot”11 1n 11conditions;T ,...,T Failure times of n units tested in21 2n 22”warm” conditions;μ Mean failure time;2σ Variance;r Scale parameter;H Hypothesis;0α,β,ν,μ Parameters;K (t) Cumulative distribution function of re-jdundant system;k (t) Probability density function of redun-jdant system;(K (t),K (t)) Confidence interval;jjI Fisher information matrix;−1I Inverse of the Fisher information ma-trix;L(r,θ) Likelihood function;l(r,θ) Loglikelihood function;Z(t) Degradation process;z Critical level;0(0)T Moment of the non-traumatic failure;(k)Tt of the traumatic failure of thekth mode;(0)S Survival function of the non-traumaticfailure;3(k)S Survival function of the traumatic fail-ure of the kth mode;(k)˜λ (t|Z) Conditional failure rate;P Probability;C Censoring time of the ith unit .