DISTRIBUSI DERET PANGKAT WEIBULL TERMODIFIKASI DAN TERGENERALISASI UNTUK PERMODELAN KETAHANAN HIDUP; GENERALIZED MODIFIED WEIBULL POWER SERIES DISTRIBUTION FOR LIFETIME MODELLING

Felita, Nanda Mega, Herni Utami

2016 | Skripsi | FMIPA

Lifetime modelling is importance factor in survival analysis. One of many distributions that used for lifetime modelling with parametric fit is Weibull distribution. The weibull distribution is a very popular distribution for modelling lifetime data with monotone hazard rate. However, the Weibull distribution does not provide a reasonable parametric fit for modelling phenomenon with nonmonotone hazard rate such as the bathtub-shape and unimodal which are common in reliability and biological studies. A new distribution with increasing, decreasing, bathtub-shape and unimodal hazard rate forms called as the generalized modified Weibull power series (GMWPS) distribution is created to solve the problem. The new distribution is constructed by compounding general modified Weibull (GMW) and power series distributions. The new distribution contains, as special sub model such as generalized modified Weibull Poisson (GWMP), generalized modified Weibull logarithmic (GWML), generalized modified Weibull geometric (GMWG), and generalized modified Weibull binomial (GMWB). The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates in reliability.

Kata Kunci : Weibull distribution, generalized modified Weibull distribution, power series distribution; lifetime modelling; goodness of fit test; Lambert W function; BFGS