NEW LIFETIME STATISTICAL DISTRIBUTIONS FOR SYSTEMS CONNECTED IN SERIES

Abstract

In probability distribution theory, substantial efforts have been made in developing probability distributions for modelling lifetime from systems connected in series. However, there are several significant situations where empirical data set from such systems do not follow any of these existing distributions. Hence, it is essential to generate more flexible distributions for modelling lifetime data from series connected components. In this study, the Nadarajah Haghighi generalised power Weibull (NHGPW) distribution and the power series generalised power Weibull (PGPW) class of distributions were developed based on the concept of compounding. From the results, the NHGPW distribution hazard function can be constant, monotonic, bathtub, unimodal, modified bathtub or modified unimodal.Its probability density function can also be bathtub, monotonic, positively skewed, unimodal, modified bathtub and modified unimodal. Monte Carlo simulations performed to assess the performance of the estimators of the NHGPW distribution showed that, its parameter estimates are consistent since their mean square error and average bias approaches zero as the sample size increase. Also, the NHGPW distribution provides a better fit to two lifetime data set than the other competitive distributions for system connected in series. The PGPW class of distribution have four sub-family of distribution; the generalised power geometric (GPG) family, generalised power poison (GPP) family, generalised power binomial (GPB) family and the generalised power logarithmic (GPL) family of distributions. The hazard rate and PDF plots of the four sub-family of distributions showed that, their hazard and PDF can be monotonic, bathtub, unimodal, modified bathtub or modified unimodal. Monte Carlo simulation performed on these sub-family of distribution showed that, their MLE estimators are consistent. The GPG family distributions provides a better fit failure data from air conditioning system of an aircraft whiles the GPP family also provides a better fit among the four fitted distributions to service times of aircraft data. It is therefore recommended that, these new distributions be considered in modelling lifetime data from series connected systems.