A simple adjustment to parametric failure-time distributions, which allows for much greater flexibility in the shape of the hazard-rate function, is considered. Closed-form expressions for the distributions of the power-law adjusted Weibull, gamma, log-gamma, generalized gamma, lognormal and Pareto distributions are given. Most of these allow for bathtub shaped and other multi-modal forms of th...

We introduce in this paper a new four-parameter generalized version of the linear failure rate distribution which is called Beta-linear failure rate distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing and bathtub-shaped failure rate function depending on its parameter...

The maximum likelihood equations of IDB distribution can’t be solved analytically. Solutions of the MLE equations can be obtained numerically. But the problem is to detect the initial value of the parameters to solve the nonlinear MLE equations. A technique is developed for formulating the initial value of the parameter to solve the MLE equations of IDB distribution. Considering all the facts, ...

The two-parameter linear failure rate distribution has been used quite successfully to analyze lifetime data. Recently, a new three-parameter distribution, known as the generalized linear failure rate distribution, has been introduced by exponentiating the linear failure rate distribution. The generalized linear failure rate distribution is a very flexible lifetime distribution, and the probabi...

Starting with the meaning of the word quality, diverse concepts connoted by the term are examined. Instead of a bathtub curve, the desirable shape of a failure rate covering the entire life of a good product, which might be called hockey-stick line, is introduced. From the hockey-stick line and the definition of reliability, two measurements are extracted. The terms r-reliability (failure rate)...

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-m...