The principle of maximum entropy is a well-known approach to produce a model for data-generating distributions. In this approach, if partial knowledge about the distribution is available in terms of a set of information constraints, then the model that maximizes entropy under these constraints is used for the inference. In this paper, we propose a new three-parameter lifetime distribution using the maximum entropy principle under the constraints on the mean and a general index. We then present some statistical properties of the new distribution, including hazard rate function, quantile function, moments, characterization, and stochastic ordering. We use the maximum likelihood estimation technique to estimate the model parameters. A Monte Carlo study is carried out to evaluate the performance of the estimation method. In order to illustrate the usefulness of the proposed model, we fit the model to three real data sets and compare its relative performance with respect to the beta generalized Weibull family.

An upper bound for the hazard rate function of a convolution of not necessarily independent random lifetimes is provided, which generalizes a recent result established for independent random lifetimes. Similar results are considered for the reversed hazard rate function. Applications to parametric and semiparametric models are also given.

We study the allocation strategies for redundant components in the load-sharing series/parallel systems. We show that under the specified assumptions, the allocation of a redundant component to the stochastically weakest (strongest) component of a series (parallel) system is the best strategy to achieve its maximal reliability. The results have been studied under cumulative exposure model and for a general scenario as well. They have a clear intuitive meaning; however, the corresponding additional assumptions are not obvious, which can be seen from the proofs of our theorems.

We use the properties of the Matuszewska indices to show asymptotic inequalities for hazard rates. We discuss the relation between membership in the classes of dominatedly or extended rapidly varying tail distributions and corresponding hazard rate conditions. Convolution closure is established for the class of distributions with extended rapidly varying tails.

In this paper different failure mechanisms which yield cumulative damage are investigated through two types of hazard rate functions. They have been studied during the past two decades. Type A was developed early by assuming the hazard rate as a function of reliability. There are two kinds of trend, one follows the negative logistic decay model, the other the negative Gompertz decay. Some modifications are suggested according to the failure tendency and convenience of fittings. Type B is developed recently by assuming the hazard rate as a function of the expected operation time, T, which is defined as the integration of reliability over the time, normalized by the mean-time-between-failure. In both types the proposed hazard rates grow with the time monotonically. Typical examples are taken to examine these models, meanwhile the comparisons with the Weibull-typed distribution are also made. The results show that the most of proposed relations are successful in the expression of cumulative damage phenomenon, especially the Type B is a better choice even compared with the Weibull-typed description in some respects. The advantages of the models are discussed based on the physical meanings involved in the parameters.

In this article, we consider the limit behavior of the hazard rate function of mixture distributions, assuming knowledge of the behavior of each individual distribution. We show that the asymptotic baseline function of the hazard rate function is preserved under mixture.