A New Exponential Distribution to Model Concrete Compressive Strength Data

Abstract

Concrete mixtures can be developed to deliver a broad spectrum of mechanical and durability properties to satisfy the configuration conditions of construction. One technique for evaluating the compressive strength of concrete is to suppose that it pursues a probabilistic model from which it is reliability estimated. In this paper, a new technique to generate probability distributions is considered and a new three-parameter exponential distribution as a new member of the new family is presented in detail. The proposed distribution is able to model the compressive strength of high-performance concrete rather than some other competitive models. The new distribution delivers decreasing, increasing, upside-down bathtub and bathtub-shaped hazard rates. The maximum likelihood estimation approach is used to estimate model parameters as well as the reliability function. The approximate confidence intervals of these quantities are also obtained. To assess the performance of the point and interval estimations, a simulation study was conducted. We demonstrate the performance of the offered new distribution by investigating one high-performance concrete compressive strength dataset. The numerical outcomes showed that the maximum likelihood method provides consistent and asymptotically unbiased estimators. The estimates of the unknown parameters as well as the reliability function perform well as sample size increases in terms of minimum mean square error. The confidence interval of the reliability function has an appropriate length utilizing the delta method. Moreover, the real data analysis indicated that the new distribution is more suitable when compared to some well-known and some recently proposed distributions to evaluate the reliability of concrete mixtures.