Abstract
The lognormal distribution is more extensively used in the domain of reliability analysis for modeling the life-failure patterns of numerous devices. In this paper, a generic form of the lognormal distribution is presented that can be applied to model many engineering problems involving indeterminacies in reliability studies. The suggested distribution is especially effective for modeling data that are roughly symmetric or skewed to the right. In this paper, the key mathematical properties of the proposed neutrosophic lognormal distribution (NLD) have been derived. Throughout the study, detailed examples from life-test data are used to confirm the mathematical development of the proposed neutrosophic model. The core ideas of the reliability terms, including the neutrosophic mean time failure, neutrosophic hazard rate, neutrosophic cumulative failure rate, and neutrosophic reliability function, are addressed with examples. In addition, the estimation of two typical parameters of the NLD by mean of maximum likelihood (ML) approach under the neutrosophic environment is described. A simulation experiment is run to determine the performance of the estimated parameters. Simulated findings suggest that ML estimators effectively estimate the unknown parameters with a large sample size. Finally, a real dataset on ball bearings failure times has been considered an application of the proposed model.