The weighted distributions take into account the technique of ascertainment by adjusting the probabilities of actual happening of events to arrive at the specification of the probabilities of those events as observed and recorded. Failure to make such adjustments can go ahead into erroneous conclusions. The weighted distributions provide a comprehensive understanding by adding flexibility in the existing standard distributions. In this Thesis, we considered the weighted Lindley distribution (WLD) which belongs to the justify; LINE-HEIGHT: normal; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr; mso-layout-grid-align: none" The following, the different reliability characteristics including reliability function, hazard function, and mean residual life function are also analysed. The following, we present the structural shape properties of the density and of the hazard rate function of the WLD, The probability density function of the weighted Lindley distribution is decreasing or unimodal, or decreasing-increasing-decreasing, model adds an extra shape which can be useful for modeling bimodal data. Also, The hazard rate function of the WLD is bathtub shaped or increasing, The bathtub feature of the hazard rate function of WLD is particularly useful in modeling biological data from mortality studies. For statistical analysis, The maximum likelihood estimates of the unknown parameters cannot be obtained in the closed form, So the view of Bayesian estimation parameters WLD and reliability characteristics consider of the distribution. Different types of loss functions are considered; The bayes estimators and their respective posterior risks for the parameters of the WLD are computed and compared for different loss functions and prior distributions. Monte Carlo method has been used to compute the approximate Bayes estimates. A loss function or prior having the minimum PR is considered as the best one. The MCMC was carried out for selected values of .We consider different parameters value set under uniform prior , Jeffreys prior, gamma prior, conjugate prior . The following, we are reporting results the BEs and the PRs for selected parameters value sets under different loss functions. The general conclusion drawn from simulation study is as follows: As we increase sample size, the PR goes down and also with the increase of the parameters values the PR also increases. The choice of loss function as concerned, one can easily observe that the PLF and the SELF loss function have smaller PR as compared to the other loss functions. But, if one makes comparision between the asymmetric loss function, the PLF and the SLLF performance approximately same. The JP has smaller PR than the UP (in case of noninformative priors). The conjugate prior (CP) and the gamma prior (GP) have approximately (in some cases, it differs) same PR. Also, in the study of technical system in reliability engineering , coherent systems play an important role. The following, we considered the weighted Lindley distribution first time as a lifetime distribution of components in a coherent system, with independent and identically distributed, which belongs to the ltr"