‎In this article‎, ‎the method of determining the optimal sample size is based on Linex asymmetric loss function and has been expressed through Bayesian method for normal‎, ‎Poisson and exponential distributions‎. ‎The desirable sample size has been calculated through numerical method‎. ‎In numerical method‎, ‎the average posterior risk is calculated and then it is added to the Lindley linear cost function to achieve the average of the total cost‎. ‎Then‎, ‎the diagram of sample size is drawn in comparison to the average of total cost and eventually‎, ‎the optimal sample size that minimizes the cost has been achieved.

‎In this paper‎, ‎a new distribution of the three-parameter lifetime model called the Marshall-Olkin Gompertz is proposed on the basis of the Gompertz distribution‎. ‎It is a generalization of the Gompertz distribution having decreasing failure rate and can also be increasing and bathtub-shaped depending on its parameters‎. ‎The probability density function‎, ‎cumulative distribution function‎, ‎hazard rate function and some mathematical properties of this model such as‎, ‎central moments‎, ‎moments of order statistics‎, ‎Renyi and Shannon entropies and quantile function are derived‎. ‎In addition‎, ‎the maximum likelihood of its parameters method is estimated and this new distribution compared with some Gompertz distribution generalizations by means of a set of real data‎.