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The  main  assumptions  in  liner  mixed  model  are normality  and  independency  of  random  effect component.   Unfortunately,   these   two  assumptions   might   be  unrealistic   in  some   situations. Therefore, in this paper, we will discuss about the analysis of Bayesian analysis of non-normal and non-independent mixed model using skew-normal/independent distributions, and finally, this methodology is illustrated through an application  to a triglyceride data from Isfahan’s Mobarakeh Steel Company Cohort Study.