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In this article study summery of reversed hazard rate and mixture distributons then introduce reversed hazard rate mixture and waiting times of failure also introduce mixture reversed hazard rate additive modele and multiplicative and introduce behavioure mixture of k increasing reversed hazard rate (IRFR) Increasing(IRFR).

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Abstract One of the main goal in the mixture distributions is to determine the number of components. There are different methods for determination the number of components, for example, Greedy-EM algorithm which is based on adding a new component to the model until satisfied the best number of components. The second method is based on maximum entropy and finally the third method is based on nonparametric. In this manuscript it is considered the mixture distributions with Skew-t-Normal components.

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Profile monitoring is usually faced by control charts and mostly the response variable is observable in those problems‎. ‎We confront here with a similar problem where the values of the reward function are observed instead of the response variable vector and we use the dart model to make it easier to understand‎. ‎Supposing there exists at most one change-point‎, ‎a sequence of independent points resulted by darts throws is observed and the estimation of parameters and the change-point (if there exists any) are presented using the‎ ‎frequentist and Bayesian approaches‎. ‎In both the approaches‎, ‎two possible precision scalar and matrix are studied separately‎. ‎The results are examined through a simulation study and the methods applied on a real data‎.