Most of the modern technological systems are deployed with high redundancy but still they fail mainly on account of common cause failures (CCF). Various models such as Beta Factor, Multiple Greek Letter, Binomial Failure Rate and Alpha Factor exists for estimation of risk from common cause failures. Amongst all, alpha factor model is considered most suitable for high redundant systems as it arrives at common cause failure probabilities from a set of ratios of failures and the total component failure probability QT. In the present study, alpha factor model is applied for the assessment of CCF of safety systems deployed at two nuclear power plants. A method to overcome the difficulties in estimation of the coefficients viz., alpha factors in the model, importance of deriving plant specific alpha factors and sensitivity of common cause contribution to the total system failure probability with respect to hazard imposed by various CCF events is highlighted. An approach described in NUREG/CR-5500 is extended in this study to provide more explicit guidance for a statistical approach to derive plant specific coefficients for CCF analysis especially for high redundant systems. The procedure is expected to aid regulators for independent safety assessment.