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Observations strongly deviating from the bulk of data, usually labeled as outliers are troublesome and may cause misleading results. Therefore, the solitariness of outliers is important for quality assurance. In the given study, systematic approaches have been derived from general principles in this regard. The first idea of the present study uses arrangement of sample data in ascending order for particular cases of Uniform and Exponential distributions and tests for outlier have been developed. Second idea presented Additive white noise in time discrete differential equation as a special case of ARMA (p, q) model. Working with Poisson Process, the special form of variance-covariance matrix has enabled to develop a new procedure for the detection of outlier. The likelihood estimation originally proposed by Fox (1972) has been used with the assumption of known autoregressive parameters. The distribution of the test has been evaluated through characteristic function and discrete convolution formula. A minimum variance estimate in the sense of least square has also been established through Kalman Filtering recursive method.