Abstract: Based on grey system theory, a novel method of hypothesis testing is proposed to solve some problems of classical statistics. This method is called grey hypothesis testing. Started with generating the order and normative data ranks, the grey rejected region of hypothesis testing, characterized by defining the spe-cial conceptions, for example grey confidence level, grey difference, and attribute weighting mapping, etc, is suggested using grey relational element. Perfect systems such as normal distribution, uniform distribution, Rayleigh distribution and periodic change system, etc, and practical engineering systems such as system about vibration and noise of rolling bearings are investigated. The method proposed permits probability distribution unknown and sample data small, without any especial requirement for attribute of systems and independence between systems. Some good efficacy by dint of the grey hypothesis testing method is validated, and the approximate 95% grey confidence level is yielded.

Key words: Grey system theory, Mechanical engineering, Statistical tests, System analysis