Summary: Statistical inference is one of the most useful statistical tools that are widely adopted in scientific research and practical application fields. This article deals with statistical inference of parameters subject to order restrictions. This is a very common situation encountered in areas such as health sciences, drug development and industrial quality control. An new methodology is provided for statistical inference of location parameters when the parameters have unbounded support. The application is suitable particularly for problems in Health Sciences is to the fact that the study subjects or objects are usually randomly grouped into treatment groups, or produce a typical covariance structure in the experiment. The article also provides a new alternative to and discussion on the general cases for various underlying distributions, the type of parameters and the pattern of order restrictions.