As same as Buddha tried to find reason for sadness before cure, doctors try to find reason for illness before cure, Engineers do test and evaluate before thinking a cure for those mechanical objects. It is one of the most important parts of engineering which is closely linked to aerospace engineering, civil engineering, electrical engineering, material science and engineering, mechanical engineering, nuclear engineering, petroleum engineering, physics etc… It’s often used in both constructional and service sides.
The term "technical diagnostics", which I think is the most suitable, is very often used through out Russia. Although I haven't seen it in the other countries. you may correct me if it's used in your part of the world :)
Technical diagnostic is a way to determine the condition of the physical object. Engineers test and evaluate internal or external defects of a machine part or the whole machine, find reasons for defects, prognosis of a possible object failure in the future, and finally the genesis of the object during a catastrophic situation in order to find reasons for this failure.
As we can see, this is one of the important sciences with a wide range of use. Main purpose technical diagnostics is to provide reliability, economical efficiency and most importantly the safety of the passengers or the people who uses that construction. There are plenty of methods which engineers use in order to evaluate the health of technical objects. They can divide in to two main sections.
1) Testing/ Evaluation Methods
2) Functional Methods
Testing/ Evaluation methods are well known as Non Destructive Testing or Evaluation (NDT or NDE). There are plenty of methods such as, Visual inspection, Liquid penetrent test, Magnetic particles test, Eddy current, Ultrasonic, Radiography etc...
The functional methods are based on the statistical data. for example,long term increment of the temperature can say about a failure of the cooling system. Vibration diagnostics is also a very important part of the functional methods.
as one can see, it's a widely used science which has a greater influence for safety. Deeper details about those methods will appear in the near future :)