Some standards that may suite some Requirements for Third Party Inspection  this list is by no means complete

Pressure equipment related
AS/NZS 1200  Pressure Equipment
AS 1210  Pressure Vessels
AS 1228  Pressure Equipment  Boilers
AS 4041  Pressure Piping
AS 2971  Serially produced Pressure vessels
AS 3509  LP Gas Fuel Vessels for automotive use
AS 4037  Pressure Equipment Examination & Testing
AS 4458  Pressure Equipment - Manufacture
AS 3920.1  Assurance of Product quality

Pressure Equipment Manufacture
AS 4343  Pressure Equipment  Hazard Levels
AS 3992  Pressure Equipment  Welding & Brazing qualification
AS/NZS 3788  Pressure Equipment  In-service Inspection

Pressure equipment supporting
AS 4942 - Glossary of terms - Pressure equipment
AS 2812  Glossary of terms - Welding, brazing  and cutting of metals
AS 1796  Certification of Welders and Welding Supervisors
AS/NZS ISO 3834  Quality requirements for fusion welding of metallic materials (series)
AS/NZS ISO 9001  Quality Management Systems
AS/NZS ISO/IEC 17020  General requirements for the operation of various types of bodies performing inspection
AS ISO/IEC 17025 - General requirements for the competence of testing and calibration laboratories
Various material Standards e.g. AS 1548, AS 3597
Various Testing Standards e.g. AS 2205 seriesOther fabrication related
Various global Pressure vessel related e.g. ASME
AS 2885  Gas & Petroleum Pipeline

Various storage tanks related Standards e.g API
AS/NZS 1554 series  Structural steel
AS/NZS 1665  Welding of Aluminium Structures
AS 4100  Steel Structures
AS/NZS 3679.2  Welded Structures
Other Structural fabrication Standards e.g. AWS