when to reject ready mixed concrete on-site according to its strengths?

Talking of RMC than the designation Mix is certified on the supply challan. Further in case of doubt you can seek copy of the design mix formula followed. As regards slump test it is simply done to check the workability so as to ensure that delay in supply has not stiffened it which can create problems of flow into moulds. Strength is known after 7/8 days of casting which you can randomly do @45 cum of a lot.

Tests of RMC on site:

Introduction: 

• Tests of ready mix concrete onsite is really very important parameter to know the good type of concrete.
• RMC is tested on-site as per standards decided by ASTM international.
• The various test is conducted on-site to check whether the given RMC is in good quality or not.

Following are some important tests conducted on RMC on site:

• Temperature (ASTM C 1064)
• Slump (ASTM C 143/ C143M)
• Air content(ASTM 173, ASTM C 231)
• Density( ASTM 138, ASTM 567)

Laboratory test: 

• Flexural strength( ASTM C 78 or ASTM 293)
• Compressive strength (ACI 318-14, CSA A23, 3-14)

Please have a look at the following article regarding quality control of ready mix in the field.

https://theconstructor.org/practical-guide/inspection-testing-ready-mix-concrete/25716/