I would expect that the Management Team would participate in this activity. It is normal to have regular Management meetings to discuss performance which should include Key Performance Indicators (KPIs) related to the results of verification activities such as the results of audits and product non-conformances.
There is some guidance in ISO 22004: Food safety management systems — Guidance on the application of ISO 22000:2005, here are a couple of extracts:
A schedule of verification activities is developed as part of the food safety management system (planned according to 7.8 and evaluated according to 8.4.2 of ISO 22000:2005). This schedule should include the procedures or methods to be utilized, the frequency and the person(s) responsible for performing the activity. Examples of verification activities that should be considered as part of the system include
— reviewing monitoring records,
— reviewing deviations and their resolution or corrective action, including the handling of affected product,
— calibrating thermometers or other critical measuring equipment,
— visually inspecting operations to observe if control measures are under control,
— analytically testing or auditing monitoring procedures,
— randomly collecting and analysing samples of in-process or end product,
— sampling for environmental and other concerns, and
— reviewing consumer or customer complaints to determine whether they relate to the performance of the control measures or reveal the existence of unidentified and/or need for additional control measures.
The periodic verification activities involve the overall assessment of the system (see 8.4.3 of ISO 22000:2005). This is usually performed during a management or verification team meeting, and all the above evidence over a period of time is reviewed to ascertain if the system is functioning as planned and if updating or improvement is necessary. Notes of the meeting should be kept and should include any decisions made regarding the system. At a minimum, verification of the entire system in this manner should take place on an annual basis.