Being a customer support engineer, when there is a place of debate between product support head and customer and you already knew there is a fault of your organization for delaying the service/parts to customer.how to cope up with the situation?

first read the situation. than talk to customer and offer discount. say sorry  also and promise him to improvement. invitation  for next  visit

Well the best way , you need to be very polite and calm to the customers because we know that customers comes first and customer pay our wages , you need to tackle the situation either by offering something complementary or any thing else you can make them happy.

Firstly i would like to read the customers mind how he is reacting, after i will take any action.

If he is being hot or aggressive so i will explain him the details of our product that actually its our fault we will rectify it soon so you have to keep patience, some time its happen with everyone.