Can someone help me how to have back up team member when the employee will be illness or have family issue?

Following a buddy system where the knowledge can be mapped and there is no dependency of individual to complete a certain task – be it Project or Operational work.
Also, internal training program defined for team based on the area of interest and skill sets.

Categorizing the skills set of team members into Low – Intermediate – Expert level within different job profile / tasks and mapping them together will help in planning the buddy system and training program.

I too faced this problem while managing an Operations team where either the individuals are sick, family commitments or going for maternity break, The above method has helped in smooth running of the operations and also increased team morale in adding up multiple skills sets into their portfolio.

In addition to centralized knowledge, and consistent taxonomy suggested by Andrew.

Make it a requirement that people are pair, and require to be able to know enough to take over immediately for short term and could take over for longer term. That need part of their evaluation criteria, so a few times a month they meet and exchange on progress.