I did some additional testing and found the following:
1. when I use the following settings: PHP version 5.6.31, Joomla 3.8.5 and Fabrik 3.7.5 everything works fine. This is the current setting of my production site.
2. when I upgrade my test environment from there to: Fabrik 3.8.1 the site still works except for Fabrik.
3. when I then disable Fabrik and step by step enable all Fabrik components, the problem occurs when enabling 'System - Fabrik Scheduled Tasks' or 'Content - Fabrik' all other components do not cause the problem.
4. when I use PHP version 7.0.n the complete testsite goes down (=blanc pages with only the correct URL in the header, no warning or anything).
Please advise on what I can do now
thanks, Henk