Based on the elements of your question, I would say that your problem could be readily shaped into a Black Belt project. I would assume that a Pareto analysis has already been conducted.
As a more advanced diagnostic, you should consider employing a multi-vari chart. Although simple in nature, such a chart has considerable power. It can help you isolate the major (dominant) family of variation. For example, does most of the variation in downtime occur within-machine, machine-to-machine, within-operator, operator-to-operator, within shift, shift-to-shift, within-location, or location-to-location?
For a good overview of this particular analytical method, reference Juran’s Handbook of Quality. In closing, it is most likely a lack of knowledge that is holding you hostage, not the machines.