**Abstract**

In this chapter, we study well-known distribution-free Shewhart-type monitoring schemes based on order statistics. In order to empower the in- and out-ofcontrol performance of the control charts being under consideration, several runstype rules are enhanced. The simulation-based experimentation carried out reveals that the proposed schemes achieve remarkable efficiency for detecting possible shifts in the distribution of the underlying process.

**Keywords:** distribution-free monitoring schemes, average run length, false alarm rate, Lehmann alternatives, statistical process control, order statistics
