Step 1: Concept $S_{N}1$ reactivity depends primarily on the stability of the carbocation intermediate formed during the rate-determining step.
Step 2: Meaning Carbocation stability generally follows the order: tertiary $>$ secondary $>$ primary.
Step 3: Analysis Reaction conditions that favor the formation of more substituted or resonance-stabilized carbocations will increase reactivity in $S_{N}1$ processes.
Step 4: Conclusion Based on the comparative structural analysis of substrates X, Y, and Z, the reactivity order is $Z > Y > X$.