Actually they do. They might not use common logic, but rather their own skewed one. Many such murders committed by schizophrenics are actually planned - and mostly their families or family members are the targets.
For now this has to stand as my claim (I am working), but when I have time, I will find material on this.
Alias,,you're right in what you say about them targeting families..Schizophrenics will only attack if ( 1),they haven't taken their prescribed medication,,or ( 2 ),,if they've taken any form of substance,if taken alongside their medication, will immediately cancel out the effect of the medication. So however long Sheila had relied on substance abuse,,she may as well have not been taking medication at all.
The Haloperidol,an old medication by todays standards of treatment,,would give off side effects worse than her illness itself,,as without her other medication to stop these side effects,,,she was a bigger danger to others as one would realise.