It is permitted to set an alarm system on a private residence which will operate on Shabbat, especially when there is a real possibility of life threatening situations.
The alarm system must be activated before Shabbat begins. If possible, one should by-pass one of the doors to be used by the family (some people would recommend to by-pass the front door, which ironically is less used by burglars to break in) and leave all other doors and windows 'activated'. If this cannot be done, please consult a rabbi how to set the alarm system.
When the alarm is activated, there are motion sensors, typically located close to the ceiling, which some people cover or deactivate before Shabbat begins. In any case, it is not forbidden to walk though those sensors, although small led lights are activated by the motion of family members inside the house (pesik resheh derabanan dela nicha leh).
If the alarm accidentally goes off on Shabbat, and won't stop by itself, one should try to have a gentile to turn it off. If that is not possible, it would be permitted for a Jew to shut off the alarm, because 1. the noise is disturbing the entire neighborhood, and it could affect sick people, etc. and 2. preventing or stoping the flow of electrical current is not Biblical -deoraiita- prohibition, (adapted from Practical laws of Shabbat, I, 335).
There are many different alarm and surveillance systems, and I can't possibly cover all details. Here, I just referred to a few principles which I believe apply to most systems. Please, consult a knowledgeable rabbi for more details.
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Shabbat ends in NYC: 5:23 PM
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Rabbi Yosef Bitton. YMJC | 130 Steamboat Rd. | Great Neck | NY | 11024