The problem with some simple alarm circuits is that they don't have an exit or entry delay. So for example when you switch them on, they are armed immediately and give you no time to leave. Or there is no entry delay, meaning that unless you can get to the keyswitch without triggering the alarm, it will always sound an alarm for the time it takes to disarm it. Also unless the alarm has a timer for the alarm duration, it's going to be sounding indefinitely or at least until the battery goes flat.

This circuit overcomes these problems by providing 3 timings.

EXIT DELAY
When first switched on the alarm is disabled initially, meaning it can not be triggered giving time to exit.
This time is set by R1 and C1 which keep the resets to the 555's low until the capacitor reaches about 1/3 of the supply.
The values showngive approx. 5 seconds, but it is recommended to change R1 to at least 150K if using a PIR. this will ensure it has time to settle after power on, in this case 15 seconds.

ENTRY DELAY
When the alarm is triggered by the PIR, the monostable IC1 begins timing giving time to diable the alarm with the key. This causes both plates of C3 to go low until it charges. This pulse is very brief but enough to trigger the second 555 monostable.After the monostable has finished timing the output goes low at pin 3

it triggers the second monostable activating the alarm. This delay time is controlled by R2 and C2 and follows the formula
t = 1.1 C R, standard for a 555.
The values shown give around 5 seconds.

ALARM DURATION
This is the length of time the alarm sounds for until it resets. This is controlled by R3 and C3 and again follows the formula
t = 1.1 C R so with the values shown about 50 seconds.

It should be noted that electrolytic capacitors often are considerably higher than their value - up to 40%. I have known 100uF capcitor measure at 146uF before when it was brand new. Maybe old stock from the manufacturer??