The Old Criteria (Up to 1419 AH)
Most people think that Saudi Arabia always adopt the actual sighting of the crescent as the basis to start Islamic months. But during the previous years [ie. before 1998], it was very clear to the public as well as to astronomers that most of the Saudi months were wrong if the actual sighting is the basis for starting the Islamic month. Fortunately, the Jordanian Astronomical Society (JAS) received a telegram from The Highest Religious Council "Majlis al-Ifta' al-A'ala" in Saudi Arabia showing the basis of the Saudi official calendar (Umm-ul Qura). Below is a literal translation of this telegram.
"( To Jordan/ Al-Yadodeh/ M.Kh./ Al-Sook/ Mr. Hayel Mamdooh Abu-Zeid, dated January 21, 1998/Ramadan 23, 1418H.
We wish to thank you for sending us your greetings of Ramadan, and for reminding us of the date of the New Moon of Shawwal for the year 1418 H. We would like to remind you that determining the first day of the Islamic month is like determining the prayer times, and the aim of His Almighty from these times is to inform us not to take it as worship. It is adopted in Umm-ul-Qura Calendar that if the Moon's age at Sunset is 12 hours or more after the New Moon then the PREVIOUS day is the first day of the Islamic month, since the Islamic day starts at Sunset, and the night is before the daylight, as well as the time of fasting is in the civil daylight. May Allah accept your worship. May Allah bless this Ramadan. Thanking you for your good cooperation.
From: Kingdom of Saudi Arabia/ Al-Riyadh/ The Higher Religious Council "Majlis al-Ifta' al-A'ala"/ Mohammad Bin Ehmead.)"
Mr. Hayel of JAS received other letters also, about the same subject, which were clearer than this telegram. The following example may make their system clearer: If for example 29th Dec is 29 Sha'ban, and the New Moon Phase occurs after Sunset in Riyadh, say at 11 pm on 29th Dec., then the next day (30th Dec.) at the Sunset (For example at 5 pm) the Moon's age will be 18 hours which is more than 12 hours, so that day (30th Dec.) is the first day of Ramadan, even though the New Moon was not even born at the Sunset on 29 Sha'ban (29th Dec.), and generally in such cases the Moon will set before Sunset! Below is a copy of the telegram.