The elements of the Inauguration of the Mishkan are specified (Lev. 8: 1-3):
the appropriate Kohanim,
vestments,
anointing oil,
bull for the sin offering,
two rams, and
basket of unleavened bread.
The next verses conclude the Inauguration ceremony:
(3) and assemble the community leadership at the entrance of the Tent of Meeting. (4) Moses did as יהוה commanded him. And when the leadership was assembled at the entrance of the Tent of Meeting, (5) Moses said to the leadership, “This is what יהוה has commanded to be done.”
Yom Kippur was probably the most important service done by the Kohanim. It rendered the Mishkan pure so the Avodah could take place within it. The sprinkling of the blood on the Golden Ark was a central element of this service. Lev. 16 (source 4) describes the YK service in which the blood was sprinkled on the Golden Altar inside the Ohel Moed. No one witnessed this rite. Lev. 9 (source 5/6) describes the Inaugural ritual in which the blood was sprinkled on the outer Copper Altar.
(יד) וְלָקַח֙ מִדַּ֣ם הַפָּ֔ר וְהִזָּ֧ה בְאֶצְבָּע֛וֹ עַל־פְּנֵ֥י הַכַּפֹּ֖רֶת קֵ֑דְמָה וְלִפְנֵ֣י הַכַּפֹּ֗רֶת יַזֶּ֧ה שֶֽׁבַע־פְּעָמִ֛ים מִן־הַדָּ֖ם בְּאֶצְבָּעֽוֹ׃ (טו) וְשָׁחַ֞ט אֶת־שְׂעִ֤יר הַֽחַטָּאת֙ אֲשֶׁ֣ר לָעָ֔ם וְהֵבִיא֙ אֶת־דָּמ֔וֹ אֶל־מִבֵּ֖ית לַפָּרֹ֑כֶת וְעָשָׂ֣ה אֶת־דָּמ֗וֹ כַּאֲשֶׁ֤ר עָשָׂה֙ לְדַ֣ם הַפָּ֔ר וְהִזָּ֥ה אֹת֛וֹ עַל־הַכַּפֹּ֖רֶת וְלִפְנֵ֥י הַכַּפֹּֽרֶת׃ (טז) וְכִפֶּ֣ר עַל־הַקֹּ֗דֶשׁ מִטֻּמְאֹת֙ בְּנֵ֣י יִשְׂרָאֵ֔ל וּמִפִּשְׁעֵיהֶ֖ם לְכׇל־חַטֹּאתָ֑ם וְכֵ֤ן יַעֲשֶׂה֙ לְאֹ֣הֶל מוֹעֵ֔ד הַשֹּׁכֵ֣ן אִתָּ֔ם בְּת֖וֹךְ טֻמְאֹתָֽם׃ (יז) וְכׇל־אָדָ֞ם לֹא־יִהְיֶ֣ה ׀ בְּאֹ֣הֶל מוֹעֵ֗ד בְּבֹא֛וֹ לְכַפֵּ֥ר בַּקֹּ֖דֶשׁ עַד־צֵאת֑וֹ וְכִפֶּ֤ר בַּעֲדוֹ֙ וּבְעַ֣ד בֵּית֔וֹ וּבְעַ֖ד כׇּל־קְהַ֥ל יִשְׂרָאֵֽל׃ (יח) וְיָצָ֗א אֶל־הַמִּזְבֵּ֛חַ אֲשֶׁ֥ר לִפְנֵֽי־יְהֹוָ֖ה וְכִפֶּ֣ר עָלָ֑יו וְלָקַ֞ח מִדַּ֤ם הַפָּר֙ וּמִדַּ֣ם הַשָּׂעִ֔יר וְנָתַ֛ן עַל־קַרְנ֥וֹת הַמִּזְבֵּ֖חַ סָבִֽיב׃ (יט) וְהִזָּ֨ה עָלָ֧יו מִן־הַדָּ֛ם בְּאֶצְבָּע֖וֹ שֶׁ֣בַע פְּעָמִ֑ים וְטִהֲר֣וֹ וְקִדְּשׁ֔וֹ מִטֻּמְאֹ֖ת בְּנֵ֥י יִשְׂרָאֵֽל׃
(14) He shall take some of the blood of the bull and sprinkle it with his finger over the cover on the east side; and in front of the cover he shall sprinkle some of the blood with his finger seven times. (15) He shall then slaughter the people’s goat of sin offering, bring its blood behind the curtain, and do with its blood as he has done with the blood of the bull: he shall sprinkle it over the cover and in front of the cover. (16) Thus he shall purge the Shrine of the impurity and transgression of the Israelites, whatever their sins; and he shall do the same for the Tent of Meeting, which abides with them in the midst of their impurity. (17) When he goes in to make expiation in the Shrine, nobody else shall be in the Tent of Meeting until he comes out. When he has made expiation for himself and his household, and for the whole congregation of Israel, (18) he shall go out to the altar that is before יהוה and purge it: he shall take some of the blood of the bull and of the goat and apply it to each of the horns of the altar; (19) and the rest of the blood he shall sprinkle on it with his finger seven times. Thus he shall purify it of the defilement of the Israelites and consecrate it.
(8) Aaron came forward to the altar and slaughtered his calf of sin offering. (9) Aaron’s sons brought the blood to him; he dipped his finger in the blood and put it on the horns of the altar; and he poured out the rest of the blood at the base of the altar. (10) The fat, the kidneys, and the protuberance of the liver from the sin offering he turned into smoke on the altar—as יהוה had commanded Moses; (11) and the flesh and the skin were consumed in fire outside the camp. (12) Then he slaughtered the burnt offering. Aaron’s sons passed the blood to him, and he dashed it against all sides of the altar. (13) They passed the burnt offering to him in sections, as well as the head, and he turned it into smoke on the altar.
Koschitzky stated: "The biblical authors present the biblical inauguration service and much of the cult service in general in a manner that distances it from the more secretive cult practices of ancient Near Eastern priesthoods."
J. Levenson (Harvard Divinity School) stated: "The religious traditions recorded in the Hebrew Bible include no parallel to the monasticism that was to develop in the church."
Pritchard (ANET):
(re a Mesopotamian ritual) "This ritual...only the properly qualified person shall view. An outsider who has nothing to do with the ritual shall not view it. If he does may his remaining days be few."
(כב) וַיִּשָּׂ֨א אַהֲרֹ֧ן אֶת־יָדָ֛ו אֶל־הָעָ֖ם וַֽיְבָרְכֵ֑ם וַיֵּ֗רֶד מֵעֲשֹׂ֧ת הַֽחַטָּ֛את וְהָעֹלָ֖ה וְהַשְּׁלָמִֽים׃
(כג) וַיָּבֹ֨א מֹשֶׁ֤ה וְאַהֲרֹן֙ אֶל־אֹ֣הֶל מוֹעֵ֔ד וַיֵּ֣צְא֔וּ וַֽיְבָרְכ֖וּ אֶת־הָעָ֑ם
וַיֵּרָ֥א כְבוֹד־יְהֹוָ֖ה אֶל־כׇּל־הָעָֽם׃ (כד) וַתֵּ֤צֵא אֵשׁ֙ מִלִּפְנֵ֣י יְהֹוָ֔ה וַתֹּ֙אכַל֙ עַל־הַמִּזְבֵּ֔חַ אֶת־הָעֹלָ֖ה וְאֶת־הַחֲלָבִ֑ים וַיַּ֤רְא כׇּל־הָעָם֙ וַיָּרֹ֔נּוּ וַֽיִּפְּל֖וּ עַל־פְּנֵיהֶֽם׃
(22) Aaron lifted his hands toward the people and blessed them; and he stepped down after offering the sin offering, the burnt offering, and the offering of well-being. (23) Moses and Aaron then went inside the Tent of Meeting. When they came out, they blessed the people; and the Presence of יהוה appeared to all the people. (24) Fire came forth from before יהוה and consumed the burnt offering and the fat parts on the altar. And all the people saw, and shouted, and fell on their faces.
In the context of the Inauguration of the Mishkan, two sons of Aharon suddenly are killed.
(1) Now Aaron’s sons Nadab and Abihu each took his fire pan, put fire in it, and laid incense on it; and they offered before יהוה alien fire, which had not been enjoined upon them. (2) And fire came forth from יהוה and consumed them; thus they died at the instance of Others “before.” יהוה. (3) Then Moses said to Aaron, “This is what יהוה meant by saying:
Through those near to Me I show Myself holy,
And gain glory before all the people.”
And Aaron was silent.
H. Koschitzky concludes: "Herein lies the sin of Nadav and Avihu: they performed a "secret" ritual, hidden from the viewing of the people. No ritual...was supposed to be performed inside the Tabernacle during this service. This was adhered to so strictly that even the format of the high priest's sin offering was changed to have the blood sprinkled on the outside altar instead of inside the sanctum....
God is telling the Israelites that as opposed to foreign cultures, Israel's cult will be accessible to the public; even the cloistered rituals are described to the people so they know what happens inside the Tabernacle. To demonstrate the open nature of Israel's cult, the inauguration ceremony is performed entirely in public.
But entering the sanctum and performing the incense offering there, Nadav and Avinu reverted to the non-Israelite ethos of secluded worship. This was the strange fire that YHWH did not ask for, since, as Moses reminds Aaron, YHWH gains glory before "all the people," not in the privacy of the sanctum with only the priests. Thus, the punishment is harsh and public, reestablishing the ritual of the day along the lines that YHWH intended: God needs to be visible to everyone on inaugural day."