Captain reported misreading multiple MEL's and departed an airport with a non airworthy aircraft.

Attributes
ACN	1740637
Time
Date	202004
Local Time Of Day	1201-1800
Place
Locale Reference	ZZZZ.Airport
State Reference	FO
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	B767-300 and 300 ER
Operating Under FAR Part	Part 121
Flight Phase	Takeoff
Flight Plan	IFR
Component
Aircraft Component	Air Conditioning and Pressurization Pack
Person 1
Function	Captain Pilot Flying
Qualification	Flight Crew Multiengine Flight Crew Instrument Flight Crew Air Transport Pilot (ATP)
Events
Anomaly	Aircraft Equipment Problem Critical Deviation - Procedural MEL Deviation - Procedural Published Material / Policy

Narrative:

We flew aircraft X from ZZZZ to ZZZZ1 to ZZZ. We operated with deferral 36-11-8-1-1a and 21-51-1-1. Under these conditions; the left AC pack should have been operated off. It wasn't! The flight should have not departed ZZZZ. The crew that was scheduled to fly aircraft X from ZZZ to ZZZ1 noticed the discrepancy. The flight from ZZZ thru ZZZ1 to ZZZ was uneventful. I accept full responsibility for this event. I failed to take the proper time to review the MEL prior to the flights. After maintenance was performed on the aircraft; I reviewed the MEL items with mechanic in ZZZZ. My review of the MEL was obviously not thorough enough. I don't understand how I could have overlooked several of the items in the MEL; but I did. I should have been more proactive in including the first officer in the decision making process. First officer is an excellent pilot and this should not reflect poorly on him. I was very tired that day. This may have been a distraction. Considering everybody involved with this event; several people dropped the ball. Ultimately I am responsible.

Original NASA ASRS Text

Title: Captain reported misreading multiple MEL's and departed an airport with a non airworthy aircraft.

Narrative: We flew Aircraft X from ZZZZ to ZZZZ1 to ZZZ. We operated with deferral 36-11-8-1-1a and 21-51-1-1. Under these conditions; the left AC pack should have been operated off. It wasn't! The flight should have not departed ZZZZ. The crew that was scheduled to fly Aircraft X from ZZZ to ZZZ1 noticed the discrepancy. The flight from ZZZ thru ZZZ1 to ZZZ was uneventful. I accept full responsibility for this event. I failed to take the proper time to review the MEL prior to the flights. After maintenance was performed on the aircraft; I reviewed the MEL items with mechanic in ZZZZ. My review of the MEL was obviously not thorough enough. I don't understand how I could have overlooked several of the items in the MEL; but I did. I should have been more proactive in including the First Officer in the decision making process. First Officer is an excellent pilot and this should not reflect poorly on him. I was very tired that day. This may have been a distraction. Considering everybody involved with this event; several people dropped the ball. Ultimately I am responsible.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.