An individual can maintain more than one oneworld program. My question is that if I have take a flight on a program where I am a member, can I choose not to accredit the miles to this program and assign my miles to my other program?

For example if I belong to both CX and BA, if I take a CX flight, can I accredit miles to my BA program for accumulation to a higher tier?

You can credit anywhere you like, as soon as:

1. It is creditable to that program.

2. You tell the operating airline where to credit.

3. You credit the flight once only (in most of the case).

Yes.
But if the CX flight been taken with your CX ff number in the reservation and therefore credited, it is very hard to get uncredited.
You cannot double dip. [There are sometimes FQTR FQTV technical exceptions]

Note many low cost CX flights do not credit to other ffp's [nil earning]
https://www.wheretocredit.com/cx

What are the cases when I can credit one flight twice?

When you are rebooked to a partner flight involuntarily.

For example, you are originally booked on BA and you are rebooked on CX due to IRROPS, you can ask BAEC to credit your original booking and MPC to credit your rebooked flight.

It is commonly known as double dipping.

Wooooo. That's some good news! I have at least 6 missed connections in the past 6 months. But it works only if I was rebooked on other airlines? Then I have no luck. Always was rebooked BA to BA, and Swiss to LOT, but they share the ffp.

Can I then credit both: original and rebooked flight to one program (BAEC) in the example you gave?

No. BA to BA (same ffp) or Swiss to LOT (same ffp) is unlikely to work. You can ask

But if the new route means you get less ff miles/TP's you can ask for what you should have got. Here on FT people often fly the long way for extra miles/TP's.

But if, for example BA put you on a Swiss flight, then you can claim for both to separate ffp's. Often works if you ask for "original routing credit". At times it can be declined, but such is the life of a frequent flyer.

Most ffp's have a time limit for retro credits. 3 or 6 months is common.

You tell me.... I have never flown LAX to LAS directly - always through PHX

I realize about the time limit for the retro claims - that's why I wrote about only last 6 months.
It's good to know - then I guess it should be done over the phone rather the online automatic form to enquire for the "original routing credit".
One time I was downgraded from CE to ET on my rebooked flight from LHR to WAW (then I was still crediting to QR and those two points difference between J and Y weren't of big importance) but now I will know to ask them for the Tier Points according to original booking
Only two months ago due to late arrival from SFO to LHR I didn't catch the last BA to WAW and I didn't ask for rebooking to LO later that day only to get my OW tier points... But on the other hand it was a better option for me: I got Hilton Points for staying the night and also 600€ under the 261 regulation. So every cloud has a silver lining I guess

But now thanks to you I'm smarter - so hello again bookings with the MCT and hoping for delays

To legally (per the program) double-dip, you must credit the flights separately.

Yes, just done this on QR trip LHR-DOH-MCT - credited outbound to BA to get silver (just, but only 7 collecting s days left in my year) and then return to AA to keep points valid. Happy days!

This double dipping relates to original routing credits, (there is a guide linked to in the BAEC board dashboard). Basically if you are rebooked on to another flight due to IRROPS you can do an ORC claim to get the originally booked flights credited to BAEC.

If you are rebooked on to a non-oneworld airline like Swiss you can double dip quite easily since you can credit your Swiss flight to whatever *A program you use by either adding it at the Swiss counter or retro claiming, and do your ORC for the original flights to BAEC.

If you are rebooked on to oneworld flight unless you remove your BAEC number your rebooked flight will credit as normal to BAEC. On doing your ORC that rebooked flight entry would be removed and the original flight TP and avios manually added. If you apply to credit that rebooked flight to another oneworld airline program it may be rejected on the basis it was already credited to BAEC. As noted you definitely won't get original and rebooked flights credited to BAEC.

It is generally possible to credit different flights on a single ticket/itinerary (eg a oneworld explorer ticket) although deleting and adding a new FF number can be problematic.

Also note that AA has recently been preventing other codes being added to AA bookings - I believe this is because of AAs shift to EQDs