iMac shuts down randomly for no apparent reason

We've been plagued by this for the last 8 months. My wife's 18 month old imac was shutting down randomly. Only an unplug/replug/power on got it running. random activities happening when shutdown occurred. 4 phone calls to apple support and 2 visits to the genius bar. Finally, last visit to the genius bar, Apple decided to replace the power supply, even though their testing dis not seem to indicate that was the problem. The support guy on the phone said, "It sure sounds like a hardware/power supply issue to me, so let's fix that". Got the computer back with a new power supply almost 2 weeks ago. No shutdowns since. It sure seems to be solved!

What could possibly be the issue with this machine after all the testing and interventions that have been done?

A hardware fault. Don't waste your time with any "malware detection software", "antivirus scans", or any similarly categorized garbage.

Open Console - it's in your Mac's Utilities folder. To determine the shutdown cause, examine system.log for "shutdown cause". The log entry will be "Previous shutdown cause:" followed by a numeric code. What is that code?

Is there any way to access system logs further back in time.

Yes. Archived logs are named system.log.0.gz and so forth. They can be opened and examined the same way as system.log, which is normally archived daily at midnight system time.

Previous shutdown cause: 0

That code will appear if the power to your Mac is suddenly interrupted. You can confirm that yourself by disconnecting its power cord from the wall receptacle while the Mac is operating.

The causes can be due to any one of the following

1. a defective power cord, which might not be evident by inspecting its exterior
2. an intermittent connection between the power cord and the Mac's power receptacle
3. a faulty (household / office) power receptacle
4. a faulty power strip / surge suppressor
5. a defective Mac power supply
6. a crack or similar break in the Mac's circuit board

The most likely cause given the history you reported is #1. You can substitute any standard electronic device power cord that fits.

Power interruption is causing the random shutdowns. Apple's support "geniuses" should have been able to determine that within minutes of accepting it for repair the first time, much less three or four return visits.

If it is a defective Mac power supply or a crack in Mac circuit board wouldn't that have been identified in a hardware assessment?

No, other than to identify the cause of the shutdown being a power interruption. The power supply itself might be defective, but all the logic board (the SMC to be specific) is able to determine and report is an unexpected loss of power. The same shutdown cause would occur if there were a break in any circuit between the iMac's power source and the logic board. The break might be microscopic and difficult to find. It might also change during physical movement or thermal expansion, which can be induced by bending or stressing various connectors for example.

It could also be brought on by a short anywhere in the power supply, perhaps an intermittent one which could have been caused by an object becoming dislodged from the back of the iMac. 27 inch iMacs such as yours have been known to have that bracket fail internally. It's possible an internal fastener became loose and found itself conducting an electrical path where one ought not to be. Loose things or otherwise conductive debris inside a computer will cause random failures that can be difficult to find.

As you see there can be quite a few potential causes. A problem such as that might require board-level repair, which has become a lost art. Most computer repair shops would prefer to substitute components, such as the power supply (which is not expensive) or the logic board (which is), observe the results, and stick you with the bill.

At what point was someone going to discuss or target the only item that powers on or off a machine? A power controller takes various inputs to decide when to power cycle. It even determines when the CPU is permitted to execute. One controller input is the front panel power button. Controller even acts differently depending on how long that button is pressed. Another input comes from the OS - when the OS asks for a power off. If the OS asks for a sudden power off, then the OS also says so in logs. Another input is monitor circuits in the power supply. If those demand a power off, then the OS and its logs know nothing about it.

How to find an informed tech? He knows about this hardware and how to measure it.

What diagnostics did Apple techs run? A processor called the power controller has no hardware diagnostics. CPU cannot monitor or obtain status information. CPU is simply told by this processor when to and not to execute. What diagnostic could Apple (software) techs run to diagnosis a part of hardware that software cannot see? IOW get an informed tech.

Power cord and surge protector clearly are irrelevant. Your Apple must work just fine even when incandescent bulbs dim to 40% intensity. How did a power cord or power strip cause voltage to drop that much - without also getting hot and dangerous?

Your problem clearly requires someone who knows hardware. Who does not blame things without any reason to. And has simple layman tools to view what that hardware is doing. Again, find a tech who knows how electricity works. That is a first problem. Power off solution comes later.

I recommend you bring it back to them and tell them it's not fixed yet. Whether to replace the logic board, power supply, or both is a question of who's paying the bill.

The problem you describe is identical to, and indistinguishable from, a power interruption. That power interruption can be internal to your Mac or external to it. That's all anyone knows. I described the potential causes, and they are not limited to the power supply or the logic board. It would be unfortunate to replace one or the other just to find that your building power is unreliable. You could eliminate that possibility by using a UPS from a reputable manufacturer.