Is engine keeping exhausting white smoke after the head set gasket replacement have anything to do with the failure of the said replace gasket? When a foreman wanted to claim the gasket due to this reason it is really headach, as the real problem may not come from the gasket, it may occur due to Head Bolt didn't replace, or engine valve failure.
Any way we may give a quick glance on the engine smoke problem as below,
A glance at an engine's exhaust pipe can be both frightening and enlightening. There's a moment of panic when a thick cloud of black smoke rolls out of the tailpipe. Sometimes the cloud is gray or white. What does it all mean? Should you shut down the engine and call for help? The good news is that most engine smoke signals don't mean immediate trouble. Some smoke is a normal sign of a healthy engine. And some of it means the power plant is headed for serious surgery. But it's easy to interpret engine smoke. Just consider the chemicals and combustion process inside the engine, and take note of the outside air temperature. Normal engine exhaust is composed primarily of water and carbon dioxide (the bubbly stuff in soft drinks). Gasoline and diesel fuel is a hydrocarbon that creates intense heat when combined with oxygen from the air. The fuel's carbon atoms go into (CO2); the hydrogen atoms go to produce (H2O).
When the engine and exhaust pipe system is fully warmed up, the exhaust is a hot stream of moist carbon dioxide (and traces of other chemicals). The mixture is colorless and invisible, except in cold weather when most engines produce white exhaust for a minute or two after first starting. This is because the exhaust gas cools down when it runs through the pipes and muffler. The cool water droplets can freeze rapidly when they hit the outside air, producing a visible cloud of ice crystals. As the pipes heat up, so does the exhaust gas. It still ends up freezing, but over a wider zone because it takes longer for the water drops to cool down, and they're farther from the tailpipe. But white exhaust can mean problems. Here's a rundown of colors and conditions and what troubles they may indicate. 
Steady white smoke; warm engine; any air temperature. This is bad news. The engine's coolant is leaking into the combustion chamber and creating a steady flow of steam. Caused by a leaking head gasket or a crack in a cylinder head, most commonly in the exhaust port area. Usually requires serious surgery on the engine.
Puff of white smoke during cranking, before the engine starts; cold engine; gas or diesel. This smoke is unburned fuel vapor being pumped out the exhaust pipe. The white is tiny droplets of fuel. In a gas engine, the spark plugs aren't firing, or the fuel mixture is too rich to ignite. It may mean the choke plate is stuck closed, or a load of bad gasoline. In a diesel, this cranking smoke indicates defective glow plugs, but may also come from low compression caused by worn rings or valves.
Gray smoke seen only briefly when the engine first fires up; gas or diesel. This is engine oil that has gotten into the cylinder head combustion area or onto the back side of the exhaust valves as a result of worn valve stems or seals. The oil smolders and smokes at first, but then burns off when the engine gets running, and the smoke disappears. This can be an early warning sign of serious trouble. But if the engine isn't using a lot of oil, it's not a fatal condition.
Gray smoke when the engine is warmed up. Usually appears when the engine is accelerated and may be especially notable when the engine is idling. This is unburned oil drawn into the combustion chamber past worn rings or valve guides. In the best case, the oil is just too thin (old oil, wrong weight) and is slipping past the piston rings and valve seals. The oil sump may be overfull. The cure is a simple oil change. But that won't solve gray smoke resulting from a worn engine. In the worst case, gray smoke means the engine needs replacement or serious internal repair.
Black smoke in a steady stream; cold engine, gas or diesel. Black smoke contains carbon particles from fuel molecules that have broken down but have not burned completely. On gas engines, this can mean the choke is not fully opened, the air filter is badly clogged, the ignition system is not firing every time or the carburetor or fuel injection system is set too rich. Normally fixable without tearing down the engine. On diesels, black smoke during warmup can result from a plugged air filter. It can also be a sign of weak compression in one or more cylinders or a maladjusted injection system. In gas and diesel engines, black smoke means excess fuel in the combustion chamber, which washes vital lubricating oil off the cylinder walls. Get it fixed quickly.
Black smoke, in occasional puffs, warm engine. In diesels, black smoke is normal when the engine is suddenly put under load. Modern (mid-'90s and newer) diesels generally limit this puff of particulates, but it may still be visible. The diesel's governor injects extra fuel to kick up the engine speed and power, and this excess fuel makes black smoke while the engine is revving up. It usually disappears in a few seconds. If it continues while under steady load, there may be a leaking fuel injector or incorrect adjustment of the fuel injection governor. Gasoline engines typically don't belch black smoke under sudden load, but they can if the accelerator pump is set wrong, the choke plate is partially closed, or the air filter is filthy. If everything checks out mechanically with the engine, there may be something in the drive line (like dragging brakes) that is causing excess load.
