Why do you think 16 minutes is not enough? When it is a life & death situation, why would one make it a long process?
Exactly because it is a life & death situation, no one wants to rush into a wrong decision. That is why the decision must be made with thorough consideration.
Let's think some scenarios again:
Assume both China and India have the same number of warheads/missiles (300) and the same population kill rate: 30 millions people (the maximum) without considering other tech issues. Each country has 1/3 missiles stay in SILOs as first strike (these missiles can kill 10 millions), the rest is kept as second strike force.
One day, your radars tell you there are massive scale of Chinese missiles launched (100 missiles), they are targeting your SILOS (in reality, both China and India's nuclear missiles only target the enemy's big cities)
Scenario 1: you immediately inform Modi (without any verification from other department) and he gives his launch order immediately (again without consulting with other leaders). Within 8 minutes after detection, all Indian SILO missiles are launched.
There are 2 possible results:
A. You and Modi are right - Chinese starts the nuclear war, India strikes back by killing 30 millions Chinese when India loses 20 millions population;
B. You and Modi are wrong, there is no massive Chinese missile launch, or the Chinese missiles only have conventional warheads for limited war, then you and Modi successfully bring India's casualty from 0 or 30k up to 30 millions.
Scenario 2: after a 16+ minutes long decision making, India misses the opportunity to launch SILO missiles.
There are 2 possible results too:
A. Chinese did start the nuclear war, you lose 100 SILO missiles, but you still get 200 other missiles, but China also has only 200 other missiles now, so both sides can kill 20 millions people;
B. There is no Chinese nuclear missiles launch, the system makes mistake, there is no nuclear war or only conventional war which India can fight back, so basically India will suffer 0 or 30k casualty when China suffer 0 or 30k casualty.
Now, tell me which one you want to see.
Detecting incoming missiles is not hard given the radar quality. Also, if one spots hundreds of missiles incoming, there is no room for speculation or assessment. If it is just 1 missile, only then one can take some time for assessment but just fire back at the source.
During cold war period, there were plenty of false warning on both sides' radar networks. So, yes, both sides came to the same conclusion: they would rather lose 1000 SILO missiles than starting a nuclear war based on false alarm.
Second point is that SILOs can be built even in current installations like nuclear sites, aerospace manufacturing units, defence industrial sites, overhaul & repair sites, training camps etc. It is extremely hard to detect silos if constructed in camouflaged areas. For every SILO you think is detectable, there will be ten more which are camouflaged. Even satellites can't detect if a construction activity is an ammunition depot, underground hanger, bunker or SILO if done in a secretive & camouflaged manner. India has its own satellites and can ask its experts to observe and tell whether any of the activity is detectable and then improvise on the stealth nature of cosntruction till its becomes undetectable.
The SILOs are not staying there for a few month, they will be there for years or decades. In such a long period of time, no one can guarantee the secrets will be guarded well.
Secondly, SILOs tend to have thick concrete cover which becomes indestructible unless hit directly spot on which almost no ICB can. Most ICBMs have accuracy in range of 10 metres which is enough for a SILO to survive. The opening of the SILO can be rigged with shaped explosives to burst through if it is blocked with rubble.
During cold war, based on the public information, the US SILO can resist 2000 PSI by direct hit. Someone suggested to upgrade them to 10000 PSI, but it was rejected because the cost and useless.
It turned out that a 300k bomb detonated within 94m of the SILO can produced 10000 PSI already.
In 1980s, Amercian missiles had already got that accuracy. How do you think today.
So, there is no hope that SILO can win the race against warhead.
I don't disagree about security importance over profits but cost still matters as that improves efficiency in terms of increasing damage to enemy & lowers loss to oneself when scaled up.
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The missile life itself will lower if subject to stress by regular movement, pressure, operating heat, handling etc. So, that is where SILOs will help improve serviceability of ICBMs
For this part, I think we should stop arguing. After all, all nuclear countries were coming to the same conclusion regarding SILOs after decades of planning, simulation and calculation. We have to trust these guys since both of us are outsiders unless you know something they don't know.