Here is the Question:

The time to failure $($in days$)$ of $15$ components is as follows: $1,1,2,3,3,8,11,16,20,24,25,25,26,28,30.$ Suggest a burn$-$in time to improve the mean reliable life $($MRL$)$ of this component for the consumer and justify your choice.

Here is the Solution:

The optimal burn$-$in time is $3$ days. The MRL is improved to $18\mathrm{.}30$ days $($from $14\mathrm{.}87$ days$).$ A $3$ day burn in time increases average lifespan by approximately $25\%,$ with a loss of one$-$third of units. This is the optimal trade$-$off between lifespan extension and attrition.

Please Explain each step how they got this solution with step by step calculation.