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tusharsinghtanw 

Although you asked about Power BI, I would highly recommend using the "IFS" function in Excel instead of nested IF statements.  It is both easier/simpler to write, and easier for other people to understand.

DAX does not have IFS, instead you can use the SWITCH function.  Something like this:

COLUMN = 
SWITCH(
	TRUE()

	, table[period] = 201809 
	|| table[period] = 201809 - 1 
	|| table[period] = 201809 - 2
	, "Condition 1"

	, CALCULATE(
		SUM(table[Complete/Sent Approval Sites])
		, FILTER(
			table
			, table[Engineer Name] = EARLIER(table[Engineer Name])
			)
		, FILTER(
			table
			, table[Period] = EARLIER(table[Period])
			)
		)
	> 0
	, "Condition 2"

	, "Everything Else"
	)

Obviously your formula is much more complicated, so you will have to build this out, but that is the basic structure.

More broadly speaking, Power BI is not Excel.  It has different strengths and a different way of approaching things.  This same result can be achieved much easier using a built out data model and the functionality of measures / visuals in Power BI.