If you suspect poor or bad pump, test pump output you ned to get over 1 litre of fuel in 20 seconds, disconnect fuel line at fuel distributor bridge f/p relay
with line in container 1litre in 20 seconds if not , find out why, the fuel regulator,accumulator, or leaking imjectors will cause hard start after car shutdown, the cis system relies on correct pressure to work correctly , bosch
has an excellant book explaining how cis works , recommend reading book
to understand this system, its reliable and easy to work on , testing takes time , you need a gauge to diagnose , but here will try and talk you thru.