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No never, they are linked to each other, but don't run parallel.
never
The product life cycle starts with the introduction of the product, and the graph climbs as sales pick up. At its peak and when profits are highest, the product matures off and then reaches saturation, and eventually declines.The service life cycle begins after the sale has been made, and then intersects the product life cycle graph near maturity. This is where services go higher and earn possibly higher profits, when market proliferation of the product is maximum. As the product market saturates, services level off to a constant before they decline and the graph will not intersect as service life cycle generally tends to continue for a while longer even after the demise of the product.However, this stands for a regular life cycle of a product and a linked service. In case more technical products where it introduces a refinement or a new application, the graph alters itself accordingly to make way for a higher level of product-service linkage.
In any case, product and service life cycles are inextricably linked to each other and might run parallel in sub-phases after sales where movement of each function is relative.
To me they are reciprocal to each other.
A product is Introduced called Brand Evolution and you work on its growth it reaches its maturity called Brand Power and shows decline in profits after certain period of time depending upon the factors external as well as inernal.
Service behind the product in its creation and ideation,Market ,Customer,Competitor Research,Updation of Service and product in line with market requirement, profit compromise when saturation in market with too many competitors.Line extension to product and facelift to product and you extend its life to certain period, a point of stagnation reaches wherein you cannot continue to extend service line to this product and it starts to creep into its base profit margin and breakeven point reaches where you stop and think of discontnuing the product and service.