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Value analysis and Value Engineering refer to the same concepts. Value Engineering can not be associated only with design stage. You can check the resource below for both Value Engineering and Analysis
Though I've seen both terms used together, a slight difference may exist and I will go with Sameh Nasr's answer.
I would say that value analysis is a subset of value engineering.
Analysis requires something to assess, to gain knowledge. Engineering is the application of knowledge to develop a solution.
Before there is an existing product, there may be multiple proposed products and value engineering would be employed during trade studies to select the best option. By the same token, "reverse engineering" a product involves analysis, so value engineering may be applied to existing products also.
@Keith hit the nail. Just trying to add something, to direct you to PMI documentation, take a look to Business Realization Management Practice Guide.
Keith made good point.
Value Analysis can be related not only in terms of physical products only it can be related to Services as well as Brand Perceived value.
While Value Engineering is broadly related to the application of engineering fundamental to enhance or optimize the product features for better customer experience with or without any cost impact.
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