The waterfall model is a sequential software development process, in which progress is seen as flowing steadily downwards (like a waterfall) through the phases of Conception, Initiation, Analysis, Design (validation), Construction, Testing and maintenance.
It should be readily apparent that the waterfall development model has its origins in the manufacturing and construction industries; highly structured physical environments in which after-the-fact changes are prohibitively costly, if not impossible. Since no formal software development methodologies existed at the time, this hardware-oriented model was simply adapted for software development. Ironically, the use of the waterfall model for software development essentially ignores the 'soft' in 'software'.
The first formal description of the waterfall model is often cited to be an article published in 1970 by Winston W. Royce (1929-1995), although Royce did not use the term "waterfall" in this article. Ironically, Royce was presenting this model as an example of a flawed, non-working model (Royce 1970). This is in fact the way the term has generally been used in writing about software development-as a way to criticize a commonly used software practice.
Waterfall Model
In Royce's original Waterfall model, the following phases are followed in order:
1. Requirements specification
2. Design
3. Construction (AKA implementation or coding)
4. Integration
5. Testing and debugging (AKA Validation)
6. Installation
7. Maintenance
To follow the waterfall model, one proceeds from one phase to the next in a purely sequential manner. For example, one first completes requirements specification, which are set in stone. When the requirements are fully completed, one proceeds to design. The software in question is designed and a blueprint is drawn for implementers (coders) to follow - this design should be a plan for implementing the requirements given. When the design is fully completed, an implementation of that design is made by coders. Towards the later stages of this implementation phase, separate software components produced are combined to introduce new functionality and reduced risk through the removal of errors.
Thus the waterfall model maintains that one should move to a phase only when its preceding phase is completed and perfected. However, there are various modified waterfall models (including Royce's final model) that may include slight or major variations upon this process.

Waterfall Model
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