The maritime industry, undoubtedly, is a haven of immense complexity. With a variety of vessels traversing the world's vast water bodies, the incidence of wear and tear, coupled with outright damages, is inevitable. At the heart of maintaining these vessels in pristine condition are entities often referred to as Boat Repair Companies. These corporate bodies, armed with a plethora of technical know-how and an arsenal of tools, undertake the arduous task of restoring these seafaring machines to their optimal state.

To truly appreciate the operations of boat repair companies, it is advantageous to comprehend the expanse of their roles. They are not merely establishments that fix broken-down vessels; they encompass a broader sphere of activities closely linked to structural integrity, performance, safety, and aesthetics of boats. From repairing hull damages, fixing engines, painting, winterization (a term used to denote the preparation of a boat for periods of non-use or storage), to electrical repairs and navigation systems upgrades, the list of services offered by these companies is quite exhaustive.

The operation of boat repair companies takes on a systematic approach, commencing with a thorough assessment of the vessel in question. This diagnostic phase involves an all-encompassing examination, ascertaining the extent of damage, and identifying latent issues that may not be immediately evident. It is a critical phase that informs the subsequent repair plan and involves various technologies, such as ultrasonic testing for hull integrity and thermography for electrical systems assessment, amongst others.

Following the diagnosis, the next phase is the repair phase. Here, the severity and nature of the damage dictate the repair processes applied. For instance, a hull damaged by a collision would require different techniques compared to one suffering from corrosion. The former might involve structural reformation and reinforcement, while the latter would necessitate rust removal and protective coating application.

The final phase in the operation of boat repair companies is the testing and validation phase. Post-repair, a rigorous testing regimen is carried out to ensure that the repair work meets the pre-set standards. These tests are guided by various marine laws and regulations, coupled with the repair company's internal quality control measures. From sea trials to load testing, these procedures ensure the vessel's seaworthiness, safety, and performance are up to par.

When it comes to the question of where and when these repairs are carried out, the answer largely depends on the type of vessel, the nature and extent of the damage, and the specific company guidelines. Some repairs can be carried out while the boat is afloat, known as afloat repairs. Others, however, necessitate the vessel's docking at a repair yard or dry-docking, i.e., placing the boat on a dry platform for comprehensive repairs.

An analytical contemplation of boat repair companies reveals an intricate system of operations that rival manufacturing processes in their complexity. The application of statistical process control, linear programming for resource allocation, and implementation of Six Sigma methodologies for process improvement, mirror industrial engineering concepts.

In conclusion, boat repair companies serve as vital cogs in the machinery of the maritime industry. By ensuring the optimum performance of vessels, these companies indirectly contribute to the larger global economy by aiding commerce, tourism, and transport. With advancements in technology and the advent of concepts such as predictive maintenance, the role of boat repair companies is set to evolve, further underlining their significance in the industry.