Quality is the most important risk to address during a project. Why? Because a lot of the over costs and delays are a result of poorly managed quality issues.
A lot of the quality mismanagement comes from the early stages of a project, as early as product development stage.
As a foreign business, aside from the occasional fly in to visit factories, you have 2 options. You can either trust the supplier's own procedures, or hire a specialist of QC.
The latter will dispatch employees at various times during the project, and proceed to controls and measurements. To put it bluntly, they will be completely in the dark of what it really happening to your project: You will be left with the difficult task of making operational decisions from far away, based on very fragmentary information.
On the other hand, your supplier's own procedures are indeed very important, because they are rooted in the factor's functioning. However, they are just that: Procedures made to make it work as a whole, with little tune up to your particular project.
Quality should be monitored all along the project life, from prototypes built using final mass production structure and materials, including pack, to first-offs, mass production, all being minutely tested all the way.
To make sure it doesn't go off the rails, you need someone on the field to talk to production managers, procurement, GM, and make it happen. As the Chinese say, a problem is a hidden opportunity. But you need someone here to take advantage of it!
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