I have ISO9000 career in a big electric company from which I retired several years ago. Now I am instructing quality management of a small company. The company, I think, has no strong technical engineering and moreover now is doing a wild challenge of installing quality management system (QMS) anticipating for quality improvement. But so far in spite of my efforts effective quality improvement suitable for input cost has not been achieved.
In order to solve the problem, ISO9001:2000 should show strong concerns for quality improvement of technical matters, because effective quality improvement can be done in product realization processes.
Therefore NOTE in clause 4.1 should be written as quality management system includes product realization processes themselves.

I think you may have basic misunderstanding for ISO9001:2000. ISO9001:2000 requires so simple basic quality management system elements that installing the Standards is not a wild challenge. And the Standards do not define technical matters. The Standards only deal with management matters.
Those misunderstandings will lead to false ISO9001:2000 management system with wasteful heavy documentation
Therefore, QMS does not include product realization processes, but is complementary.　In PDCA cycle, basically “Do” does not mean management activities

I cannot understand “’Do’ does not mean management activities”. In daily activities in a factory, planning of and effective resource provision for product realization (design, purchasing, and manufacturing) are performing. Are these activities management activities?

Yes, planning of and effective resource provisions for product realization　processes are management activities, but not product realization activities.
For instance, in case of car engine design an engineer may think various alternatives about shapes, materials of the engine under design and may various calculations. And he will finally make engine drawings. Do you think that these activities are management ones?
Purchasing personnel makes orders by a computer to vendors. Do you think that these activities are management ones?
In a manufacturing site, a machine operator makes processed products with machines. Do you think that these activities are management ones?
If there are no such activities, you cannot make a product, even if you have management.

In a big company often some management activities may be done in head quarter and some are done in a factory site. There are management levels, and it does not justify that management includes product realization processes.

Now I have become to understand that management activities and product realization processes are other things.
The cause of my misunderstanding may come from my experiences during working at the big company. At that time I worked at headquarter as a quality manager and all production jobs were done in factories. So I mixed up management within factories with product realization processes. In PDCA cycle at first I thought that headquarter did “Plan” and “Do” was done in factories.

It is very fortunate that you get the right place. In fact understanding difference between management and product realization processes is sometimes difficult, because when we see activities going a company both are mixed up. So we must discern the both in brain. It is a conceptual difference.
But in order to understand ISO9001:2000 correctly and install the system effectively, the right understanding of the difference is inevitable.