Is it true that improvements in quality always means reductions in costs?
No. Only by defining quality in a certain way and by taking a process, which already is somewhat inefficient and ineffective, can you make that statement true. It is perfectly possible to visualize a process where quality has been improved at the same time that cost has gone up, just as well as it is possible to improve an increase in quality at the same time as cost is going down. Quality is usually defined as conformity with specifications. These specifications should be made from a client perspective, assuming that the client is competent enough to formulate and judge such a perspective. In the U.S. we have so many different rating processes and associations that judge the quality of products, that it is often clearly decided where on the quality spectrum your particular product or service is located. If so, there will be a market price attached to that level of quality, and that means that for you to improve profitability you must be able to reduce costs.
