How can the management of quality contribute to competitive advantage?

Quality assurance can create competitive advantage in several possible ways. The first and most obvious is that buyers, whether individual consumers or other businesses, prefer reliable, consistent products. Especially with the ease of internet searches, the availability of reliability ratings from places like Consumer Reports, and the tendency for quality assurance failures to go viral, quality assurance is an important marketing tool to generate competitive advantage. For example, a survey by J. D. Powers suggests that reliability and durability are the top reason for buyers selecting certain car models; both of these are outcomes of use of quality assurance. 
Sophisticated quality assurance tools can also reduce costs, especially when integrated into every step of the production process. Rather than doing inspections after the fact and having to discard flawed products, manufacturers use techniques such as Total Quality Management and Six Sigma to build quality into every step of a process. Since these techniques reduce wastage while ensuring a more consistent product, they both cut costs and increase customer satisfaction, two elements of competitive advantage. 
https://www.jdpower.com/Cars/Shopping-Guides

The question asks how the management of quality can contribute to competitive advantage. Of course, having a product or service superior in quality to one’s competition is likely to drive increased sales and the ability to charge higher prices. The question asks about the management of quality, however. By this, we mean the approaches employed to specifically measure what aspects constitute quality and to manage processes so as to reliably replicate those product or service metrics. 
The primary concept applicable to this is TQM or Total Quality Management. As a methodology, this achieved definition and general acceptance in the 1950’s. It is based on the ideas that: 

Quality is measurable by means of defining what features are desired in a product or service and defining metrics for those features.


Quality is reproducible; the inputs and processes which produce quality can be defined and controlled.


Quality is a result of the combined action of the entire firm and the business ecosystem in which it operates, most importantly its supply chain, so managing it must take this ecosystem into account.

 That being said, effective management of quality provides a firm with advantage over its competitors in two ways. First, it makes its product features reliable, so that the firm’s customers know exactly what to expect from each purchase. Second, it defines exactly the causes of specific quality outcomes, so that sources of inconsistency may be identified and eliminated, and so that improvements to quality can be made.
The sites referenced below provide more in-depth material on TQM and associated management practices.
https://www.isixsigma.com/methodology/total-quality-management-tqm/introduction-and-implementation-total-quality-management-tqm/