Quality is a slippery concept which carries a variety of meanings and serves variety of purposes. One person's "high quality" may be an old-fashioned conceit, and their "poor quality" or another's sufficiency.
It is a notion with both absolute and relative measures, and varies according to the age and environment. The traditional approach to quality speaks of high standards of production, delivery and presentation. This suggests the kind of perfection that goes with no expense being spared, or the best that money can buy. It confers exclusiveness and status on the customer. It has class connotations: "the Quality" was once a phrase used by working-class people to describe the upper classes. The scientific approach to quality is based on the idea not of perfection but of "fitness for purpose". It involves the specification of standards to which goods or services must conform and is driven by experts ("scientific managers"), who set standards and monitoring outcomes. It grew out of the era of mass production and assembly-line working, and uses techniques such as such as performance measurement and auditing. Its limitation is that it is a closed system which finds it difficult to reconcile often radically different perceptions of providers and the public. Its opposite in this sense is the excellence approach to quality, which is a measure not of fitness for purpose but of customer satisfaction.
Liberty and equality are goals that can conflict. The process of defining and assuring quality becomes, in effect, a means of bridging the gap between them.