I don't know if actual quality of weld is addressed by this standard. I haven't studied it closely. Good Welding and Cutting safety practices can definately aid in the prevention of accidents at chemical plants by reducing the risk of fires and explosions during these operations.

A "good" weld can reduce risk to people in all industries.

I would think the quality of the welds is governed by the applicable ANSI B31 or other standard.

I have not worked with the 1910 since I retired 2 years ago but what I think you're asking about focuses around anyone performing welding in or for a chemical producing facility. This includes maintanence (repair) and new construction, piping, vessels, structural, & storage tanks. In a nutshell, it requires a facility (Owner) to establish principles, programs, and practices (specifications) ensuring that all operating processes are safe. Also known as Process Safety Mangement
I believe your question as how the 1910 relates to welding and weld quality has to do with Owner and Supplier responsibilities and how compliance is managed and ensured. Basicly this means anybody (Owner or Supplier) who's weld product is used in a facility shall have a program in place that establishes a uniform quality system which describes how they ensure and verify compliance to the design specifications and accept responsibility.
Since the Supplier may not know the details specific to chemical plant operations, weld quality is measured by industry standards and conformance to specifications. In order for the Supplier to fulfill this responsibility they must have a quality control organization that has the authority, expertise, and resources to insure that minimum levels of weld quality are delivered. Also the Supplier must have a method to determine all of the requirements for each job. The Supplier must have a method to insure, and document, that all requirements have been satisfactorily completed.
Collectively speaking, the Supplier is required to develope and implement a welding quality control/assurance program not unlike a "code" pressure vessel shop. What I've described is required of the Owner also if they do any welding of their own.
What I've tried to depict here is only a "thumbnail" sketch of my experiences of how the 1910 and the mechanical integrity process relate to weld quality. Hope I helped you out alittle and sorry I was "long-winded".