Parts Manufacturer Approval
It is generally illegal in the United States to install replacement or modification parts on a certificated aircraft without a PMA (although there are a number of exceptions to this general rule, including parts manufactured to government or industry standards, parts manufactured under technical standard order authorization [TSOA], experimental aircraft, etc.).
Thus, PMA-holding manufacturers are permitted to make replacement parts for aircraft, even though they may not have been the original manufacturer of the aircraft.
An applicant for a PMA applies for approval from the FAA. The FAA prioritizes its review of a new application based on its internal process called Project Prioritization. 
Application for a PMA is usually a two step process. First, the manufacturer-applicant must demonstrate to the FAA that it has a safe design for a part. The design must meet the requirements of the FAA's safety regulations and standards. This can be demonstrated in a number of ways. The applicant may rely on a licensing agreement with another approved manufacturer who has already obtained approval of the design in question. The applicant may use comparative analysis to show that the parts it makes are the same (in all relevant airworthiness characteristics) as other parts that are already approved. The manufacturer may rely on qualitative analysis to show through test and computation that the part directly meets the FAA's safety standards. The modern trend is to use a variety of techniques in combination in order to obtain approval of complicated parts - relying on the techniques that are most accurate and best able to provide the proof of airworthiness desired.
The second step in the application process is to seek FAA approval of the manufacturing quality assurance system (known as production approval). Production approval will be granted when the FAA is satisfied that the system will not permit parts to leave the system until the parts have been verified to meet the requirements of the approved design, and the system otherwise meets the requirements of the FAA quality system regulations.
Under the Civil Air Regulations (CARs), the government had the authority to approve aircraft parts in a predecessor to the PMA rules. This authority was found in each of the sets of airworthiness standards published in the Civil Air Regulations. CAR 3.31, for example, permitted the Administrator to approve aircraft parts as early as 1947. 
In 1952, the Civil Aeronautics Board adjusted the location of the parts production authority from the ".31" regulations to the ".18" regulations. For example, the CAR 3 authority for modification and replacement parts could be found in section 3.18 after 1952.
In 1955, the Civil Aeronautics Board separated the parts authority out of the airworthiness standards, and placed it in a more general location so that one standard would apply to replacement and modification parts for all different forms of aircraft.
In 1965 CAR 1.55 became Federal Aviation Regulation section 21.303.
The 1965 regulatory change also imposed specific obligations on the PMA holder related to the Fabrication Inspection System.
Amendment 21-38 of Part 21 was published May 26, 1972.  This was the next rule change to affect PMAs. This rule eliminated the incorporation by reference of type certification requirements in favor of PMA-specific data submission requirements. This change established the separate process and separate requirements for data that must be submitted by an applicant for a PMA (prior to this there was no explicit distinction between the application data requirements for type certificated products and the data requirements for PMAed articles).
The aircraft parts aftermarket expanded greatly in the 1980s as airlines sought to reduce the costs of spares by finding alternative sources of parts. During this time period, though, many manufacturers failed to obtain PMA approvals from the FAA.
In the 1990s, the FAA engaged in an "Enhanced Enforcement" program that educated the industry about the importance of approval and as a consequence a huge number of parts were approved through formal FAA mechanisms. Under this program, companies that had previously manufactured aircraft parts without PMAs could apply for PMAs in order to bring their manufacturing operations into full compliance with the regulations. This movement brought an explosion of PMA parts to the marketplace.
2009 Rule Change
The FAA published a significant revision to the U.S. manufacturing regulations on October 16, 2009. This new rule eliminates some of the legal distinctions between forms of production approval issued by the FAA, which should have the effect of further demonstrating the FAA's support of the quality systems implemented by PMA manufacturers. Specifically, instead of having a separate body of regulations for a PMA Fabrication Inspection System (FIS), as was the case in prior regulations, the PMA regulations now include a cross reference to the 14 C.F.R. § 21.137, which is the regulation defining the elements of a quality system for all production approval holders. In practice, all production approval holders were held to the same production quality standards before the rule change - this will now be more obvious in the FAA's regulations. Accomplishing this harmonization of standards was an important goal of the Modification and Replacement Parts Association (MARPA).
The new rule becomes effective April 16, 2011. The FAA's FAQ on Part 21 states that PMA quality systems will be evaluated for compliance by the FAA during certificate management activity after the compliance date of the rule.
Relationship to repair
The FAA is also working on new policies concerning parts fabricated in the course of repair. This practice has historically been confused with PMA manufacturing, although the two are actually quite different practices supported by different FAA regulations. Today, FAA Advisory Circular 43.18 provides guidance for the fabrication of parts to be consumed purely during a maintenance operation, and additional guidance is expected to be released in the near future. One of the key features of AFC 43.18 is that it recommends implementation of a quality assurance system quite similar to the fabrication inspection systems that PMA manufacturers are required to have.
The trade association representing the PMA industry is the Modification and Replacement Parts Association (MARPA). MARPA works closely with the FAA and other agencies to promote PMA safety. MARPA maintains a website at http://www.pmaparts.org.
- 14 C.F.R. 21.303 PMA
- 14 C.F.R. 21.9(a)
- 14 C.F.R. 21.9(a)(2)
- See Aircraft Technology, Calnek, Matthew, December 2014, A Change of Priorities, http://www.aecotechnologies.com/wp/wp-content/uploads/2014/12/AECO_AircraftTechnology_Dec2014.pdf, Seattle, January 5, 2015.
- Parts Manufacturer Approval Procedures, FAA Order 8110.42C, Chapter 2, Paragraph 5 (June 23, 2008)
- 14 C.F.R. 21.137
- See, Certification Procedures for Products and Parts, 29 Fed. Reg. 14562 (Oct. 24, 1964) (explaining in the preamble that the authority for producing parts had previously been in the ".18" sections of CARs 3, 4b, 5, 6, 7, 13, and 14).
- See 12 Fed. Reg. 7898 (1947) (promulgating Amendment 03-3 to CAR 3).
- 17 Fed. Reg. 1083 (Feb 5, 1952) (Civil Air Regulation Amendment 3-7 was effective March 5, 1952).
- Civil Air Regulation (CAR) 1.55 (adopted on April 13, 1956).
- Certification Procedures for Products and Parts, 29 Fed. Reg. 14562 (Oct. 24, 1964) (this change became effective February 1, 1965).
- 14 C.F.R. § 21.303(c) (1965).
- Replacement and Modification Parts, 37 Fed. Reg. 10658 (May 26, 1972) (this change became effective June 26, 1972).
- 14 C.F.R. § 21.303(c) (1973).
- 60 Fed. Reg. 10480 (February 27, 1995)
- Production and Airworthiness Approvals, Part Marking, and Miscellaneous Amendments, 74 Fed. Reg. 53368 (October 16, 2009)
- 14 C.F.R. 21.303(h)(2009)
- 14 C.F.R. 21.137
- See Production and Airworthiness Approvals, Part Marking, and Miscellaneous Amendments, 74 Fed. Reg. 53368, 53377 (October 16, 2009) (describing the elimination of the FIS requirements and the new cross reference to section 21.137)
- Parts Manufacturer Approval Procedures, FAA Order 8110.42C (June 23, 2008)
- See Production and Airworthiness Approvals, Part Marking, and Miscellaneous Amendments, 74 Fed. Reg. 53368, 53380 (October 16, 2009) (describing the implementation schedule, and setting the implementation date at 18 months after publication in the Federal Register)
- FAA Questions & Answers: 14 CFR Part 21 Amendments, Subpart G – Production Certificates, Section 21.137, Question Four (updated April 27, 2010)
- Compare 14 C.F.R. 21.9(a)(6)(authority for fabrication in the course of maintenance) with 14 C.F.R. 21.301 et seq. (PMA regulations)
- Agenda for the 2008 FAA-EASA International Safety Conference, in which MARPA's President (Jason Dickstein) is speaking on collaborative efforts to improve supplier control
- 70 Fed. Reg. 65713 (November 9, 2006)(FAA acknowledges the assistance of Jack Buster, MARPA Airworthiness Directive Committee)