To increase maturity in SDLC is is generally recommended to implement the Primary SDLC processes. If you already have these processes fully optimised and have reached Maturity Level 5, it is time to implement the Supporting and Organisational processes. See Maturing your SDLC for more details.
The Primary Life Cycle Processes include four process groups, they are Acquisition, Supply, Engineering and Operation process groups. Oganisations that want to improve their processes begin with these primary processes. Often many organisation commence with the Engineering process group.
Acqusition Sub Processes
The Acqusition Process Group includes Acquisition Preparation, Supplier Selection, Contract Agreement, Supplier Monitoring and Customer Acceptance.
Supply Sub Processes
The Supply Process Group includes Supplier Tendering, Product Release, Product Acceptance Support.
The Engineering Sub Process Group
The Engineering Process Group includes Requirements elicitation, System requirements analysis, System architectural design, Software requirements analysis, Software design, Software construction, Software integration, Software testing, System integration, System testing Software installation, Software and system maintenance.
The Operation Sub Processes
The Operation Sub Process Group includes Operational use and Customer Support.