What is DMAIC and DMADV ?

Six Sigma has two key methodologies DMAIC and DMADV. DMAIC is used to improve an existing business process. DMADV is used to create new product designs or process designs in such a way that it results in a more predictable, mature and defect free performance.
DMAIC
Basic methodology consists of the following five phases:

Define- formally define the process improvement goals that are consistent with customer demands and enterprise strategy.
Measure- to define baseline measurements on current process for future comparison. Map and measure process in question and collect required process data.
Analyze- to verify relationship and causality of factors. What is the relationship? Are there other factors that have not been considered?
Improve - to optimize the process based upon the analysis using techniques like Design of experiments.
Control- setup pilot runs to establish process capability, transition to production and thereafter continuously measure the process and institute control mechanisms to ensure that variances are corrected before they result in defects.
DMADV
Basic methodology consists of the following five phases:

Define- formally define the goals of the design activity that are consistent with customer demands and enterprise strategy.
Measures- to identify CTQs, product capabilities, production process capability, risk assessment, etc.
Analyze-to develop and design alternatives, create high-level design and evaluate design capability to select the best design.
Design- to develop detail design, optimize design, and plan for design verification.
This phase may require simulations.
Verify-to design, setup pilot runs, implement production process and handover to process owners. This phase may also require simulations.