There are many different types of teams that are used to attack different projects.
Six Sigma Teams
General Improvement Teams
Some have continuity and longevity but they are generally selected by any group (dept, division) that decides to solve a quality or productivity problem. Management usually chooses the problem for the team to work and acts as a sponsor but it is up to the team to identify and choose the solution.
Process Improvement Teams
A process improvement usually includes team members from multiple departments so they can examine the overall flow of the entire process from end-to-end.
Project / Task Force / Ad Hoc Teams
These teams are usually created for and last as long as the project does, disbanding shortly after. Team members are chosen based on their knowledge and experience in a particular subject. The project is usually chosen by management and has tight boundaries for the assignment. The team can be comprised of all management personnel, all work area, or any combination there of.
These are the most common teams. Generally they are comprised of a natural work team. The name cellular comes form manufacturing where groups of people will act as a cell to fabricate or assemble parts. These teams can either be led by management or self-directed.
These teams often (but not always) come together on their own, operate with minimal input from management, and have more continuity and longevity than other teams. The team selects its own leader to coordinate activities, but that team leader operates on an equal footing with the team members.
Cross Functional Teams
These teams are comprised of subject matter experts and representatives from multiple departments or areas (functional, process, geographic, etc) in the organization. Selecting these team members should be done with care and though. The team is often used on a Project or Improvement tam and are best suited for Experimentation teams.
Note: To be honest I have trouble finding an official approved definition of what a Parallel team is. I have (2) potential, not entirely disagreeing definitions. I include this material to provide background to the ASQ Black Belt sample question (included at the bottom of this page) that provides an answer I do not fully agree with. I leave it to the belt candidate to consult their own training materials to determine what the best definition is here. If anyone can find a definition of a parallel team citing an industry standard or recognized professional organization I ask that they include it below in the comments.
Parallel Teams as Competitive Insurance
One definition of parallel teams I have found is the practice of establishing 2 or more teams and tasking each with the same goal but dictating no set way of achieving the goal. In this way the organization increases their chances of finding divergent solutions that wholly or partially meet the project goal.
For example, say that you had to engineer a new kind of mobile device that was more powerful than any on the market and simultaneously required less down time to charge.
Chartering two or more teams might identify solutions as disparate as dynamic software to control battery life while another invents more efficient batteries, while a third invents a less power-hungry processor, while a 4th invents a novel display mechanism.
While it may seem counter-intuitive to charter multiple teams towards the same goal, it may be necessary for mission critical projects. Also, the parent organization gets the benefits of all solutions arrived at and has the ability to pick and choose or even combine some or all solutions.
Parallel Teams as Additional Capacity
Another definition that I found for parallel teams are as excess capacity. I’ve included a quote and the source below.
Collateral organizations are also called parallel teams Fisher, D. (2000). Communication in organizations (2nd ed.). New York, NY: Jaico. These are groups that are usually created “outside regular authority and communication structures to identify and work on problems that the formal organization is unwilling or unable to deal with.” Fisher, D. (2000). Communication in organizations (2nd ed.). New York, NY: Jaico, pg. 322. For instance, an organization like a university can hire a parallel team to create better advertising and marketing campaigns and let them focus on educating students. Parallel teams can be very beneficial because it usually happens outside the organization itself.Attribution.
Types of Teams Questions
Question: Which of the following best describes a team that has members with different skills or roles from different areas within the organization? (Taken from ASQ sample Black Belt exam.)