One definition of “Six Sigma” is a target for quality characteristics of units produced by the engineered system being improved (Shina, 2002; Tadikamalla, 1994). It is a rating that signifies “best in class”, with only 3.4 defects per million units or operations.
A part or item is classified as defective if the desired measurement, denoted by X, is outside the upper or lower specification limits (USL or LSL). In addition to specifying the USL and LSL, a target value is specified, which typically is the midpoint between the USL and LSL.
The symbol sigma (σ) is a letter in the Greek alphabet used by modern people to describe variability. In Six Sigma, the common measurement index is defects per million opportunities and can include anything from a component, piece of material, line of code, an administrative form, time frame or distance. A sigma quality level offers an indicator of how often defects are likely to occur, where a higher sigma quality level indicates a process that is less likely to create defects. Consequently, as sigma level of quality increases, product reliability improves, the need for testing and inspection diminishes, work in progress declines, cycle time goes down, costs go down, and customer satisfaction goes up.
Six sigma is a condition of the generalized formula for process capability, which is defined as the ability of a process to turn out a good product. It is a relationship of product specifications to manufacturing variability, measured in terms of Cp or Cpk, or expressed as a numerical index. Six sigma is equivalent to Cp=2 or Cpk=1.5.The definition of the capability of the process or Cp is: (1.1)
Specifically, (1.2)
This formula can be expressed conceptually as,
Cp = product Specifications / manufacturing variability (1.3)
The equation for Cpk is: (1.4)
Six sigma is achieved when the product specifications are at of the manufacturing process corresponding to Cp=2 or Cpk=1.5. Design engineers normally set the product specifications, whereas manufacturing engineers are responsible for production variability. The object of increasing the process capability to six sigma is twofold: either increase the product specifications by widening them, or reducing the manufacturing variability. Either effort can have a positive effect on reaching six sigma.
An alternative and more common definition for “Six Sigma” methods, implied by Pande and Holpp (2001) and Watson (2002a), is a series of ordered activities with associated component methods (Allen, 2003). Six Sigma is a disciplined and quantitative approach involving setting up a system and process for the improvement of defined metrics in manufacturing, service, or financial processes. The approach drives the overall process of selecting the right projects based on an organization’s business goals and selecting and training the right people to obtain the results. Improvement projects follow a disciplined process defined by a system of five macro phases. These component methods derive from statistics, marketing, and optimization and are sequenced as Define, Measure, Analyze, Improve, and Control (DMAIC). In design projects the specifics of the DMAIC steps are often modified to DMADV;
Define customer requirements and goals for the product.
Measure and match performance to customer requirements.
Analyze and assess product design.
Design and implement new product.
Verify results and maintain performance.
The phases of DMAIC are described by Rasis, Gitlow and Popovich (2003a and 2003b) as follows:
Define Phase: Define the project’s objectives by identifying customer requirements often called “CTQs” “critical to quality”, develop a team charter and define process map.
• Identify the process or product for improvement, identify customers and translate the customer’s needs into CTQs.
• The team charter involves selection of team members and defining of roles, developing the problem and goal statements, determining project scope, setting project milestones and preparing a business case to gain management support.
• Do a high level process map connecting the customer to the process.
Measure Phase: Measure the existing systems. Establish valid and reliable metrics to help monitor progress towards the project goals. Customer expectations are defined to determine “out of specification” conditions.
• Identify and describe the potential critical processes/products. List and describe all of the potential critical processes obtained from brainstorming sessions, historical data, yield reports, failure analysis reports, analysis of line fallout and model the potential problems.
• Perform measurement system analysis. Determine precision, accuracy, repeatability and reproducibility of each instrument of gauge used in order to ensure that they are capable.
Analyze Phase: Analyze the system to identify ways to eliminate the gap between the current performance of the system or process and the desired goal. In this phase, project teams explore underlying reasons for defects. They use statistical analysis to examine potential variables affecting the outcome and seek to identify the most significant root causes. Then, they develop a prioritized list of factors influencing the desired outcome.
• Isolate and verify the critical processes. Narrow the potential list of problems to the vital few. Identify the input/output relationship which directly affects specific problems. Verify potential causes of process variability and product problems.
• Perform process and measurement system capability studies. Identify and define the limitations of the processes. Ensure that the processes are capable of achieving their maximum potential. Identify and remove all variation due to special causes. Determine what the realistic specifications are. Determine confidence intervals. A process is to be considered capable when it is in control, predictable, and stable.
Improve Phase: In this phase, project teams seek the optimal solution and develop and test a plan of action for implementing and confirming the solution.
The process is modified and the outcome is measured to determine whether the revised method produces results within customer expectations.
• Conduct design of experiment. Select design of experiment factors and levels, Plan design of experiment execution. Perform design of experiment to find out the most significant factor.
• Implement variability reduction designs/assessments. Implement permanent corrective action for preventing special cause variations. Demonstrate process stability and predictability.
Control Phase: Control the new system. Ongoing measures are implemented to keep the problem form recurring. Institutionalize the improved system by modifying policies, procedures, operating instructions and other management systems.
• Specify process control methods. Establish on-going controls for the process based on prevention of special cause variation using statistical process control techniques.
• Document the improvement processes. Record all the processes/steps in improvement phase using the decision tree and reaction plan.
The methods are generally taught in the context of system improvement projects and expertise is often characterized by an analogy to karate “belts”: “black belt”, “green belt”, etc. For thousands of participants at the lowest “green belt” level of accreditation, one of the main benefits of “Six Sigma” training is that it simplifies (through restriction) the sequence and choice of available techniques to apply to a particular case. Therefore, the value of the six sigma movement derives partly from standardization of problem solving methods and partly in how it guides people to suggest which techniques to apply in which order to an improvement project.
Contributing to the widespread deployment of Six Sigma is an abundance of anecdotal evidence attributing quality, productivity, and costs benefits to this particular quality improvement initiative. Scientific evidence to lead credence to the anecdotal evidence has been rather limited and exists primarily as small-sample case studies. Moreover, while the empirical results from these case studies have generally been atheoretical in nature, their conduct had not been governed by rigorous, a priori theory development.
Bisgaard and Freiesleben (2000) showed how defect elimination and prevention associated with a Six Sigma program can improve financial results. Their view was to do or not to do a project. Hild, Sanders, and Cooper (2000) discussed the different structures of Six Sigma based on processes type, continuous or discrete. Sanders and Hild (2000a and 2000b) outlined the importance of considering organizational issues in the structuring of successful Six Sigma projects. Snee (2001a) similarly stated that one of the keys was to understand the environment in order to tailor Six Sigma projects; type of company (manufacturing or service), type of function (operations, transactional, administrative, or new product development) and type of industry (assembly, processing, chemical, etc.). Pyzdek (2001b) pointed out the importance of selecting the right individual to act as project leader even before they are trained.
Pande, Neuman, and Cavanagh (2000) contributed probably the most complete and explicit version of the Six Sigma methods. Yet, even their version of the methodology leaves considerable latitude to the implementers to tailor approaches to applications and to their own tastes. This lack of standardization of the methodologies explains, at least in part, why the American Society for Quality did not have a certification process until 2001.
