Introduction to Six Sigma (Statistical Process Control)


Six sigma is a statistical approach to defect reduction. A "six-sigma" capable process produces less than 4 defects for every million parts.

To contrast Six-Sigma and Lean approaches, Six sigma is about reducing process variation and Lean is about reducing process waste.

Specification Limits

Products have a set of mechanical dimensions and performance specifications that are expected by the customer. These are typically mentioned on the product drawing and the datasheet.

Fig. A: Flange-nut

Consider a simple product - a Flange-nut - as shown in fig. A. Now, consider a mechanical specification for the flange-diameter. According to the customer, the allowed limit for the flange-diameter is 0.9" to 1.0".

The Upper Specification Limit (USL) = 0.10"
The Lower Specification Limit (LSL) = 0.09"
Range = USL - LSL = 0.10""


In our example of a simple product - a flange nut, let us assume the manufacturer produces 10 nuts and measures the flange-diameter for each nut.

Table 1: Measurement of the diameter of the ten samples – raw data

If we want to find out the most likely value of the flange-diameter of the production parts, we can calculate the number of occurrences (frequency) for each value of the flange-diameter.

Table 2: Measurement of the diameter of the ten samples – arranged by number of occurrences

If we plot this data as a bar graph, we get a histogram. A histogram is an accurate representation of the distribution of numerical data.

Fig. B: Histogram representation of the measurement of the diameter of the ten samples

Standard deviation

Standard deviation (represented by σ) is a measure the amount of variation or dispersion in a set of data-values.

In our example of a flange-nut, σ of the flange-diameter captures the dispersal between the average flange-diameter and the outliers.

The formula for standard deviation (SD) is

where ∑ means "sum of", x is a flange-diameter of a measured flange-nut in our sample-set, μ is the average flange-diameter, and N is the number of measured samples (in our example, N is 10).

This means that the flange-diameter of most of the manufactured nuts would be within a spread of 0.0017".

Fig. C: Standard deviation of the measurement of the diameter of the ten samples

Run-chart/ Control-chart/ SPC chart

Consider the histogram chart in fig. A. If we rotate the chart 90° anti-clockwise, we get an SPC chart!

Fig. D: A control-chart is simply a histogram turned 90 degrees (and divided into red, yellow and green zones)

An SPC chart is typically divided into green, yellow and red bands.

Green zone: This sub-range of the specification denotes the deviation from the nominal specification that is unavoidable even during ideal manufacturing process condition.

Yellow zone: This sub-range of the specification denotes the deviation outside of the green-zone where the parts are still considered good (because they are within the specification limit) but represent a process that is less than ideal and may require some attention to bring it back to the ideal-state. Typical preventive actions to bring a process from yellow to green may include Re-calibration, tool change, lubrication replenishment or raw material replenishment.

Red zone: This zone outside the specification limits denotes unacceptable parts from a process that has strayed too far away from its ideal state. The process requires urgent attention. Typical corrective actions to bring a process from red to green may include stopping the process and discarding all in-process parts and then recalibrating the machine or a tool change, lubrication replenishment or raw material replenishment.

Control Limits

The upper and lower limits of the green zone are called the upper and lower control limits respectively (UCL and LCL). There is no standard formula to calculate the control limits of a manufacturing process. Process engineers have to determine the control limits best-suited to their process. Some factors that may be considered to set meaningful control limits are:

  1. Transit time for your process to traverse an entire yellow band (upper or lower). That is the typical time in which the process may go from green to red. The control limit should then be set such that the equipment operators have sufficient time to take preventive action when the process enter the yellow area (i.e. crosses the control limit).
  2. Sampling frequency of in-process inspection: Once again, sampling frequency should be such that once the process is identified as being in the yellow zone, equipment operators have sufficient time to take preventive action.
  3. Cost-benefit analysis and risk analysis of corrective vs. preventive action. Here, preventive action means pre-emptively re-calibrating the process when it enters the yellow zone. Corrective action here means stopping and re-calibrating the process after it has entered the red zone.
  4. Probability of Type I (false-positive) and Type II (false negative) errors if an inspected part is in the yellow or red zone. For example, high likelihood of false-positives in yellow zones means frequent and unnecessary interventions.
  5. Inherent variation (also known as common-cause variation) in your process even when the process in is ideal-state. Control limits should be set so that common-cause variation lies within the green zone.
  6. Allowable number of defects: The number of defects that may be tolerated can be used to determine the green zone (i.e. control limits).


Implementing a six-sigma project in an organization for the first time typically involves five phases: Define, Measure, Analyze, Improve, Control.

Define phase: In this phase, identify the metrics that are important for the success of your product (i.e. customer satisfaction). The metrics may include a product's mechanical dimensions, performance specifications, shipping time, process throughput. Remember, the six-sigma philosophy can be applied to non-manufacturing processes as well. Defining the right metrics to improve in your Six-Sigma implementation is the most important phase of the project. Customer interviews, focus groups, QFD (Quality Function Deployment) diagram, SIPOC analysis and Kano analysis are some of the tools that may be used to identify the metrics that need improvement.

Measure phase: The goal of this phase is to:

  • Choose a measurement system after considering measurement uncertainty i.e. the accuracy and the precision of the gage including repeatability and reproducibility. As a thumb rule, an acceptable measurement system introduces variation that is less than 25% of the measurement range (USL - LSL). The variation introduced by a measurement system can be determined using Gage R&R test.
  • Determine the sampling plan : frequency, sample size, metrics under measurement and Gage.
  • Set improvement targets (Example: Cp or Cpk)

Analyze phase: Once sufficient data on your chosen metrics is available, it's time to decide whether the process is satisfactory in its current form or if it needs improvement. In order to improve the process capability, analysis of factors that impact the process is necessary. Statistical tools used in this phase include ANOVA (Analysis of Variance) and sub-tools like DoE (Design of Experiments) and Taguchi test. The goal of this phase is to find optimal process inputs to achieve the desired process capability.

Improve phase: The goal of this phase is to implement the optimal parameters identified in the previous phase. This is a full-scale implementation of the project.

Control phase: This is about sustaining the improvements made. Tools in this phase include control charts, error-proofing and Layered Process Audits (LPA).