Six Sigma
Read this chapter, which gives a clear description of Six Sigma, when it is used, and how to interpret the results.
Methods and Control Charts
Control charts are the basis of statistical process controls methodologies, and are used to distinguish between random/uncontrollable variations and controlled/correctable variations in a system. Control chart detects and monitors process variation over time. It also plays a role as a tool for ongoing control of a process. There are many types of SPC control charts, though centering charts are used most often. The remainder of this article will focus on the different types of centering and dispersion charts. Figure 1 displays single point centering charts and Figure 2 displays subgroup sampling charts. Each figure has a brief description of the chart type within each of the two chart families (centering and dispersion). In the centering chart, the centerline is given by the average of the data samples, where as in the dispersion chart the centerline is the frequency distribution from that average.
| Chart Family | Chart Type | Description |
|---|---|---|
| Centering Chart | Individual | Uses individual point values to provide a trend. |
| Geometric Mean | Uses the geometric mean to provide exponential smoothing. | |
| Moving Average | Uses the moving average to remove noise and indicate an overall trend. | |
| Dispersion Chart | Range (R) Chart | Commonly called an R chart. Plots the range which is the difference between the highest and lowest sample in the range. The number of samples for calculating the range is configured by the user. |
Figure 1: Control chart types and descriptions for the single point sampling method.
| Chart Family | Chart Type | Description |
|---|---|---|
| Centering Chart | Average (Xbar) | Commonly called an Xbar chart. Plots the average of data in the specified range. All subgroup samples are saved until the specified size is met. The average is then calculated, and the value is written to disk. |
| Median | Plots the median value in the same manner as the average chart plots the average value. | |
| Dispersion Chart | Range (R chart) | Commonly called an R chart. Plots the range which is the difference between the highest and lowest sample in the subgroup. Samples are collected until the subgroup is complete, and then sorted in order of size. The average or median is determined for the centering chart, and then the range is calculated. |
| Range with Sigma | Plots the R values in the same manner as in the range chart, but the limits are calculated using a derivation value (sigma) that was entered during configuration. | |
| Root Mean Squared | Use for subgroups of 12 to 25 points. Uses the root mean square (RMS) to calculate the limits and centerline. | |
| Root Mean Squared with Sigma | Plot point in the same manner as the RMS chart, but the limits and the centerline are calculated using a deviation value (sigma) that was entered during configuration. | |
| Standard Deviation | Plots the standard deviation of the subgroup points. |
Figure 2: Control chart types and descriptions for the subgroup sampling method.
A very useful type of centering chart is the Xbar chart, also known as the Shewhart chart mentioned earlier in the article. Figure 3 gives an example of an Xbar chart (on top), as well as an example of a dispersion chart (on bottom). The charts are used in combination with a system of rule based checks to determine whether the system is in statistical control. These rules can be seen in Figure 4 for both the single point centering and subgroup sampling methods. Using these rules, one can inspect a given chart over a period of time and determine whether the system is in control. If the system is not in control they must then check the controllable aspects of the system to see where the problem is occurring.
Figure 3: The centering Xbar chart (Shewhart Chart) on top is used to determine whether the centering of the process is stable. The dispersion (R) chart on bottom is used to determine whether the spread of the process is stable
| Centering Type Chart | Criteria which show that the system is not in statistical control |
|---|---|
| Single Point Values |
1. Any of the points fall outside of the control limits. 2. Seven or more consecutive points fall on the same side of the centerline. 3. Ten of eleven consecutive points fall on the same side of the centerline. 4. Three or more consecutive points fall on the same side and all are located closer to the limit than the centerline. |
| Subgroup Sampling Method |
1. Any single subgroup is more than 3 standard deviations away from the centerline (or set point). 2. Two consecutive subgroup values are more than two standard deviations away from the centerline. 3. Three consecutive subgroup values are more than one standard deviation away from the centerline and on the same side of the centerline. 4. Two out of three consecutive subgroup values are more than two standard deviations away from the centerline, with all on the same side of the centerline. 5. Five consecutive subgroup values are on the same side of the centerline. |
Figure 4: Table showing the criteria that indicate if a system is not in statistical control for different types of centering charts
Note: We only need to see if any one of the criteria objectives are achieved to claim that the system is statistically out of control.
As can be seen from the figures above, the primary tool of SPC is the control chart. Several different descriptive statistics are used in control charts along with several different types of control charts that test for different causes of failure. Control charts are also used with product measurements to analyze process capability and for continuous process improvement efforts.