Process Capability Chart

Standard Filters

  • Company
  • Year
  • Quality Order Inspection Origin
  • Business Partner
  • Item
  • Quality Aspect
  • Quality Characteristic
  • Quality Statistical Chart

Process Capability Control Chart

The Process Capability Control Chart displays data based on actual inspection results. The chart consists of an upper and a lower plotting area. The upper plotting area is used to monitor the process mean and the lower plotting area is used to monitor the process deviation from the mean.

For the three most commonly used chart types, which users can access using the Process Control Chart Type filter, see these sections:

Xbar and R control charts

These charts are used where the sample size is constant and relatively small, typically between 2 to 15 units.

This combination of charts is used where the characteristic of interest sample size is stable, fixed, and between 2 to 15 units. The upper plotting area of the chart is showing the average ( ) measured value of a sample subgroup, i.e. the samples of one inspection order. The x-axis represents the time dimension. The lower plotting area of the chart shows the spread/range (R) of the measured values within each sample. The convention is that the chart is displayed in the upper portion of the screen and the R charts in the lower portion.

To compose Xbar and R Control charts:

  1. Consider the samples of one inspection order to be a subgroup.
  2. Calculate the average of measured value for each subgroup:

    QM_Xbar_Rcontrol_formula1

  3. Calculate the range for measured values of each sub-group.

    Range subgroup = Largest Measured Value subgroup - Smallest Measured Value subgroup.

  4. Calculate the grand mean of each subgroup’s average. The grand mean of each subgroup’s average becomes the centerline for the upper plotting area of the chart:

    QM_Xbar_Rcontrol_formula2

  5. Calculate the average of subgroup ranges. The average of all subgroups becomes the centerline for the lower plotting area of the chart:

    QM_Xbar_Rcontrol_formula3

  6. Calculate UCL and LCL for averages of subgroups. Use this formula to calculate the limits, which are plotted in the upper plotting area:

    QM_Xbar_Rcontrol_formula4

    Note: The limits are calculated based on the A2 value (from Factors for Control Limits) for the corresponding subgroup size N. If the sample size is not constant, then determine the average sample size and use this as input for determining the A2 value. If the (average) sample size exceeds 15 units, do not calculate the control limits but give a warning and display the charts. For a table of factors, see Factors for Control Limits.
  7. The range limits are calculated using D3 and D4 values for the corresponding subgroup size N. Calculate the control limits for the ranges, using this formula:

    QM_Xbar_Rcontrol_formula5

    These limits are plotted in the lower plotting area. For a table of factors, see Factors for Control Limits.

Xbar and S control charts

These charts are used where the sample size is variable, or relatively large, or both, typically greater than 10 units.

This combination of charts is used where the characteristic of interest sample size is variable and/or larger than 15 units. The upper plotting area of the chart shows the average ( ) measured value of a sample subgroup, i.e. the samples of one inspection order. The x-axis represents the time dimension. The lower plotting area of the chart shows the standard deviation (S) of the measured values within each sample. The convention is that the chart is displayed in the upper portion of the screen and the S chart in the lower portion.

To compose Xbar and S Control Charts:

  1. Consider the samples of one inspection order to be a subgroup. Calculate the average of measured values for each subgroup:

    QM_Xbar_Scontrol_formula1

  2. Calculate the standard deviation S of each subgroup:

    QM_Xbar_Scontrol_formula2

  3. Calculate the grand mean of all observations. Because the sample size can be variable, this grand mean cannot be calculated by determining the grand mean of the sample averages calculated in step 1. Instead, all observations must be cumulated and divided by the number of observations. The calculated grand mean becomes the centerline for the upper plotting area of the chart.
  4. Calculate the grand mean standard deviations. This grand mean cannot be calculated by determining the grand mean of the sample averages calculated in step 2. Instead, the standard deviation across all observations within the given range selection must be determined. The calculated grand mean becomes the centerline for the lower plotting area of the chart.
  5. Calculate UCL and LCL for averages of subgroups. Use these formulas to calculate the control limits:

    QM_Xbar_Scontrol_formula3

    These limits are plotted in the upper plotting area. See Factors for Control Limits about how to calculate the c4 factor.

  6. The range limits for the standard deviations are calculated using these formulas:

    QM_Xbar_Scontrol_formula4

    These limits are plotted in the lower plotting area. See Factors for Control Limits about how to calculate the c4 factor.

Xm and R control charts

These charts are used when the characteristic of sample size is more dynamic and varied due to inherent instability in the process that is executed.

This combination of charts is used where the characteristic of interest sample size is more dynamic and varied due to inherent instability in the process being carried out. Because of this variability, the control charts cannot be used effectively. The Xm and R Control chart handles each sample as a unique observation. This control chart is a combination of two charts; the individual X chart in the upper portion of the screen and the moving R chart in the lower portion. The upper plotting area of the chart shows the measured values of all instances within a sample, the x-axis represents the time dimension. The lower plotting area of the chart shows the moving spread/range (R) of the measured values compared to the preceding measurement.

To compose the Xm and R charts:

  1. Assuming that each sample test result is an individual observation, each sample measured value is plotted as an individual X point. Consider that Xi represents the measured value of an individual sample. Individual Xi values are plotted on the x-axis in the upper plotting area.
  2. Calculate the Moving Range values between two successive Xi data points using this formula:

    QM_Xm_Rcontrol_formula1

    The Moving Range mRi is plotted on the x-axis in the lower plotting area. The brackets (| |) represent the absolute value of the number inside the brackets.

  3. Calculate the overall average of the individual Xi data points. The average of Individual X values becomes the centerline for the upper plot.

    QM_Xm_Rcontrol_formula2

  4. Calculate the average of the moving ranges. The grand average of all moving ranges becomes the centerline for the lower plotting area.

    QM_Xm_Rcontrol_formula3

  5. Calculate the upper and lower control limits for the individual X values for the upper plotting area. Use this formula for the computation:

    QM_Xm_Rcontrol_formula4

    The value 2.66 is the d2 factor for n = 2. For a table of factors, see Factors for Control Limits.

  6. There is no lower control limit for moving range charts. The upper control limit is calculated as follows:

    QM_Xm_Rcontrol_formula5