u chart

u chart is a type of control chart used in statistical process control to monitor the rate of defects per unit in a process over time, where sample sizes can vary.

Map the data fields

• Subgroup/Lot: This field represents the different lots or batches of items being inspected.
• Process variable: This field contains the number of defects found in each lot.
• Sample Size: This field indicates the number of units inspected in each lot (can vary between lots).
• UCL: Optional field for custom upper control limits.
• LCL: Optional field for custom lower control limits.
• Central Line: Optional field for custom center line values.

Calculation Methodology

The u-chart calculations are performed as follows:

Average defects per unit (ū)

ū = Total Defects / Total Samples

Standard Error for Each Sample

Standard Error = √(ū / Sample Size)

Control Limits

For each data point:

Upper Control Limit (UCL):

UCL = ū + (Z-Score × Standard Error)

Lower Control Limit (LCL):

LCL = ū - (Z-Score × Standard Error)

Center Line (CL):

CL = ū (average defects per unit)

Defects per Unit for Each Sample:

Defects per Unit = Defects / Sample Size

Notes:

• If custom limits are provided, they override the calculated values
• The Z-Score determines the confidence level (typically 3 for 99.7% confidence)
• u charts allow for variable sample sizes between lots, making control limits vary for each point
• The actual defects per unit ratio is plotted for each lot
• Control limits are recalculated for each sample based on its specific sample size