np chart

np chart

np chart is a type of control chart used in statistical process control to monitor the number of defective items in a process over time with constant sample sizes.


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 defective items in each lot.
  • Sample Size: This field indicates the number of items inspected in each lot (should be constant for np charts).
  • 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 np-chart calculations are performed as follows:


Proportion defective (p̄)

p̄ = Total Defectives / Total Samples

Number of defectives (np̄)

np̄ = Sample Size × p̄

Standard Deviation

Standard Deviation = √(np̄ × (1 - p̄))

Control Limits

For each data point:


Upper Control Limit (UCL):

UCL = np̄ + (Z-Score × Standard Deviation)

Lower Control Limit (LCL):

LCL = np̄ - (Z-Score × Standard Deviation)

Center Line (CL):

CL = np̄ (expected number of defectives)

Actual Defectives for Each Sample:

Number of Defectives = Defectives count for each lot

Notes:

  • If custom limits are provided, they override the calculated values
  • The Z-Score determines the confidence level (typically 3 for 99.7% confidence)
  • np charts are used when sample sizes are constant across all lots
  • The actual number of defectives is plotted directly (not as a proportion)
  • Control limits are calculated based on the expected number of defectives per sample