G chart

g chart is a type of control chart used in statistical process control to monitor the number of conforming units between occurrences of nonconforming units (geometric distribution).

Map the data fields

• Subgroup/Lot: This field represents the different lots or time periods being monitored.
• Process variable: This field contains the number of conforming units between nonconforming occurrences.
• 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 g-chart calculations are performed as follows:

Average gap between nonconforming units (ḡ)

ḡ = Total Conforming Units / Number of Nonconforming Units

Standard Deviation

Standard Deviation = √(ḡ × (ḡ + 1))

Control Limits

For each data point:

Upper Control Limit (UCL):

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

Lower Control Limit (LCL):

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

Center Line (CL):

CL = ḡ (average gap between nonconforming units)

Gap for Each Sample:

Gap = Number of conforming units between nonconforming occurrences

Notes:

• If custom limits are provided, they override the calculated values
• The Z-Score determines the confidence level (typically 3 for 99.7% confidence)
• g charts are based on the geometric distribution assumption
• Used when monitoring rare events or low defect rates
• Plots the actual gap counts (number of items between defects)
• Control limits remain constant since they're based on the geometric distribution
• Particularly useful for high-quality processes where defects are infrequent
• No sample size field is required as each point represents a gap between events