T chart

t chart is a type of control chart used in statistical process control to monitor the time between occurrences of rare events (exponential distribution).

Map the data fields

• Subgroup/Lot: This field represents the different time periods or sequence numbers being monitored.
• Process variable: This field represents the time elapsed between consecutive occurrences of the event.
• 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 t-chart calculations are performed as follows:

Average time between events (t̄)

t̄ = Total Time / Number of Events

Standard Deviation

Standard Deviation = t̄

Control Limits

For each data point:

Upper Control Limit (UCL):

UCL = t̄ + (Z-Score × t̄)

Lower Control Limit (LCL):

LCL = t̄ - (Z-Score × t̄)

Center Line (CL):

CL = t̄ (average time between events)

Time Between Events for Each Sample:

Time = Actual time elapsed between consecutive events

Notes:

• If custom limits are provided, they override the calculated values
• The Z-Score determines the confidence level (typically 3 for 99.7% confidence)
• t charts are based on the exponential distribution assumption
• Used when monitoring time intervals between rare events or failures
• Plots the actual time intervals between occurrences
• Control limits remain constant since they're based on the exponential distribution
• Standard deviation equals the mean (characteristic of exponential distribution)
• Particularly useful for reliability analysis and failure time monitoring
• No sample size field is required as each point represents a time interval between events