SPC Calculations and Definitions

SPC, or Statistical Process Control, is a methodology used to monitor and control processes to ensure they operate efficiently and produce quality output. Process variations in SPC refer to the fluctuations or deviations in a process's output over time. The following are some key definitions and calculations related to SPC process variations:

Mean (Average)

Definition: The central tendency of a set of data points.

Calculation: The sum of all data points divided by the number of data points.

Symbol: X̅

Range

Definition: The difference between the highest and lowest values in a data set.

Calculation: Maximum value - Minimum value

Symbol: R

Standard Deviation

Definition: A measure of the dispersion or spread of a set of data points.

Calculation: Square root of the variance.

Symbol: σ (sigma)

Sample Size

For X-Bar: 5

For I-MR: 1

Process Variation

Definition: The range of fluctuation or dispersion observed in a process.

Calculation: Often measured using the standard deviation or range.

Cp

Cp is a capability index. It compares the process cability to the maximum allowable variation as indicated by the tolerance. This index provides a measure of how well the process will satisfy the variability requirements.

Cpk

Cpk is a capability index. For bilateral tolerances, Cpk will always be less than or equal to Cp.

Cpk will only be equal to Cp if the process is centered.

Cpk is calculated as the minimum of CPU or CPL where:

and

Pp

Pp is a performance index. It compares the process performance to the maximum allowable variation as indicated by the tolerance. This index provides a measue of how well the process will satisfy the variability requirements.

Pp is not affected by the process location.

Ppk

Ppk is a performance index. It takes process location as well as the performance into account. For bilateral tolerances, Ppk will always be less than or equal to Pp.