Nominal properties

ARL(value)

Value of the in-control average run length of the control chart, i.e. if $RL = \inf\{t > 0: \text{Chart detects OC}\}$ is the run length, then the average run length $ARL$ is

$ARL = \mathbb{E}[RL|\tau = +\infty]$,

where $\{\tau = +\infty\}$ represents the process being in-control.

Arguments

• value::Float64: The nominal value of the average run length. Must be greater than 1.

QRL(value, qtl)

Value of the in-control quantile of the run length of the control chart, i.e. if $RL = \inf\{t > 0 : \text{Chart detects OC}\}$ is the run length, then value is the value of the qtl-level quantile of the distribution of $RL$ if the process is in-control.

Arguments

• value::Float64: The nominal value of the run length quantile.
• qtl::Float64: The level of the quantile, must be between 0 and 1. Default is 0.5.