Quality and Process Methods > EWMA Control Charts > The EWMA Control Chart Platform Options > Average Run Length (ARL) Report for EWMA Control Charts
Publication date: 05/24/2021

## Average Run Length (ARL) Report for EWMA Control Charts

The Average Run Length (ARL) report contains a table and a graph of ARL values. The average run length (ARL) for a specified shift is the average number of runs expected before an out-of-control signal occurs. For example, the ARL at 0 represents the average number of runs expected before seeing a false-alarm signal when the process is in control. When the process is in control, the shift size is 0.

The table and graph in the ARL report enable you to explore how various settings of the Lambda parameter affect the performance of the corresponding EWMA chart. The table and graph also enable you to compare the performance of the EWMA chart with a Shewhart chart, such as the X chart in the EWMA Chart report. The Shewhart ARL column is equivalent to the EWMA ARL column when Lambda is set to 1.

The value of EWMA ARL at 0 depends on the setting of the Constant Limits option:

If the Constant Limits option is selected, the process is assumed to have been in control long enough that the effect of the starting value is negligible. In this case, also referred to as a steady state of the EWMA chart, the value of EWMA ARL(0) is calculated using the method described in Crowder (1987).

If the Constant Limits option is not selected, the value of EWMA ARL(0) is calculated using the method described in Knoth (2004). This situation is also referred to as a zero state of the EWMA chart.

#### ARL Report

The ARL Report shows the average run length for standardized shifts (Δ) between 0 and 3 at 0.25 increments. The shift is represented by sqrt(n)*RawShift/Sigma, where n is the constant sample size in each subgroup. For the multiplier used in calculating control limits, K = 3 is assumed. This table contains ARL values for the EWMA chart as well as a Shewhart chart.

#### ARL Graph

The ARL Graph shows the average run length for standardized shifts (Δ) between 0 and 3. This graph contains the same data points as the ARL Table to the left of the ARL Graph. The solid line corresponds to the EWMA ARL values, and the dashed line corresponds to the Shewhart ARL values.