Question

A Shewhart X̅-chart was developed for an in-control process. Considering the probability of a point falling outside the 3σ control limits as 0.0026, the value of average run length for this chart is ________.

Answer 1

Concept:

Average Run Length (ARL):

Average Run Length Short for average run length, ARL is the interval between out-of-control events that can be expected. It is the expected value of the run-length, i.e (the expected number of subgroups) until a control chart first signals.

Average Run Length (ARL) = \(\frac{1}{P}\)

Where,

P = Probability of point falling outside the control limits.

Calculation:

Given:

P = 0.0026

Then, 

ARL = \(\frac{1}{P}\)

= \(\frac{1}{0.0026}\)

= 384.6