Consider a process with a target at 4.5mm and an estimated standard deviation of

Question

Consider a process with a target at 4.5mm and an estimated standard deviation of 0.4mm. You decide to monitor this process with an exponentially weighted moving average control chart with L = 2.962 and lambda = 0.2. Calculate the steady-state control limits. [6] What is the in-control average run length of this control chart? [2] What is the out-of-control average run length of this control chart for detecting a mean shift of 0.6mm? [2] What is the purpose of a Fast Initial Response feature (a.k.a. Headstart) for a CUSUM or EWMA control chart? [5]

Explanation / Answer

0 = 4.5 mm

= 0.4 mm

L = 2.962

= 0.2

Steady State Control Limits

UCL = 0 + L ( / (2- )) = 4.5 + 2.962*0.4*(0.2/(2-0.2)1/2 = 4.895

LCL = 0 - L ( / (2- )n) = 4.5 – 2.962*0.4*(0.2/(2-0.2))1/2 = 4.105

In-Control Average Run Length

ARL = 1/

Out-of-Control Average Run Length for detecting a mean shift of 0.6 mm

ARL = 1 / (1-)

Purpose of Fast Initial Response

If a shift occurred at the beginning, Fast Initial Response can detect the shift more quickly to decrease ARL. If in control at the beginning, CUSUM will quickly drop to zero, there will be little effect on the performance.

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