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ycow [4]
3 years ago
5

An EWMA control chart uses λ = 0.5. What is the value of L such that the control limits of this EWMA control chart in the steady

state have the same width with a 3σ X_bar control chart?
Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
3 0

Answer:

5.199

Step-by-step explanation:

From the  information provided;

We know that λ = 0.5.

However, the control limits for a steady-state EMWA control chart is:

\mu_o \pm L \sigma \sqrt{\dfrac{\lambda }{(2-\lambda )n}}

where;

UCL = \mu_o + L \sigma \sqrt{\dfrac{\lambda }{(2-\lambda )n}}

LCL = \mu_o- L \sigma \sqrt{\dfrac{\lambda }{(2-\lambda )n}}

Given that the data is chosen from an individual sample;

Then; we can express the width as:

L \sigma \sqrt{\dfrac{\lambda}{(2-\lambda)}}= 3 \sigma

L \sqrt{\dfrac{\lambda}{(2-\lambda)}}= 3

L \sqrt{\dfrac{0.5}{(2-0.5)}}= 3

L \sqrt{\dfrac{0.5}{(1.5)}}= 3

L \sqrt{0.333}= 3

L\times 0.577= 3

L=\dfrac{ 3 }{0.577}

L = 5.199

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