Answered

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?

Answer :

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:

[tex]\mu_o \pm L \sigma \sqrt{\dfrac{\lambda }{(2-\lambda )n}}[/tex]

where;

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

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

Given that the data is chosen from an individual sample;

Then; we can express the width as:

[tex]L \sigma \sqrt{\dfrac{\lambda}{(2-\lambda)}}= 3 \sigma[/tex]

[tex]L \sqrt{\dfrac{\lambda}{(2-\lambda)}}= 3[/tex]

[tex]L \sqrt{\dfrac{0.5}{(2-0.5)}}= 3[/tex]

[tex]L \sqrt{\dfrac{0.5}{(1.5)}}= 3[/tex]

[tex]L \sqrt{0.333}= 3[/tex]

[tex]L\times 0.577= 3[/tex]

[tex]L=\dfrac{ 3 }{0.577}[/tex]

L = 5.199

Other Questions