Question

A process sampled 20 times with a sample of size 8 resulted in  = 27.5and R = 1.8. Compute the upper and lower control limits for the x chart for this process. (Round your answers to two decimal places.)

UCL=

LCL=

Compute the upper and lower control limits for the R chart for this process. (Round your answers to two decimal places.)

UCL=

LCL=

Answer 1

Answer:

Given Data

A process sampled 20 times with a sample of size n = 8

resulted $\bar{\bar{x}}$ = 27.5

$\bar{R}$ = 1.8

Control limits of :

X - chart

$UCL=\bar{\bar{X}}+A_{2}\bar{X}$

= 27.5 + 0.373(1.8)

= 27.5 + 0.6714

= 28.1714

and

LCL = X - A, X

= 27.5 - 0.373(1.8)

= 26.8286

$A_{2}$ = 0.373 using statistical table value we get at n = 8

Sample size

UCL = 28.1714

LCL = 26.8286

CL = 27.5

Control limits for the  $\bar{R}$ :-

$UCL = D_{4}\bar{R}$

= ( 1.864)(1.8)

= 3.3552

UCL = 3.3552

CL = 1.8

$LCL = D_{3}\bar{R}$

= (0.136)(1.8)

= 0.2448

Where $D_{3}=0.136\,\,and\,\,D_{4}=1.864$ using statistical table value we get.

At sample size n = 8

UCL = 3.3552

CL = 1.8

LCL = 0.2448

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