Samples of size n=5 are taken from a process every half hour. After m-25 samples

Question

Samples of size n=5 are taken from a process every half hour. After m-25 samples have collected, we calculate been X = 662.5 A Shewhart control chart is used, Assume that both charts indicates that the process is in control and that the quality characteristics is independent and normally distributed Estimate the process standard deviation (5 pts) b) Find the control limits of the X and R charts (10 pts) d Assume that both charts exhibit control. If the specification limits are 26.4+- 0.50, estimate the fraction non-conforming. (10 pts)

Explanation / Answer

a)Rbar= 0.36 ,Sigma= Rbar/d2 , FOR n=5, value of d2 foam table is, 2.326

therefore, Sigma= 0.36/2.326 =0.1547 ............... process standarad deviation

b) Sample size n=5, m=25 xdoublebar=662.5/25= 26.5, Rbar=9/25 = 0.36............. (GIVEN)

for n=5,the constant by using table, A2= 0.577, D2=2.114, D3=0

Control limits for X-bar chart:

UCL= xdouble bar+A2*Rbar= 26.5+0.577*0.36= 26.7077

CL=xbar = 26.5

LCL= xdouble bar-A2*Rbar = 26.5-0.577*0.36= 26.29

Control limits for R-chart:

UCL= D4*Rbar = 2.114*0.36 = 0.7610

CL= Rbar= 0.36

LCL= D3*Rbar= 0*0.36 =0

c) USL= 26.4+050

LSL=26.4-05.0

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