Problem no.3 The thickness of a metal part is the quality characteristic that st

Question

Problem no.3 The thickness of a metal part is the quality characteristic that statistical process control is being applied to. Measurements are taken from 25 subgroups of subgroup size 5. The sum of the X-bar values-1.5735. The sum of the R-values 0231. Xbar/R Chart for x 0636 06396 25 001 0011 a.) Calculate the trial control limits and centerlines for the X-bar and R charts above. b.) Calculate the revised control limits and centerlines for X-bar and R charts that would represent the c.) d.) in-control process. Estimate the process standard deviation after revision. What is the probability of detecting a shift in the process mean to 0.0630 on the next sample.

Explanation / Answer

We have given sum of Xbar = 1.5735, n= 25 and sum of R = 0.0231

So Xduble bar = 1.5735 / 25 = 0.06294     And Rbar = 0.0231/ 25 = 0.000924

Control limits for Xbar are : Lower limit : Xdouble bar - A2*Rbar

                                          Upper limit : Xdouble bar + A2*Rbar

So,   Lower limit = 0.06294 - 0.577*0.000924 = 0.06241

       Upper limit = 0.06294 + 0.577*0.000924 = 0.06347

And Control limit for Rbar :

     Lower limit = D3*Rbar = 0 * 0.000924 = 0

     Upper limit = D4*Rbar = 2.114 * 0.000924 = 0.001953

There are two numbers for xbar which are out side th upper limit .

So we have to remove those points from data set .

So revesied Xbar = 1.4459

So X double bar = 1.4459/23 = 0.062867 , Rbar = 0.0206/23 = 0.000896

So revised control limits are :   

        Lower limit = 0.062867 - 0.577*0.000896 = 0.06235
       Upper limit = 0.062867 + 0.577*0.000896 = 0.063384

And R control limits are   :  

Lower limit = D3 * Rbar = 0   

Upper limit =D4*Rbar = 0.01893

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