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

(B) Control limits for x chart

= Xbar bar +- A2 Rbar

= 1.5735/25+- 0.577x 0.0231/25

= 0.0629+-0.0005

UCL = 0.0634

LCL = 0.0624

R values

UCL of R = Rbar xD4 = Rbar x 2.114 = 0.0231x2.114/25

= 0.0019

LCL of R = Rbar xD3 = 0 as D3 =0

(C) S.D. = Rbar /d2 = 0.0231/25x 1/ 2.326 = 0.00039

(A) pre revised values

UCL of Xbar= 0.06396

Xbar = 0.06396 -0.577x 0.00066

= 0.06357

UCL of R = 0.0014

Rbar x D4 = 0.0014 gives Rbar = 0.0014 /2.114 =0.00066

D. Z = 0.0630 - 0.0629 / 0.00039 = 0.25

Probability corresponding to z = 0.25 is 40%.

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