Control charts for X-bar and R, using a subgroup size of 5, are to be applied to control the critical dimension of a certain manufacturing process. Specifications call for a nominal dimension of 1,250.000 + 0.050 mm. The process is believed to have a σ of 0.015 mm Determine appropriate control limits for the X-bar and R charts.

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Control charts for X-bar and R, using a subgroup size of 5, are to be applied to control the
critical dimension of a certain manufacturing process. Specifications call for a nominal dimension of
1,250.000 + 0.050 mm. The process is believed to have a σ of 0.015 mm Determine appropriate control limits for the X-bar and R charts.

a) After 12 subgroups have been drawn and X-bar and R plotted on the charts, a computation of X-
double bar give 1,250.015. b1) What is the probability that a value of X-bar will fall within the limits if this is the true value of the mean setting? b2) What is the probability that all 12
values fall within the control limits?

b) Make the necessary calculations to determine if the process can meet specifications by solving
for Cp, Cpu, CpL, Cpk . Assume a normal distribution of product output. Illustrate how the process
would look like relative to the result of the computations of the process capability analysis.

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