For constructing a Xbar chart x bar and r are computed for e

For constructing a X-bar chart, x bar and r are computed for each of 24 preliminary samples using a sample size n=5. The summary data are sigma i = 1 to 24 x bar_i = 816, sigma i = 1 to 24 r_i = 113. Find the center line, upper control limit, and lower control limit for X bar chart. Find the center line, upper control limit, and lower control limit for R chart. Calculate the fraction of defective when the specification is 34 plusminus 2. Assume the process is normally distributed. Calculate the expected number of defectives when 1,000,000 products are produced from this process.

Solution

Calculate the X-bar Chart Upper Control Limit, or upper natural process limit, by multiplying R-bar by the appropriate A2 factor (based on subgroup size) and adding that value to the average (X-bar-bar). UCL (X-bar) = X-bar-bar + (A2 x R-bar) Plot the Upper Control Limit on the X-bar chart. 9. Calculate the X-bar Chart Lower Control Limit, or lower natural process limit, for the X-bar chart by multiplying R-bar by the appropriate A2 factor (based on subgroup size) and subtracting that value from the average (X-barbar). LCL(X-bar) = X-bar-bar - (A2 x R-bar)

a) central line -153.2 UCL- 195.6 LCL - 121.6

b) central line - 22.6 UCL - 42.6 LCL - 2.6

c) 5%

d) 5000