TM 620
Fall 2010
Session Eight Homework Solutions
Chapter Eleven Problems
6. Interpret control charts
a. alternating above and below the center line, could be a problem – look for strategy for selection of random sub-group
b. Special cause variation caused out-of-control in samples 2 and 3 – appears to be back in control
c. 5 data points in a row below center line – look for cause of sustained low mean
d. first 8 data points indicate a shift trend in the process – appears to be back in control
e. process appears random
f. process appears random
11. A production process for the JMF Semicon is monitored using x-bar and R charts. Ten samples of n = 15 observations have been gathered with the results as listed in the book.
A. Develop a control chart and plot the means.
B. Is the process in control? Explain.
Both the x-bar and R charts contain points outside of the control limits, suggesting that the process is not in statistical control and should be investigated.
Summary for data in problem 13.
1 2 3 4 5 6 7 8
68.51 68.94 68.66 68.49 68.64 68.34 68.99 68.92
68.46 68.2 68.44 68.94 68.63 68.42 68.94 68.91
68.54 68.54 68.55 68.56 68.62 68.99 68.95 68.97
68.34 68.56 68.77 68.62 68.32 68.02 68.95 68.93
68.46 68.7 68.7 68.69 68.34 68.03 68.94 68.96
68.46 68.7 68.64 68.56 68.24 68.47 68.97 68.95
X-bar = 68.46 68.61 68.63 68.64 68.47 68.38 68.96 68.94
S = 0.068 0.245 0.117 0.160 0.184 0.357 0.020 0.024
X bar bar = 68.63 B3 = 0.03 UCLs = 0.289
S-bar = 0.147 B4 = 1.97 LCLs = 0.004
USL = 68.75 Cpu = 0.384
LSL = 68.25 Cpl = 1.283
13. A finishing process packages assemblies into boxes. You have noticed variability in the boxes and desire to improve the process to fix the problem because some products fit too tightly into the boxes and others fit too loosely. In the text are width measurements for the boxes. Using x-bar and R charts, plot and interpret the process.
Both the x-bar and R charts contain points outside of the control limits, suggesting that the process is not in statistical control and should be investigated.
14. For the data in problem 13, if the mean specification is 68.5 ± .25 and the estimated process standard deviation is .10, is the process capable? Compute Cpu, Cpl, and Cpk.
Cpu = 0.384 Cpl = 1.283 => Cpk = 0.384
Since Cpk is far less than the “capable” benchmark of 1.25, the process is not currently capable.
17. For the data in problem 13, compute the limits for the Xbar, S charts.
Using B3, B4, and s-bar we calculate UCL = B4*sbar = .289, LCL = B3*sbar = .004
21. The data listed in the book are for a component used in the space shuttle. Since the process dispersion is closely monitored, use x-bar and s charts to see if the process is in control.
This process appears to be in control.