1) Leah's Toys makes rubber balls. The current process is capable of producing balls that weigh on average 3 ounces with a standard deviation of .25 ounces. What is the PCR, assuming upper and lower tolerance limits of 3.5 and 2.5 ounces? Is Leah's able to meet the tolerance limits 99.7% of the time? Explain
2) Suppose Leah's Toys invests in process improvements that lower the standard deviation in Problem 2 to just .10 ounces. Is this enough for Leah's to achieve Six Sigma levels with regards to the weight of the balls? Explain
3) The River Rock Company sells 200 lb decorative rocks for landscaping use. The current bagging process yields samples with X and R values of 200 lbs and 12 lbs respectively. Each sample consists of 12 observations. Develop the appropriate control charts
4) LaBoing produces springs which are categorized as either acceptable or defective During a period in which the manufacturing process are under control, LaBoing takes multiple samples of 100 springs each, resulting in a calculated p value of 0.07. Develops the appropriate control chart for the springs
5) Anderset Labs produces rough lenses that will ultimately be rounded into precision lenses for use in lab equipment. The company developed the following thickness measures, based on 15 samples of size 10 that were taken when the processes were under control
|
Mean
|
Minimum
|
Maximum
|
|
3.9
|
3.617
|
3.989
|
|
4.206
|
3.971
|
4.302
|
|
4.214
|
4.062
|
4.4
|
|
3.89
|
3.749
|
3.937
|
|
4.036
|
3.501
|
4.084
|
|
4.134
|
3.543
|
4.584
|
|
3.037
|
2.935
|
3.929
|
|
5.082
|
3.797
|
5.695
|
|
3.404
|
2.837
|
4.255
|
|
5.246
|
5.106
|
6.382
|
|
4.197
|
4.085
|
4.239
|
|
4.312
|
3.949
|
4.356
|
|
4.302
|
3.989
|
4.4
|
|
3.867
|
3.617
|
3.9
|
|
4.17
|
4.046
|
4.206
|
Use the data above to calculate X and R, and create the appropriate control charts
6) Suppose Anderset Labs take some additional samples of the same size, yielding the results shown below. Plot these samples on the control charts and circle any observations that appear to be out of control.
|
Mean
|
Minimum
|
Maximum
|
|
4.134
|
4.011
|
4.612
|
|
3.913
|
3.891
|
4.474
|
|
4.584
|
4.499
|
5.145
|
|
4.009
|
3.934
|
4.891
|
|
4.612
|
4.085
|
4.983
|
|
5.627
|
5.183
|
6.08
|
7) Lazy B Ranch produces leather hides for use in the furniture and automotive upholstery industry. The company has taken ten samples of 9 observations each, measuring the square footage of each hide. Summary data is shown below
|
Mean
|
Minumum
|
Maximum
|
|
13.2
|
12.7
|
13.5
|
|
12.8
|
12.5
|
13.3
|
|
13.3
|
12.6
|
13.7
|
|
13.1
|
12.5
|
13.5
|
|
12.7
|
12.2
|
13
|
|
12.9
|
12.5
|
13.3
|
|
13.2
|
12.9
|
13.5
|
|
13
|
12.6
|
13.6
|
|
13.1
|
12.7
|
13.4
|
|
12.7
|
12.3
|
13.5
|
Use the data set to setup the control limits for the hides. Why would it be important for the Lazy B Ranch to track this information? Why might it be harder for the Lazy B to reduce process variability than it would be for a typical manufacturer?
8) EK Chemical Company sells a specialty chemical in packages marked 100 grams. In reality, EK has set the process mean at 100.5 grams, and the process currently has a standard deviation of 0.50 grams. Suppose the customer will accept anywhere from 98 to 102 grams as long as the average package has 100 grams.
A) Calculate the process capability index for the current manufacturing process. Is the process capable of meeting the tolerance limits more than 99.7% of the time? Explain.
B) Now suppose EK re-centers the manufacturing process so that the mean is exactly 100 grams while the standard deviation remains the same. Calculate the process capability ratio. Is the process still capable of meeting the tolerance limits more than 99.7% of the time?