Process Control: Back to the Pasta Homework

Homework Problem Set: X Bar and R

Problem #1

A certain dimension is specified in inches as 3.5100 +/- 0.0050. Control Charts for X bar and R indicate that the X bar chart shows a lack of control but the R chart always shows control. From the R chart the estimate of s = 0.0010. If the middle of the spec is the desired target for the average chart then; What should be the upper and lower control limits for the X bar chart given a sample size of 4 ? What is the capability ratio, capability index, and Cpk for this product?

Problem #2

a. Construct a X Bar and R chart for the following data: b. Determine the process capability ratio using the average R given the specifications are 1.996 -1.990". 1.9896 1.9904 1.9889 1.9903 1.9893 (subgroup 1) 1.9890 1.9894 1.9907 1.9907 1.9910 (subgroup 2) 1.9898 1.9890 1.9917 1.9899 1.9935 1.9869 1.9917 1.9915 1.9912 1.9931 1.9905 1.9874 1.9905 1.9883 1.9899 1.9899 1.9887 1.9886 1.9905 1.9931 1.9892 1.9895 1.9918 1.9930 1.9896 1.9896 1.9883 1.9904 1.9919 1.9896 1.9911 1.9905 1.9924 1.9876 1.9905 1.9916 1.9932 1.9906 1.9903 1.9893 1.9924 1.9898 1.9915 1.9896 1.9868 1.9904 1.9904 1.9890 1.9900 1.9917 1.9910 1.9915 1.9900 1.9882 1.9891 1.9917 1.9899 1.9928 1.9905 1.9913 1.9897 1.9909 1.9897 1.9913 1.9922 1.9914 1.9902 1.9867 1.9889 1.9888 1.9901 1.9893 1.9872 1.9912 1.9905 1.9871 1.9915 1.9914 1.9890 1.9928 1.9893 1.9886 1.9896 1.9909 1.9909 1.9899 1.9863 1.9894 1.9883 1.9885