Question

A technology student project group worked with a machine shop that employs a CNC lathe in the machining of a part produced for a heavy equipment manufacturer. Some summary statistics for a diameter on the part obtained from 25 samples of n=4 parts turned on the lathe are given below. The units are inches.

Sample                                   x-bar                                       R

                 1                                      1.18093                                  .0001

                 2                                      1.18085                                  .0002

                 3                                      1.18095                                  .0002

                 4                                      1.18063                                  .0008

                 5                                      1.18053                                  .0007

                 6                                      1.18053                                  .0005

                 7                                      1.18053                                  .0005

                 8                                      1.18195                                  .0001

                 9                                      1.18100                                  .0003

                10                                     1.18095                                  .0001

55 Sum 11.80885 .0007

Find retrospective control limits for the values above (both means and ranges). What do the x-bar and R values indicate about the stability of the turning process

Answer 1

Solution: Here the given information are

=11.80885,    =0.0035

Subgroup size n=4

Total number of sample = m =10

First find the mean for and R

= = 11.80885/10 = 1.180885

= = 0.0035/10= 0.00035

Control limits for

To find the control limits on the chart, we use A2= 0.729 from variable control chart table for variable

UCL = + A2* = 1.180885+0.729*0.00035 = 1.18114

= 1.180885

LCL = + A2* = 1.18063

To find the control limits on the R chart, we use =0 and =2.282 from variable control chart table for variable

UCL = * =2.282*0.00035 = 0.000799

=0.00035

LCL =* =0*0.00035 =0

The standard chart for variables data, X-bar and R charts help determine if a process is stable and predictable. The X-bar chart shows how the mean or average changes over time and the R chart shows how the range of the subgroups changes over time. It is also used to monitor the effects of process improvement theories.

Here from the control limits of and R we can conclude that the process is not in control state. Some of the points outside the control limits. That means variation present in the turning process. From the control chart we need to be improvement in the process.