Cylinder Liner Boring Case Study
The cylinder liner boring case study demonstrates the use and application of X bar and R charts in manufacturing. The use of these control charts help in identification of both sporadic and chronic faults in the process, and help to formulate improvement actions. A supplier to an engine manufacturer produces cast iron cylinder liners. Due to a recent management change, the supplier is initiating a companionway quality improvement strategy.
A vertically and horizontally study team was formed to Identify sources of variation In the process of the cylinder liner reduction. The first action performed by this team was to conduct a flow chart of the cylinder liner production.
After the flow chart for the manufacturing process was completed, the new specifications were applied to the subset of historical data. A Parent chart was prepared that showed the defect data when the new specifications were applied. By examining the Parent chart, out-of-spec liner inside diameter was shown to be the most sensitive to the planned change in specification.
The focus of the group shifted to drawing a cause-and-effect diagram, summarizing the collective knowledge relative to the potential root causes for out-of-spec inner diameter liner. Data Collection #1 Data was collected to assess the stability of the boring process. A sample of size n = 5, was taken every 25 minutes, for a total of 40 separate samples throughout the day.
For each sample, the sample mean and sample range was calculated. The grand average and the average range were calculated to be 200. 25″ and 7. 60″ respectively. For the X bar chart the upper control limit (CUL) and lower control Limit (LLC) were calculated to be 204.
4″ and 195. 86″ respectively. The R chart CUL and LLC were 16. 07″ and O” respectively. When examining the X bar and R charts, it is important to examine the R chart first.
By examining the R chart for the initial sample set it showed that there were two extreme points that exceeded the upper control limit. To determine the possible causes of the two points, the team consulted the cause-and- effect diagram to look for potential causes. It was determined that a lack of trailing for the substitute operator was the cause for these extreme points. The substitute operator was trained accordingly.
Data Collection #2 After the substitute operator was trained accordingly, an additional 40 samples of size n = 5 were taken at the same frequency as the previous data collection.
The grand average and the average range were calculated to be 200. 24″ and 6. 55″ respectively. For the X bar chart the CUL and LLC were calculated to be 204. 02″ and 196. 46″ respectively.
The R chart CUL and LLC were 13. 85″ and O” respectively. Looking at the R chart no statistical signals were evident. This showed that training the substitute operator was effective in reducing the variability of the operation.
When looking at the X bar chart many rules were violated (Point above the upper intro limit, 2 out of 3 points in zone A or beyond above the mean, 4 out of 5 points in zone B or beyond above the mean, Run of 8 points that avoid zone C, Point above the upper control limit, and 2 out of 3 points In zone A or beyond below the mean). I en signals on ten x oar can’t Analytical ten presence AT special causes In ten process.
The study team reflected back again on the cause-and-effect diagram and concluded that the machine warm-up could be the cause of problems. The team constructed a scatter plot pertaining to the X bar vs.. Mime since start-up. The Cottrell showed that the X bar values seemed to stabilize between 60 and 90 minutes.
The approach to correct this problem was to have the workers come in early to start up the machine and to leave the machine running over the lunch break. Data Collection #3 After the machine warm-up issue was addressed, a new set of data was collected in the same fashion as the previous two data sets. The grand average and the average range were calculated to be 200. 005″ and 6. 6″ respectively.