Statistical Process Control

Question: Describe about the Statistical Process Control? Answer: Problem Statement To check whether the reservation process for the first 10 days and second 10 days is in statistical control Findings / Analysis We are comfortable with control limits. We used the 3 sigma control limits for monitoring the statistical process control. We used the control limits as the three standard deviations from the average. We used x-bar and R control chart for monitoring process. We have to see the x-bar and R control chart for the reservation process in the first 10 days of monitoring. We have to check whether the process shows out of control or not. If it is out of control, we have to check for which day, the process is out of control. The x-bar and R control chart is given below: X-bar Chart: X-bar control chart shows that the reservation process is out of control for the fourth day. For all other days, the process is within control limit. The Range chart is given as below: The range chart also shows that the process is out of control for the fourth day. The x-bar chart for the reservation process for the second 10 days of monitoring is given below: Above x-bar chart shows that the reservation process is in statistical control. The R control chart for the reservation process for second 10 days of monitoring is given below: Recommendations / Conclusion For the first 10 days of monitoring reservation process, the x-bar and R control chart shows that the statistical process is out of control. We need to investigate the reason for out of control process. Both control chart shows that the process is out of control for the fourth day of first 10 days. We need to focus the investigation on the fourth day of first 10 days. We have to investigate that why the variation increased for the fourth day for monitoring the reservation process. For the second 10 days of monitoring reservation process, the x-bar and R control chart shows that the reservation process is in statistical control and there is no need to investigation for the reservation process for second 10 days of monitoring. References: Duncan, Acheson J. Quality Control and Industrial Statistics. 5th ed. Homewood: Richard D. Irwin, Inc., 1986. Keller, Paul. Statistical Process Control Demystified, New York: McGraw-Hill, 2011. Montgomery, Douglas C. Introduction to Statistical Quality Control. New York: John Wiley Sons, 1991. Appendices The data sets for the reservation process are given below: 1st 10 Days of Monitoring Reservation Processing Time Day 1 2 3 4 5 1 6.2 5.4 5.1 5.6 5.2 2 5.4 5.1 5.4 5.3 5.2 3 5.4 5.5 5.2 5.1 5.0 4 4.6 4.5 5.8 4.2 4.8 5 5.4 5.2 5.3 5.3 5.2 6 5.2 5.4 5.2 5.4 5.5 7 5.3 4.8 5.0 6.1 5.2 8 5.0 5.4 5.3 5.1 5.4 9 5.2 5.8 5.1 5.0 4.7 10 5.0 5.5 5.2 5.5 5.3 2nd 10 Days of Monitoring Reservation Processing Time Day 1 2 3 4 5 1 4.3 5.6 4.3 5.8 6.3 2 5.5 4.4 5.4 3.9 3.9 3 6.1 4.0 4.3 3.9 6.1 4 4.9 4.6 4.3 5.8 3.9 5 5.2 4.7 4.2 5.4 4.4 6 4.1 4.6 5.5 6.1 4.1 7 5.3 5.7 5.1 6.0 5.5 8 6.4 6.5 3.5 6.1 5.2 9 6.5 4.1 4.9 6.4 4.1 10 4.4 4.8 5.7 4.7 6.3