1. 1. Introduced in 1926 by WALTER SHEWART, who concluded that a distribution can be transformed into normal shape by estimating mean and standard deviation. Control chart is a device which specifies the state of statistical control. Control chart detects the variation in processing and warns if there is any deviation from the specified tolerance limits. The purpose of using control chart is to stabilize process by keeping it under control and carrying out necessary adjustments (on line). 8/1/2015 2
2. 2. A control chart indicate whether the process is in control or out of control. It determines the process variability and detects unusual variations in a process. It ensures product quality level. It warns in time and if process is rectified at that time percentage of rejection can be reduced. It provides information about selection of process and setting up of tolerance limits. 8/1/2015 3
3. 3. CONTROL CHART VARIABLE CONTROL CHART X- BAR & R CHART X-BAR & S CHART X & m R CHART ATTRIBUTE CONTROL CHART PERCENTAGE OF DEFECTS 1.P-CHART 2.np- CHART NO OF DEFECTIVIES 1.C-CHART 2.U-CHART 8/1/2015 4
4. 4. No two natural items in any category are the same. Variation may be quite large or very small. If variation very small, it may appear that items are identical, but precision instruments will show differences. 8/1/2015 5
5. 5. Within-piece variation One portion of surface is rougher than another portion. A piece-to-piece variation Variation among pieces produced at the same time. Time-to-time variation Service given early would be different from that given later in the day. 8/1/2015 6
6. 6. Equipment Tool wear, machine vibration, Material Raw material quality Environment Temperature, pressure, humidity Operator Operator performance- physical & emotional 8/1/2015 7
7. 7. Variation due to Common or chance causes Assignable causes 8/1/2015 8 Control chart may be used to discover assignable causes
8. 8. Control charts are powerful aids to understanding the performance of a process over time. 8/1/2015 9 PROCESS Input Output Whats causing variability?
9. 9. Chance causes - common cause inherent to the process or random and not controllable if only common cause present, the process is considered stable or in control Assignable causes - special cause variation due to outside influences if present, the process is out of control 8/1/2015 10
10. 10. Separate common and special causes of variation Determine whether a process is in a state of statistical control or out-of-control Estimate the process parameters (mean, variation) and assess the performance of a process or its capability 8/1/2015 11
11. 11. To monitor output, we use a control chart we check things like the mean, range, standard deviation To monitor a process, we typically use two control charts mean (or some other central tendency measure) variation (typically using range or standard deviation) 8/1/2015 12
12. 12. Variable data Product characteristic that can be measured Length, size, weight, height, time, velocity Attribute data Product characteristic evaluated with a discrete choice Good/bad, yes/no 8/1/2015 13
13. 13. 8/1/2015 14
14. 14. A single measurable quality characteristic ,such as dimension, weight, or volume, is called variable. Since statistical control for continuous data depends on both the mean and the variability, variables control charts are constructed to monitor each. The most commonly used chart to monitor the mean is called the X-BAR chart. There are two commonly used charts used to monitor the variability: the R chart and the S chart. 8/1/2015 15
15. 15. X-BAR Chart: This chart is called the X-BAR chart because the statistic being plotted is the sample mean. The reason for taking a sample is because we are not always sure of the process distribution. By using the sample mean we can "invoke" the central limit theorem to assume normality. 8/1/2015 16
16. 16. R Chart The R chart is used to monitor process variability when sample sizes are small (n20), compute the control limits for the charts. The following additional calculations will be necessary: 8/1/2015 21
17. 21. V. If any points fall outside of the control limits, conclude that the process is out of control, and begin a search for an assignable or special cause. When the special cause is identified, remove that point and return to step 4 to re-evaluate the remaining points. VI. If all the points are within limits, conclude that the process is in control, and use the calculated limits for future monitoring of the process. 8/1/2015 22
18. 22. EXAMPLE PROBLEM A large hotel in a resort area has a housekeeping staff that cleans and prepares all of the hotel's guestrooms daily. In an effort to improve service through reducing variation in the time required to clean and prepare a room, a series of measurements is taken of the times to service rooms in one section of the hotel. Cleaning times for five rooms selected each day for 25 consecutive days appear below: Day Room 1 Room 2 Room 3 Room 4 Room 5 1 15.6 14.3 17.7 14.3 15 2 15 14.8 16.8 16.9 17.4 3 16.4 15.1 15.7 17.3 16.6 4 14.2 14.8 17.3 15 16.4 5 16.4 16.3 17.6 17.9 14.9 6 14.9 17.2 17.2 15.3 14.1 7 17.9 17.9 14.7 17 14.5 8 14 17.7 16.9 14 14.9 9 17.6 16.5 15.3 14.5 15.1 10 14.6 14 14.7 16.9 14.2 8/1/2015 23
19. 23. 11 14.6 15.5 15.9 14.8 14.2 12 15.3 15.3 15.9 15 17.8 13 17.4 14.9 17.7 16.6 14.7 14 15.3 16.9 17.9 17.2 17.5 15 14.8 15.1 16.6 16.3 14.5 16 16.1 14.6 17.5 16.9 17.7 17 14.2 14.7 15.3 15.7 14.3 18 14.6 17.2 16 16.7 16.3 19 15.9 16.5 16.1 15 17.8 20 16.2 14.8 14.8 15 15.3 21 16.3 15.3 14 17.4 14.5 22 15 17.6 14.5 17.5 17.8 23 16.4 15.9 16.7 15.7 16.9 24 16.6 15.1 14.1 17.4 17.8 25 17 17.5 17.4 16.2 17.9 8/1/2015 24
20. 24. CALCULATE THE MEAN, RANGE, STANDARD DEVIATION Day Average Range St. Dev 1 15.4 3.4 1.41 2 16.2 2.6 1.19 3 16.2 2.2 0.85 4 15.5 3.1 1.27 5 16.6 3 1.19 6 15.7 3.1 1.4 7 16.4 3.4 1.69 8 15.5 3.7 1.71 9 15.8 3.1 1.24 10 14.9 2.9 1.16 11 15 1.7 0.69 12 15.9 2.8 1.13 13 16.3 3 1.39 14 17 2.6 1 15 15.5 2.1 0.93 16 16.6 3.1 1.26 17 14.8 1.5 0.65 18 16.2 2.6 0.98 19 16.3 2.8 1.02 20 15.2 1.4 0.58 21 15.5 3.4 1.37 22 16.5 3.3 1.59 23 16.3 1.2 0.51 24 16.2 3.7 1.56 25 17.2 1.7 0.64 8/1/2015 25
21. 25. CALCULATE THE CONTROL LIMITS 15.94 2.7 1.14 X R s x Chart Control Limits UCL = x + A R LCL = x - A R 2 2 R Chart Control Limits UCL = D R LCL = D R 4 3 X-BAR , R CHART X- BAR ,S CHART 8/1/2015 26
22. 26. TABLE FOR CONSTANTS SQC A MODERN INTRODUCTION 6th Edition, D.C. Montgomery 8/1/2015 27
23. 27. CONSTANTS FOR X-BAR ,R & X-BAR, S CHARTS X-BAR , R CHART X-BAR , S CHART A2 D4 D3 0.577 2.004 0 A3 B4 B3 1.427 2.089 0 X-BAR CHART CL =15.94 UCL = 15.94+ 0.577(2.7) = 17.49 LCL = 15.94 0.577(2.7) = 14.38 R CHART CL = 2.7 UCL = 2.004(2.7) = 5.41 LCL = 0 (2.7) = 0 X-BAR CHART CL =15.94 UCL = 15.94+ 1.427(1.14) = 17.56 LCL = 15.94 1.427(1.14) = 14.31 S CHART CL = 1.14 UCL = 2.089(1.14) = 2.38 LCL = 0 (1.14) = 0 8/1/2015 28
24. 28. X-BAR , R CONTROL CHART 8/1/2015 29
25. 29. X-BAR,S CONTROL CHART 8/1/2015 30
26. 30. 8/1/2015 31