Control chart for variables

This presentation gives an overall view of one of the seven QC tools - control charts with special reference to variables

1. CONTROL CHARTS

2. INTRODUCTION 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

3. ADVANTAGES 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

4. CLASSIFICATION 8/1/2015 4

5. Variation 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

6. 3 Categories of variation 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

7. Source of variation Equipment Tool wear, machine vibration, … Material Raw material quality Environment Temperature, pressure, humidity Operator Operator performance- physical & emotional 8/1/2015 7

8. Control Chart Viewpoint Variation due to Common or chance causes Assignable causes 8/1/2015 8 Control chart may be used to discover “ assignable causes ”

9. Control chart functions Control charts are powerful aids to understanding the performance of a process over time. 8/1/2015 9 PROCESS Input Output What’s causing variability?

10. Control charts identify variation 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

11. Control charts help us learn more about processes 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

12. Control charts to monitor processes 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

13. Types of Data 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

14. 8/1/2015 14 Control Charts for Variables

15. Introduction 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

16. Variable control charts 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

17. Variable control charts R Chart   The R chart is used to monitor process variability when sample sizes are small (n<10), or to simplify the calculations made by process operators.  This chart is called the R chart because the statistic being plotted is the sample range.  Using the R chart, the estimate of the process standard deviation, σ ,is R/d2 .  8/1/2015 17

18. Variable control charts S Chart The s chart is used to monitor process variability when sample sizes are large (n*10), or when a computer is available to automate the calculations. This chart is called the s chart because the statistic being plotted is the sample standard deviation. Using the s chart, the estimate of the process standard deviation, σ , is 8/1/2015 18

19. X-bar and R charts The X- bar chart is developed from the average of each subgroup data. used to detect changes in the mean between subgroups. The R- chart is developed from the ranges of each subgroup data used to detect changes in variation within subgroups 8/1/2015 19

20. X-bar and S charts The X- bar chart is developed from the average of each subgroup data. used to detect changes in the mean between subgroups. The S- chart is developed from the standard deviation of each subgroup data used to detect changes in variation within subgroups 8/1/2015 20

21. PROCEDURE FOR USING VARIABLES CONTROL CHARTS: Determine the variable to monitor. At predetermined, even intervals, take samples of size n ( usually n=4 or 5). Compute X BAR and R (or s) for each sample, and plot them on their respective control charts. Use the following relationships : After collecting a sufficient number of samples, k (k>20), compute the control limits for the charts. The following additional calculations will be necessary: 8/1/2015 21

22. 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. 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

23. 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

24. 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

25. 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

26. CALCULATE THE CONTROL LIMITS 15.94 2.7 1.14 X-BAR , R CHART X- BAR ,S CHART 8/1/2015 26

27. TABLE FOR CONSTANTS SQC A MODERN INTRODUCTION 6th Edition, D.C. Montgomery 8/1/2015 27

28. CONSTANTS FOR X-BAR ,R & X-BAR, S CHARTS X-BAR , R CHART X-BAR , S CHART A2 D4 D3 0.577 2.004 A3 B4 B3 1.427 2.089 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

29. X-BAR , R CONTROL CHART 8/1/2015 29

30. X-BAR,S CONTROL CHART 8/1/2015 30

31. 8/1/2015 31 THANK YOU