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### Spc training

1. 1. <ul><li>HEIL </li></ul>INTRODUCTION TO SPC (Statistical Process Control)
2. 2. <ul><li>TRAINING AGENDA </li></ul><ul><li>HANDS ON LEARNING!! </li></ul><ul><li>Limitation of Inspection </li></ul><ul><li>Specification discussion </li></ul><ul><li>What is SPC? </li></ul><ul><li>Why SPC is a better? </li></ul><ul><li>How SPC works? </li></ul><ul><li>Control Chart </li></ul><ul><li>You may learn to like statistics. </li></ul>
3. 3. <ul><li>F EXERCISE </li></ul>F EXERCISE IMAGINE FOR ONE BRIEF MOMENT THAT EACH OF THE ONE HUNDRED AND FORTY-ONE WORDS OF THIS PARAGRAPH IS A SEPARATE COMPONENT FORM A FIRST SHIFT RUN OF FOURTEEN-INCH FLYWHEELS. YOU ARE ONE OF FIVE INSPECTORS PERFORMING THE FINAL INSPECTION OF THSES FINSISHED COMPONENTS WHICH WERE PRODUCED ON FOUR FAIRLY SMALL DIAL INDEX MACHINES THAT ARE NOT BEING CONTROLLED BY THE USE OF STATISTICAL TECHNIQUES. AS CAN BE EXPECTED FROM AN OPERATION OF THIS NATURE, THERE ARE A NUMBER OF DEFECTIVES COMPONENTS BEING MADE. EACH WORD THAT CONTAINS AN F REPRESENTS A DEFECTIVE COMPONENT. HOW MANY OF THE DEFECTIVES ARE YOU ABLE TO FIND? CHECK AGAIN AND INSPECT FOR THE PRESENTS OF F'S. WRITE YOUR FINAL COUNT IN THE BOTTOM LEFT HAND CORNER OF THIS PAGE. THIS EXAMPLE SHOULD GIVE YOU A FAIR IDEA OF HOW RELIABLE 100% INSPECTION CAN BE.
4. 4. <ul><li>INSPECTION </li></ul>Draw sample Meets spec. ? ACCEPT REJECT <ul><ul><li>YES </li></ul></ul><ul><ul><li>NO </li></ul></ul><ul><li>How good was it? </li></ul><ul><li>Barely meet spec? </li></ul><ul><li>middle of spec? </li></ul><ul><li>Same as before? </li></ul><ul><li>How bad was it? </li></ul><ul><li>Just outside spec? </li></ul><ul><li>Way out of spec? </li></ul><ul><li>Same as before? </li></ul>
5. 5. <ul><li>INSPECTION </li></ul>Lower Spec. A B What's the difference between ball A and B? Why is the spec there and not somewhere else? What is the purpose of the spec?
6. 6. <ul><li>SPECIFICATION </li></ul>Great!!! I'm in spec.
7. 7. <ul><li>SPECIFICATION </li></ul>Hey!!!!! But I'm in spec.
8. 8. <ul><li>TARGET </li></ul>Every specification has a TARGET. The upper and lower specification is meant to serve as a guide line. What you really want is the stuff that hits the TARGET.
9. 9. <ul><li>SCREW SPECIFICATION </li></ul>TARGET= .25 UPPER SPEC = .27 LOWER SPEC = .23 SCREW TOLERANCE = +/- .02&quot;
10. 10. <ul><li>NUT SPECIFICATION </li></ul>TARGET= .26 UPPER SPEC = .28 LOWER SPEC = .24 NUT TOLERANCE = +/- .02&quot;
11. 11. <ul><li>TARGET= .26 </li></ul>UPPER SPEC = .28 LOWER SPEC = .24 TARGET= .25 UPPER SPEC = .27 LOWER SPEC = .23 SCREW NUT SCREW = 26.8&quot; NUT = 24.8&quot; COMBINED TOLERANCE
12. 12. <ul><li>Meeting specification is not enough </li></ul><ul><li>we need a way to communicate more. </li></ul><ul><li>What ??? </li></ul>LEANRING 1
13. 13. Average Income Country X Country Y 10,000 Rs/Month 11000 Rs/Month Which country is ECONOMICALLY more stable ??? Example
14. 14. Country X Country Y 8000 46000 12000 3000 10000 1000 9000 3000 11000 2000 Avg. 10000 11000 Std dev. 1414 17516
15. 15. <ul><li>Meeting specification is not enough </li></ul><ul><li>we need a way to communicate </li></ul><ul><ul><li>How close to target </li></ul></ul><ul><ul><li>How spread out the results were </li></ul></ul>LEANRING 2
16. 16. <ul><li>Statistical Process Control </li></ul><ul><li>A monitoring tool that let's us know when a process is changing before products become unacceptable </li></ul><ul><li>It is a prevention tool </li></ul><ul><ul><li>Inspection = defect detection </li></ul></ul><ul><ul><li>SPC =detect process change </li></ul></ul><ul><ul><ul><li>defect prevention </li></ul></ul></ul>What is SPC?
17. 17. <ul><li>Inspection does not assure quality </li></ul><ul><li>inspection is too late, its after the fact </li></ul><ul><li>need to detect process change before defectives are produced </li></ul><ul><li>Meeting specification does not go far enough </li></ul>WHY SPC?
18. 18. <ul><li>Quantitify the Mue and the Sigma of a process and detects change from the standard deviation by calculating the control limit by estimating the Rbar over d2 to estimate the inherent variation of a process for a given alpha and beta risks. </li></ul>SPC, how does it work Ooopps tough to understand……
19. 19. <ul><li>JUST KIDDING! </li></ul>SPC quantifies variability and allows you to determine if a process changed. It is simple and easy to understand.
20. 20. <ul><li>First order </li></ul>size DISCUSSION ON VARIABILITY lower spec. Upper spec.
21. 21. <ul><li>Second order </li></ul>size lower spec. Upper spec.
22. 22. <ul><li>After 6 orders </li></ul>size lower spec. Upper spec.
23. 23. <ul><li>After 12 orders </li></ul>size lower spec. Upper spec.
24. 24. <ul><li>Over the long run a pattern begins to develop. Notice there is a large cluster in the middle. As further from </li></ul><ul><li>the middle you go, there are less and less </li></ul>size lower spec. Upper spec.
25. 25. <ul><li>lower </li></ul><ul><li>spec. </li></ul>size If the source of the material is stable, over a long time period, a bell like shaped curve will emerge from the inspection. The Bell shape curve is also commonly referred to as the Normal distribution Upper spec.
26. 26. Plot HISTOGRAM for following DATA What is HITOGRAM? Why we need it to understand? What is this BELL shape and normal distribution?
27. 27. <ul><li>CHARACTERISTICS OF A NORMAL DISTRIBUTION </li></ul>LOCATION SPREAD LEANRING 3 LOCATION: The central tendency it is usually expressed as the AVERAGE SPREAD: The dispersion it is usually expressed as SIGMA
28. 28. Distribution Patterns Saw tooth Positively Skewed Negatively Skewed Sharp Drop Twin Peak Bell Shape
29. 29. <ul><li>Average different </li></ul><ul><li>Spread same </li></ul>A B
30. 30. <ul><li>Average same </li></ul><ul><li>Spread different </li></ul>A B
31. 31. <ul><li>A </li></ul>B Average different Spread different
32. 32. <ul><li>SIGMA -measure of spread </li></ul>LEANRING 4 sigma
33. 33. <ul><li>32% </li></ul>32% 14% 14% 2% 2% +/- 1 sigma +/- 2 sigma +/-3 sigma
34. 34. <ul><li>32% </li></ul>32% 14% 14% 2% 2% 64.25% 96.45% 99.73% +/-3 sigma +/-2 sigma +/-1 sigma
35. 35. 34.13% 34.13% 13.6% 13.6% 2.14% 2.14% +/- 1 sigma +/- 2 sigma +/-3 sigma 68.26% 95.45% 99.73% LEANRING 5
36. 36. <ul><li>64% </li></ul>14 2 32 gallons IF the upside-down bell curve could hold 100 gallons of water..... 96% 99.7% +/-3 sigma +/-2 sigma +/-1 sigma
37. 37. <ul><li>It is symmetrical , unimodel and bell shaped. </li></ul><ul><li>It is uniquely determined by the two parameters , namely mean and standard deviation. </li></ul><ul><li>In the family of normal curves smaller the standard deviation , higher will be the peak. </li></ul><ul><li>If the original observations follow a normal model with mean mu and std dev sigma then the averages of random sample of size n drawn from this distribution will also follow a normal distribution. </li></ul><ul><li>The mean of the new model is same as the original model I.e mu but the standard deviation gets reduced to  (sigma)/root &quot;n&quot; </li></ul>Properties of a normal model curve :- LEANRING 6
38. 38. Sources of Variation Common Cause Special Cause
39. 39. <ul><li>TIME </li></ul>PREDICTION If only common cause of variation are present, the output of a process forms a distribution that is stable over time and is PREDICTABLE. LEANRING 7
40. 40. <ul><li>That's great, we can make prediction based </li></ul><ul><li>on sigma, So what? </li></ul><ul><li>Once we know the sigma of a process then; </li></ul><ul><ul><li>Process has not changed if it is inside +/- 3 sigma. </li></ul></ul><ul><ul><li>If outside +/- 3 sigma, process has changed </li></ul></ul>SO WHAT?
41. 41. <ul><li>SINCE WE CAN NOT SAMPLE 100 UNITS TO </li></ul><ul><li>DETERMINE IF OUR MANUFACTURING PROCESS </li></ul><ul><li>HAS CHANGED WE NEED A QUICK EFFECTIVE </li></ul><ul><li>WAY TO MEASURE THE TWO ATTRIBUTE OF </li></ul><ul><li>A PROCESS; THE CENTER AND THE SPREAD </li></ul><ul><li>CENTER = AVERAGE </li></ul><ul><li>SPREAD = RANGE </li></ul><ul><ul><ul><li>= (MAXIMUM - MINIMUM) </li></ul></ul></ul>Why Average ???? LEANRING 8
42. 42. The Central Limit Theorem The Central Limit Theorem states that the mean values of samples taken from ANY distribution tend towards a normal distribution as the sample size increases . This computer demonstration provides convincing evidence of this surprising fact. Thus, taking samples from a distribution and averaging the observations within the samples effectively eliminates the effect of the underlying distribution, however 'non-normal' it may be. This demonstration works with two symmetrical distributions: one is triangular and has some features in common with the normal distribution while the other is a 'V'-shaped notch - almost the total opposite of the type of distributions we see in applied statistics. Both distributions have a mean of 50.00. We can model these distributions by supposing we have two packs containing cards numbered 1 - 99. The first pack would have: One 1, two 2s .... fifty 50s, forty nine 51s, .... two 98s, and one 99 While the second would have: Fifty 1s, forty nine 2s ... two 48s, one 50, two 51s, ..... fifty 99s The computer draws cards according to these distributions for sample sizes of 1 (to verify the concept of 'distribution'), 2, 5 and 10. When the sample size is 1, we are really confirming that the data 'in the long run' will behave like the distribution - which is in itself an important statistical lesson. The case {Sample Size = 2} is particularly interesting. It is not easy to to 'outguess' the computer and predict the shape of the lower curve; however, once the curve is seen, it can be readily explained in terms of basic probability. Although the second case is very extreme (literally!) compared with the first, it eventually falls into a 'normal' shape although it takes longer to do so. LEANRING 9
43. 43. The Arithmetic mean : Most of the time when we refer to the average of something we are talking about arithmetic mean only. To find out the arithmetic mean , we sum the values and divide by the number of observation. Advantages : it's a good measure of central tendency.It easily understood by most people Disadvantages :- Although the mean is reliable in that it reflects all the values in the data set, it may also be affected by extreme values that are not representative of the rest of the data.
44. 44. The Median : The median is a single value from the data set that measures the central item in the set of numbers.Half of the item lie above this point and the other half lie below it. We can find median even when our data are qualitative descriptions. For example we have five runs of the printing press the results of which must be rated according to the sharpness of the image. Extremely sharp, very sharp, sharp slightly blurred, and very blurred. Mode :- The mode is a value that is repeated most often in the data set. Infect it is the value with highest frequency.
45. 45. <ul><li>23 </li></ul>23 24 26 27 1 2 3 4 5 Average Range How was our process behaving over time? Let's calculate the average and range of each set average = (23+23+24+26+27)/5 = 24.6 Range = 27 - 23 = 4 CONTROL CHART TEMPLATE
46. 46. <ul><li>1 </li></ul>23 23 24 26 27 24.6 4 22 25 25 26 27 25.0 5 23 23 24 27 27 22 24 24 25 26 24.8 24.2 4 4 Plott the average and the range on the control chart template Notice the center and the spread of the process varies much like when we looked at the histogram 2 3 4 5 avg Min. Max Range average range CONTROL CHART TEMPLATE
47. 47. <ul><li>x </li></ul>x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x-bar Chart If you thought of the control charts as a stretched out slinky, it would look like a histogram if you collapsed it. Since the control chart is nothing more than a histogram expressed over time, what we said about SIGMA applies to the control chart as well. LEANRING 9
48. 48. <ul><li>64% </li></ul>14 2 32 gallons IF the upsidedown bell curve could hold 100 gallons of water..... Reminder, what we said about sigma 96% 99.7% +/-3 sigma +/-2 sigma +/-1 sigma
49. 49. <ul><li>x </li></ul>x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x +/- 3 sigma We can calculate the sigma of all the points in the control charts and draw lines at +/- 3 sigma. Since 99.7% of the vaules are suppose to fit in the line we can say that a process has changed if it one of the points are outside the +/- 3 sigma lines. We will call the +/-3 sigma lines the CONTROL LIMIT
50. 50. <ul><li>HOW DO YOU CALCULATE CONTROL LIMITS? </li></ul>In the past it was important for operators and auditors to be able to calculate the control limit. Today, in most manufacturing plants the computer calculates the control limits and people interpret them. This makes sense because computers are excellent at calculating number. However, computers are not too intelligent. They can not reason and make good decisions. People are very capable of reasoning and making good decision. However, people need good information. SPC is a tool that converts process data to information allowing people to focus on what they do best.
51. 51. Control Limits for Average and Range Chart R = R+R+R+…R 1 2 3 n n UCL = X + A 2 R CL = X LCL = X - A 2 R UCL = D 4 R CL = R LCL = D 3 R LEANRING 10 X = X+X+X+…X 1 2 3 n n
52. 52. <ul><li>HOW LONG DOES IT TAKE TO GET TO WORK? </li></ul>WE USE STATISTICS EVERYDAY
53. 53. <ul><li>TYPES OF VARIABILITY </li></ul><ul><ul><li>Common cause= normal, Inherent </li></ul></ul><ul><ul><li>Arrive work between 7:55 to 8:01due to number traffics lights that you stopped at on your way to work. </li></ul></ul><ul><ul><li>Special cause = assignable </li></ul></ul><ul><ul><li>Arrived to work today at 8:45 because; </li></ul></ul><ul><ul><ul><li>a) flat tire on the way to work </li></ul></ul></ul><ul><ul><ul><li>b) Accident on the interstate </li></ul></ul></ul><ul><ul><ul><li>c) I met up with an old drinking buddy and </li></ul></ul></ul><ul><ul><ul><li>I stayed out later than I should have. </li></ul></ul></ul>
54. 54. <ul><li>PROCESS CAPABILITY ANALOGY </li></ul>Bill, Nice guy. works in the accounting department. He lives 10 miles away from work. In order to get to work he takes the interstate I-95 and gets off at exit 23 and zips right into work. He never hits any trafficand there is no traffic light between his home and work. He's never late to work. Judge Lance Ito. Nice guy. Works in Los Angeles. He lives 5 miles from work. In order to get to work he has to get through 5 traffic light onto interstate I-5(which is frequently backed up) to downtown Los Angeles. There he has to find parking and then fight the reporters on his way into the court to preside over the O.J. Simpson trial. He is late to work quite frequently.
55. 55. <ul><li>PROCESS CAPABILITY ANALOGY </li></ul>Bill Arrives to work between 7:48 to 7:56 AM. Judge Lance Ito Arrives to work between 7:48 to 8:06 AM 8:06 8:12 8:00 7:54 7:48 7:42 Late to work Arrival time at work Early to work
56. 56. <ul><li>PROCESS CAPABILITY ANALOGY </li></ul>Bill Judge Ito 8:06 8:12 8:00 7:54 7:48 7:42 Late to work Arrival time at work Early to work If we thought of being early or late to work as our specification, then we can say that Bill IS capable meeting the specification. Judge Ito IS NOT capable of meeting the specification.
57. 57. <ul><li>PROCESS CAPABILITY ANALOGY </li></ul>Bill Arrives to work between 7:48 to 7:56 AM 99.7% of time. 6 sigma = 7:56 -7:48 = 8 min. Judge Lance Ito Arrives to work between 7:48 to 8:06 AM 99.7% of time. 6 sigma = 8:06 - 7:48 = 18 min. Tolerance = late - early = 8:00 - 7:46 = 14 minutes Capability = tolerance if greater than 1 we say it 6 sigma is capable of meeting spec. Bill's Capability = 14 / 8 = 1.75 (Bill is capable) Ito's Capability = 14/18 = .78 (Ito IS NOT capable)
58. 58. LEANRING 11 Cp = Tol band / 6 sigma Cpk = Min of (Avg - LSL) or (USL - Avg) / 3 sigma  (R abr) R d 2 =  (n-1) = √ (x-x ) + (x-x ) + … (x-x ) (n - 1) _ _ _ 1 2 n 2 2 2
59. 59. <ul><li>x </li></ul>The control limits can be drawn around both the average (x-bar) and the Range chart. Therefore, you can detect several different types of change. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x +/- 3 sigma +/- 3 sigma X-bar chart Range chart
60. 60. <ul><li>LOCATION SHIFTS </li></ul>Process spread remains same while center increases let's see what that looks like in a control chart
61. 61. <ul><li>+/- 3 sigma </li></ul>+/- 3 sigma X-bar chart Range chart Spread remains same Center shifts up
62. 62. <ul><li>SPREAD CHANGE </li></ul>Process spread increase while center remain same let's see what that looks like in a control chart
63. 63. <ul><li>+/- 3 sigma </li></ul>+/- 3 sigma X-bar chart Range chart Spread increased Center remain same ?
64. 64. <ul><li>+/- 3 sigma </li></ul>+/- 3 sigma X-bar chart Range chart Spread increased Center remain same
65. 65. <ul><li>Note that when the process variation increased </li></ul><ul><li>the Range chart points shifted to a higher level. </li></ul><ul><li>However, the process center (X-bar) seems to </li></ul><ul><li>swing wildly going out of both Upper and Lower </li></ul><ul><li>control limit while the average is still the same. </li></ul><ul><li>Because of the tendency of the X-bar chart to </li></ul><ul><li>swing with increase variability, the Range chart </li></ul><ul><li>must be reviewed first to determine if the process </li></ul><ul><li>variability increased prior to looking at the X-bar </li></ul><ul><li>chart to determine if the process shifted . </li></ul>LEANRING 12
66. 66. <ul><li>+/- 3 sigma </li></ul>target TREND Rule of thumb, if there are 7 points in a row all higher or lower than the preceeding point. In this case from the start of the trend to the time a point went outside the control limit there were 12 samples. An experinced operator/auditor would begin looking for assignable cause much sooner.
67. 67. <ul><li>+/- 3 sigma </li></ul>target SHIFT Rule of thumb, if there are 6 consequetive points above or below the target line, a process shift has occurred. In this case, because the process shifted to somewhere between the target and the upper control limit, there is a good chance that a point will be outside the control limit soon. In the above example, it took about 11 points to go outside the control limit. An experienced operator/auditor would have looked for assignable cause sooner.
68. 68. <ul><li>Summary.. Process changes </li></ul>Small shift .. in Center while Spread same in Spread while Center same Large shift in Center up or down while Spread same Spread increase while Center same Center slowly trending up or down while spead same Center shift up or down at the same time the spread increase
69. 69. <ul><li>So you now know how to detect change in a process. You even know how to detect different type of change to the process distribution. Up to now we have not talked about the QUALITY of the products being produced while the process is controlled using SPC methods. </li></ul><ul><li>If we control the process the process will produce parts with variation as the equipment is CAPABLE of producing. We call this PROCESS CAPABILITY. </li></ul>PROCESS CAPABILITY
70. 70. <ul><li>8:06 </li></ul>8:12 8:00 7:54 7:48 7:42 Lower spec. Upper spec. Cp Cpk TARGET Cp Cpk..... Say what?
71. 71. <ul><li>8:06 </li></ul>8:12 8:00 7:54 7:48 7:42 Lower spec. Upper spec. Cpk TARGET Cpk = Target - lower spec or Upper spec - Target 3 sigma 3 sigma Cpk looks at the likelihood of making product outside either lower or upper specification Cpk
72. 72. <ul><li>IT IS IMPORTANT TO KNOW WHAT YOUR MACHINE IS CAPABLE OF PRODUCING. OTHERWISE YOU MAY BE CHASING YOUR TAIL TRYING TO GET THE MACHINE TO DO WHAT IT IS NOT CAPABLE OF DOING. </li></ul>LEANRING
73. 73. <ul><li>X-bar chart </li></ul>x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x UPPER SPEC LOWER SPEC Each point is an average of five indivdual points x x x = x x x Each red x represents five individual reading (blue x) that are spread out more than the average (red x) Control chart will not differentiate a capable and a not capable process. it will only signal change. The control chart does not care what the spec is. UpperControl Limit LowerControl Limit x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
74. 74. <ul><li>x </li></ul>machine capability Upper spec Lower spec If your process is not capable, then there is a good chance that some of your sample will have values outside the specification. Chances are if you are not running SPC control chart, you may be tempted to make an adjustment. Let's see what would happen. LEANRING x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
75. 75. <ul><li>x </li></ul>machine capability Upper spec Lower spec x x xx = x x If by the luck of the draw you get a reading below the lower specification even though the process has not changed, and adjusted the machine up. The distribution will shift up. Sample Adjust machine up LEANRING x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
76. 76. <ul><li>x </li></ul>machine capability Upper spec Lower spec After the distribution shifted up, there is now a much greater chance of getting a value outside upper specification. So the machine is adjusted down, slightly more than it was adjusted up. Chance of out of spec is now = 40% Chance of out of spec was = 10% Adjust machine down LEANRING x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
77. 77. <ul><li>x </li></ul>The adjustments continues until, the actual products produced varies much more than the capability of the machine. LEANRING 13 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Actual range of product produced machine capability Upper spec Lower spec
78. 78. <ul><li>x </li></ul>machine capability Upper spec Lower spec If you are controlling your process using SPC Method, even if your process is not capable, no adjustment would take place. Therefore, the product you produced is what the machine is capable of and not more. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x = x x x UpperControl Limit LowerControl Limit LEANRING 14 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
79. 79. ATTRIBUTE CONTROL CHARTS Variable Sample Fixed Sample Defects Defectives
80. 80. Measurement System Analysis (MSA)