Unit-3CONTROL CHARTS                 Represented by:-                  Deepa chauhan
BASICS OF STATISTICAL PROCESSCONTROL   Statistical Process    Control (SPC)       monitoring production        process t...
VARIABILITY   Random                        Non-Random     common   causes               special causes     inherent ...
SPC IN TQM   SPC      toolfor identifying problems and make improvements      contributes to the TQM goal of continuous...
QUALITY MEASURES   Attribute    a  product characteristic that can be evaluated with a      discrete response     good ...
APPLYING SPC TO SERVICE Nature of defect is different in services Service defect is a failure to meet customer  requirem...
APPLYING SPC TO SERVICE (CONT.)   Hospitals       timeliness and quickness of care, staff responses to        requests, ...
APPLYING SPC TO SERVICE (CONT.) Fast-Food   Restaurants   waiting time for service, customer complaints,    cleanliness,...
WHERE TO USE CONTROL CHARTS Process   has a tendency to go out of control Process is particularly harmful and costly  if...
CONTROL CHARTS A graph that                   Types of charts  establishes control              Attributes  limits of a...
PROCESS CONTROL CHART                                 Out of control   Upper  control    limit  Process  average   Lower  ...
NORMAL DISTRIBUTION                        95%                       99.74%     -3σ   -2σ   -1σ    µ =0    1σ   2σ   3σ   ...
A PROCESS IS IN CONTROL IF … … no sample points outside limits … most points near process average … about equal number ...
CONTROL CHARTS FORATTRIBUTES   p-charts     uses   portion defective in a sample   c-charts     uses   number of defec...
P-CHART   UCL = p + zσ p   LCL = p - zσ p          z      =       number of standard          deviations from process aver...
P-CHART EXAMPLE             NUMBER OF    PROPORTION    SAMPLE   DEFECTIVES    DEFECTIVE       1           6          .06  ...
P-CHART EXAMPLE (CONT.)             total defectives   p = total sample observations = 200 / 20(100) = 0.10               ...
P-CHART EXAMPLE (CONT.)                           0.20                           0.18              UCL = 0.190            ...
C-CHART   UCL = c + zσ c                           σc =   c   LCL = c - zσ c   where           c = number of defects per s...
C-CHART (CONT.)  Number of defects in 15 sample rooms            NUMBER   SAMPLE     OF            DEFECTS                ...
C-CHART (CONT.)                        24                                     UCL = 23.35                        21       ...
CONTROL CHARTS FOR VARIABLES   Mean chart ( x -Chart )     uses   average of a sample   Range chart ( R-Chart )     us...
X-BAR CHART   = = x1 + x2 + ... xk   x             k   UCL = x=+ A R              =- A R                        LCL = x   ...
X-BAR CHART EXAMPLE                OBSERVATIONS (SLIP- RING DIAMETER, CM)     SAMPLE k    1      2      3      4      5   ...
X- BAR CHART EXAMPLE(CONT.)     = ∑x   50.09     x=   =       = 5.01 cm        k    10         =   UCL = x + A2R = 5.01 + ...
5.10 –                 5.08 –                              UCL = 5.08                 5.06 –                 5.04 –       ...
R- CHART      UCL = D4R        LCL = D3R                   ∑R                R=                    k     where           R...
R-CHART EXAMPLE                OBSERVATIONS (SLIP-RING DIAMETER, CM)     SAMPLE k    1      2      3      4      5      x ...
R-CHART EXAMPLE (CONT.)       ∑R   1.15             UCL = D4R = 2.11(0.115) = 0.243    R=    =      = 0.115        k    10...
R-CHART EXAMPLE (CONT.)            0.28 –            0.24 –   UCL = 0.243            0.20 –    Range            0.16 –    ...
USING X- BAR AND R-CHARTSTOGETHER Process average and process variability must be  in control. It is possible for sample...
CONTROL CHART PATTERNSUCL                               UCLLCL      Sample observations      consistently below the   LCL ...
CONTROL CHART PATTERNS (CONT.)UCL                                UCLLCL      Sample observations      consistently increas...
PROCESS CAPABILITY  It gives satisfactory indication after x bar and R control   charts.  It is done to ensure that tole...
deviation1 = R bar/d2Where dev.1 = S.D. for individual observation R = A.V range of samples size from table d2 = factor a...
PROCESS CAPABILITY                                      Design                                   Specifications(a) Natural...
PROCESS CAPABILITY (CONT.)                                        Design                                     Specification...
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Control chart qm

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Control chart qm

  1. 1. Unit-3CONTROL CHARTS Represented by:- Deepa chauhan
  2. 2. BASICS OF STATISTICAL PROCESSCONTROL Statistical Process Control (SPC)  monitoring production process to detect and UCL prevent poor quality Sample  subset of items produced LCL to use for inspection Control Charts  process is within statistical control limits 4-2
  3. 3. VARIABILITY Random  Non-Random  common causes  special causes  inherent in a process  due to identifiable  can be eliminated only factors through improvements  can be modified in the system through operator or management action 4-3
  4. 4. SPC IN TQM SPC  toolfor identifying problems and make improvements  contributes to the TQM goal of continuous improvements . 4-4
  5. 5. QUALITY MEASURES Attribute a product characteristic that can be evaluated with a discrete response  good – bad; yes - no Variable a product characteristic that is continuous and can be measured  weight - length 4-5
  6. 6. APPLYING SPC TO SERVICE Nature of defect is different in services Service defect is a failure to meet customer requirements Monitor times, customer satisfaction 4-6
  7. 7. APPLYING SPC TO SERVICE (CONT.) Hospitals  timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts Grocery Stores  waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors Airlines  flight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance 4-7
  8. 8. APPLYING SPC TO SERVICE (CONT.) Fast-Food Restaurants  waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy Catalogue-Order Companies  order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time Insurance Companies  billingaccuracy, timeliness of claims processing, agent availability and response time 4-8
  9. 9. WHERE TO USE CONTROL CHARTS Process has a tendency to go out of control Process is particularly harmful and costly if it goes out of control Examples  atthe beginning of a process because it is a waste of time and money to begin production process with bad supplies  before a costly or irreversible point, after which product is difficult to rework or correct  before and after assembly or painting operations that might cover defects  before the outgoing final product or service is delivered 4-9
  10. 10. CONTROL CHARTS A graph that  Types of charts establishes control  Attributes limits of a process  p-chart  c-chart Control limits  Variables  upper and lower bands of a control chart  range (R-chart)  mean (x bar – chart) 4-10
  11. 11. PROCESS CONTROL CHART Out of control Upper control limit Process average Lower control limit 1 2 3 4 5 6 7 8 9 10 4-11 Sample number
  12. 12. NORMAL DISTRIBUTION 95% 99.74% -3σ -2σ -1σ µ =0 1σ 2σ 3σ 4-12
  13. 13. A PROCESS IS IN CONTROL IF … … no sample points outside limits … most points near process average … about equal number of points above and below centerline … points appear randomly distributed 4-13
  14. 14. CONTROL CHARTS FORATTRIBUTES p-charts  uses portion defective in a sample c-charts  uses number of defects in an item 4-14
  15. 15. P-CHART UCL = p + zσ p LCL = p - zσ p z = number of standard deviations from process average p = sample proportion defective; an estimate of process average σp = standard deviation of sample proportion p(1 - p) σp = n 4-15
  16. 16. P-CHART EXAMPLE NUMBER OF PROPORTION SAMPLE DEFECTIVES DEFECTIVE 1 6 .06 2 0 .00 3 4 .04 : : : : : : 20 18 .18 200 20 samples of 100 pairs of jeans 4-16
  17. 17. P-CHART EXAMPLE (CONT.) total defectives p = total sample observations = 200 / 20(100) = 0.10 p(1 - p) 0.10(1 - 0.10) UCL = p + z = 0.10 + 3 n 100 UCL = 0.190 p(1 - p) 0.10(1 - 0.10) LCL = p - z = 0.10 - 3 n 100 LCL = 0.010 4-17
  18. 18. P-CHART EXAMPLE (CONT.) 0.20 0.18 UCL = 0.190 0.16 0.14 Proportion defective 0.12 p = 0.10 0.10 0.08 0.06 0.04 0.02 LCL = 0.010 4-18 2 4 6 8 10 12 14 16 18 20 Sample number
  19. 19. C-CHART UCL = c + zσ c σc = c LCL = c - zσ c where c = number of defects per sample 4-19
  20. 20. C-CHART (CONT.) Number of defects in 15 sample rooms NUMBER SAMPLE OF DEFECTS 190 1 12 c= = 12.67 15 2 8 UCL = c + zσ c 3 16 = 12.67 + 3 12.67 : : = 23.35 : : LCL = c + zσ c 15 15 = 12.67 - 3 12.67 190 = 1.99 4-20
  21. 21. C-CHART (CONT.) 24 UCL = 23.35 21 18 Number of defects c = 12.67 15 12 9 6 3 LCL = 1.99 4-21 2 4 6 8 10 12 14 16 Sample number
  22. 22. CONTROL CHARTS FOR VARIABLES Mean chart ( x -Chart )  uses average of a sample Range chart ( R-Chart )  uses amount of dispersion in a sample 4-22
  23. 23. X-BAR CHART = = x1 + x2 + ... xk x k UCL = x=+ A R =- A R LCL = x 2 2 where = x = average of sample means 4-23
  24. 24. X-BAR CHART EXAMPLE OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 1 2 3 4 5 1 5.02 5.01 4.94 4.99 4.96 2 5.01 5.03 5.07 4.95 4.96 3 4.99 5.00 4.93 4.92 4.99 4 5.03 4.91 5.01 4.98 4.89 5 4.95 4.92 5.03 5.05 5.01 6 4.97 5.06 5.06 4.96 5.03 7 5.05 5.01 5.10 4.96 4.99 8 5.09 5.10 5.00 4.99 5.08 9 5.14 5.10 4.99 5.08 5.09 10 5.01 4.98 5.08 5.07 4.99 4-24Example 15.4
  25. 25. X- BAR CHART EXAMPLE(CONT.) = ∑x 50.09 x= = = 5.01 cm k 10 = UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08 = LCL = x - A2R = 5.01 - (0.58)(0.115) = 4.94 Retrieve Factor Value A2 4-25
  26. 26. 5.10 – 5.08 – UCL = 5.08 5.06 – 5.04 – 5.02 – = Mean x = 5.01 5.00 –X- BAR 4.98 –CHART 4.96 –EXAMP 4.94 – LCL = 4.94LE 4.92 –(CONT.) | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 Sample number 4-26
  27. 27. R- CHART UCL = D4R LCL = D3R ∑R R= k where R = range of each sample k = number of samples 4-27
  28. 28. R-CHART EXAMPLE OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 4-28Example 15.3
  29. 29. R-CHART EXAMPLE (CONT.) ∑R 1.15 UCL = D4R = 2.11(0.115) = 0.243 R= = = 0.115 k 10 LCL = D3R = 0(0.115) = 0 Retrieve Factor Values D3 and D4 4-29Example 15.3
  30. 30. R-CHART EXAMPLE (CONT.) 0.28 – 0.24 – UCL = 0.243 0.20 – Range 0.16 – R = 0.115 0.12 – 0.08 – 0.04 – LCL = 0 | | | | | | | | | | 0– 1 2 3 4 5 6 7 8 9 10 Sample number 4-30
  31. 31. USING X- BAR AND R-CHARTSTOGETHER Process average and process variability must be in control. It is possible for samples to have very narrow ranges, but their averages is beyond control limits. It is possible for sample averages to be in control, but ranges might be very large. 4-31
  32. 32. CONTROL CHART PATTERNSUCL UCLLCL Sample observations consistently below the LCL center line Sample observations consistently above the 4-32 center line
  33. 33. CONTROL CHART PATTERNS (CONT.)UCL UCLLCL Sample observations consistently increasing LCL Sample observations consistently decreasing 4-33
  34. 34. PROCESS CAPABILITY  It gives satisfactory indication after x bar and R control charts.  It is done to ensure that tolerance is possible through process control.  Frequency distribution is done for a new process.  It is better to study process capability before production.  Process study capacity is defined as 6 deviations. This is for individual observation. 4-34
  35. 35. deviation1 = R bar/d2Where dev.1 = S.D. for individual observation R = A.V range of samples size from table d2 = factor as per sampleProcess capability = 6 dev.1And dev.1 = R bar/d2Hence 6*R bar/d2 4-35
  36. 36. PROCESS CAPABILITY Design Specifications(a) Natural variationexceeds designspecifications; processis not capable ofmeeting specificationsall the time. Process Design Specifications (b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time. 4-36 Process
  37. 37. PROCESS CAPABILITY (CONT.) Design Specifications(c) Design specificationsgreater than naturalvariation; process iscapable of alwaysconforming tospecifications. Process Design Specifications (d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification. 4-37 Process
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