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Statistical Process Control A. A. Elimam A. A. Elimam.

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Presentation on theme: "Statistical Process Control A. A. Elimam A. A. Elimam."— Presentation transcript:

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2 Statistical Process Control A. A. Elimam A. A. Elimam

3 Two Primary Topics in Statistical Quality Control n n Statistical process control (SPC) is a statistical method using control charts to check a production process - prevent poor quality. In TQM all workers are trained in SPC methods.

4 Two Primary Topics in Statistical Quality Control n n Acceptance Sampling involves inspecting a sample of product. If sample fails reject the entire product - identifies the products to throw away or rework. Contradicts the philosophy of TQM. Why ?

5 Inspection n n Traditional Role: at the beginning and end of the production process n n Relieves Operator from the responsibility of detecting defectives & quality problems n n It was the inspection's job n n In TQM, inspection is part of the process & it is the operator’s job n n Customers may require independent inspections

6 How Much to Inspect? n n Complete or 100 % Inspection. Viable for products that can cause safety problems Does not guarantee catching all defectives Too expensive for most cases n n Inspection by Sampling Sample size : representative A must in destructive testing (e.g... Tasting food)

7 Where To Inspect ? n n In TQM, inspection occurs throughout the production process n n IN TQM, the operator is the inspector n n Locate inspection where it has the most effect (e.g.... prior to costly or irreversible operation) n n Early detection avoids waste of more resources

8 Quality Testing n n Destructive Testing Product cannot be used after testing (e.g.. taste or breaking item) Sample testing Could be costly n n Non-Destructive Testing Product is usable after testing 100% or sampling

9 Quality Measures:Attributes Attribute is a qualitative measure Product characteristics such as color, taste, smell or surface texture Simple and can be evaluated with a discrete response (good/bad, yes/no) Large sample size (100’s)

10 Quality Measures:Variables A quantitative measure of a product characteristic such as weight, length, etc. Small sample size (2-20) Requires skilled workers

11 Variation & Process Control Charts n n Variation always exists n n Two Types of Variation Causal: can be attributed to a cause. If we know the cause we can eliminate it. Random: Cannot be explained by a cause. An act of nature - need to accept it. n n Process control charts are designed to detect causal variations

12 Control Charts: Definition & Types n n A control chart is a graph that builds the control limits of a process n n Control limits are the upper and lower bands of a control chart n n Types of Charts: Measurement by Variables: X-bar and R charts Measurement by Attributes: p and c

13 Process Control Chart & Control Criteria 1. No sample points outside control limits. 2. Most points near the process average. 3. Approximately equal No. of points above & below center. 4. Points appear to be randomly distributed around the center line. 5. No extreme jumps. 6. Cannot detect trend.

14 Basis of Control Charts n n Specification Control Charts Target Specification: Process Average Tolerances define the specified upper and lower control limits Used for new products (historical measurements are not available) n n Historical Data Control Charts Process Average, upper & lower control limits: based on historical measurements Often used in well established processes

15 Common Causes 425 Grams

16 Assignable Causes (a) Location Grams Average

17 Assignable Causes (b) Spread Grams Average

18 Assignable Causes (b) Spread Grams Average

19 Assignable Causes (c) Shape Grams Average

20 Effects of Assignable Causes on Process Control Assignable causes present

21 Effects of Assignable Causes on Process Control No assignable causes

22 Sample Means and the Process Distribution 425 Grams Mean Process distribution Distribution of sample means

23 The Normal Distribution -3  -2  -1  +1  +2  +3  Mean 68.26% 95.44% 99.97%  = Standard deviation

24 Control Charts UCL Nominal LCL Assignable causes likely 1 2 3 Samples

25 Using Control Charts for Process Improvement  Measure the process  When problems are indicated, find the assignable cause  Eliminate problems, incorporate improvements  Repeat the cycle

26 Control Chart Examples Nominal UCL LCL Sample number (a) Variations

27 Control Chart Examples Nominal UCL LCL Sample number (b) Variations

28 Control Chart Examples Nominal UCL LCL Sample number (c) Variations

29 Control Chart Examples Nominal UCL LCL Sample number (d) Variations

30 Control Chart Examples Nominal UCL LCL Sample number (e) Variations

31 The Normal Distribution Measures of Variability: Most accurate measure  = Standard Deviation Approximate Measure - Simpler to compute R = Range Range is less accurate as the sample size gets larger Average  = Average R when n = 2

32 Control Limits and Errors LCL Process average UCL (a) Three-sigma limits Type I error: Probability of searching for a cause when none exists

33 Control Limits and Errors Type I error: Probability of searching for a cause when none exists UCL LCL Process average (b) Two-sigma limits

34 Type II error: Probability of concluding that nothing has changed Control Limits and Errors UCL Shift in process average LCL Process average (a) Three-sigma limits

35 Type II error: Probability of concluding that nothing has changed Control Limits and Errors UCL Shift in process average LCL Process average (b) Two-sigma limits

36 Control Charts for Variables Mandara Industries

37 Control Charts for Variables Sample Number1234RangeMean 10.50140.50220.50090.5027 20.50210.50410.50320.5020 30.50180.50260.50350.5023 40.50080.50340.50240.5015 50.50410.50560.50340.5039 Special Metal Screw

38 Control Charts for Variables Sample Number1234RangeMean 10.50140.50220.50090.5027 20.50210.50410.50320.5020 30.50180.50260.50350.5023 40.50080.50340.50240.5015 50.50410.50560.50340.5039 0.5027 - 0.5009=0.0018 Special Metal Screw

39 Control Charts for Variables Sample Number1234RangeMean 10.50140.50220.50090.50270.0018 20.50210.50410.50320.5020 30.50180.50260.50350.5023 40.50080.50340.50240.5015 50.50410.50560.50340.5039 0.5027 - 0.5009=0.0018 Special Metal Screw

40 Control Charts for Variables Sample Number1234RangeMean 10.50140.50220.50090.50270.00180.5018 20.50210.50410.50320.5020 30.50180.50260.50350.5023 40.50080.50340.50240.5015 50.50410.50560.50340.5039 0.5027 - 0.5009=0.0018 (0.5014 + 0.5022 + 0.5009 + 0.5027)/4=0.5018 0.5009 + 0.5027)/4=0.5018 Special Metal Screw

41 Control Charts for Variables Sample Number1234RangeMean 10.50140.50220.50090.50270.00180.5018 20.50210.50410.50320.5020 30.50180.50260.50350.5023 40.50080.50340.50240.5015 50.50410.50560.50340.5039 0.5027 - 0.5009=0.0018 (0.5014 + 0.5022 + 0.5009 + 0.5027)/4=0.5018 0.5009 + 0.5027)/4=0.5018 Special Metal Screw

42 Control Charts for Variables Sample Number1234RangeMean 10.50140.50220.50090.50270.00180.5018 20.50210.50410.50320.50200.00210.5029 30.50180.50260.50350.50230.00170.5026 40.50080.50340.50240.50150.00260.5020 50.50410.50560.50340.50390.00220.5043 R =0.0020 x =0.5025 Special Metal Screw

43 Control Charts for Variables Control Charts - Special Metal Screw R - Charts R = 0.0020 UCL R = D 4 R LCL R = D 3 R

44 Control Charts for Variables Control Charts - Special Metal Screw R - Charts R = 0.0020 D 4 = 2.2080 Control Chart Factors Control Chart Factors Factor for UCLFactor forFactor Size ofand LCL forLCL forUCL for Samplex-ChartsR-ChartsR-Charts (n)(A 2 )(D 3 )(D 4 ) 21.88003.267 31.02302.575 40.72902.282 50.57702.115 60.48302.004 70.4190.0761.924

45 Control Charts for Variables Control Charts - Special Metal Screw R - Charts R = 0.0020 D 4 = 2.282 D 3 = 0 UCL R = 2.282 (0.0020) = 0.00456 in. LCL R = 0 (0.0020) = 0 in. UCL R = D 4 R LCL R = D 3 R

46 0.005 0.004 0.003 0.002 0.001 0 123456123456 Range (in.) Sample number UCL R = 0.00456 LCL R = 0 R = 0.0020 Range Chart - Special Metal Screw

47 Control Charts for Variables Control Charts - Special Metal Screw R = 0.0020 x = 0.5025 x - Charts UCL x = x + A 2 R LCL x = x - A 2 R Control Chart Factors Control Chart Factors Factor for UCLFactor forFactor Size ofand LCL forLCL forUCL for Samplex-ChartsR-ChartsR-Charts (n)(A 2 )(D 3 )(D 4 ) 21.88003.267 31.02302.575 40.72902.282 50.57702.115 60.48302.004 70.4190.0761.924

48 Control Charts for Variables Control Charts - Special Metal Screw R = 0.0020 A 2 = 0.729 x = 0.5025 x - Charts UCL x = x + A 2 R LCL x = x - A 2 R UCL x = 0.5025 + 0.729 (0.0020) = 0.5040 in.

49 Control Charts for Variables Control Charts - Special Metal Screw R = 0.0020 A 2 = 0.729 x = 0.5025 x - Charts UCL x = x + A 2 R LCL x = x - A 2 R UCL x = 0.5025 + 0.729 (0.0020) = 0.5040 in. LCL x = 0.5025 - 0.729 (0.0020) = 0.5010 in.

50 0.5050 0.5040 0.5030 0.5020 0.5010 123456123456 Average (in.) Sample number x = 0.5025 UCL x = 0.5040 LCL x = 0.5010 Average Chart - Special Metal Screw

51 0.5050 0.5040 0.5030 0.5020 0.5010 Average (in.) x = 0.5025 UCL x = 0.5040 LCL x = 0.5010 123456123456 Sample number   Measure the process   Find the assignable cause   Eliminate the problem   Repeat the cycle Average Chart - Special Metal Screw

52 Control Charts for Attributes MANDARA Bank UCL p = p + z  p LCL p = p - z  p  p = p (1 - p )/ n

53 MANDARA Bank UCL p = p + z  p LCL p = p - z  p  p = p (1 - p )/ n SampleWrongProportion NumberAccount NumberDefective 1150.006 2120.0048 3190.0076 420.0008 5190.0076 640.0016 7240.0096 870.0028 9100.004 10170.0068 11150.006 1230.0012 Total147 p = 0.0049 n = 2500 Control Charts for Attributes

54 Control Charts for Attributes MANDARA Bank UCL p = p + z  p LCL p = p - z  p  p = 0.0049(1 - 0.0049)/2500 n = 2500 p = 0.0049

55 Control Charts for Attributes MANDARA Bank UCL p = p + z  p LCL p = p - z  p  p = 0.0014 n = 2500 p = 0.0049

56 Control Charts for Attributes MANDARA Bank UCL p = 0.0049 + 3(0.0014) LCL p = 0.0049 - 3(0.0014)  p = 0.0014 n = 2500 p = 0.0049

57 Control Charts for Attributes MANDARA Bank UCL p = 0.0091 LCL p = 0.0007  p = 0.0014 n = 2500 p = 0.0049

58 12345678910111213 Sample number UCL p LCL 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 Proportion defective in sample p -Chart Wrong Account Numbers

59 12345678910111213 Sample number UCL p LCL 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 Proportion defective in sample p -Chart Wrong Account Numbers   Measure the process   Find the assignable cause   Eliminate the problem   Repeat the cycle

60 Process Capability Nominal value 80100120 Hours Upper specification Lower specification Process distribution (a) Process is capable

61 Process Capability Nominal value 80100120 Hours Upper specification Lower specification Process distribution (b) Process is not capable

62 Process Capability Lower specification Mean Upper specification Two sigma

63 Process Capability Lower specification Mean Upper specification Four sigma Two sigma

64 Process Capability Lower specification Mean Upper specification Six sigma Four sigma Two sigma

65 Upper specification = 120 hours Lower specification = 80 hours Average life = 90 hours s = 4.8 hours Process Capability Light-bulb Production C p = Upper specification - Lower specification 6s Process Capability Ratio

66 Process Capability Light-bulb Production Upper specification = 120 hours Lower specification = 80 hours Average life = 90 hours s = 4.8 hours C p = 120 - 80 6(4.8) Process Capability Ratio

67 Process Capability Light-bulb Production Upper specification = 120 hours Lower specification = 80 hours Average life = 90 hours s = 4.8 hours C p = 1.39 Process Capability Ratio

68 Process Capability Light-bulb Production Upper specification = 120 hours Lower specification = 80 hours Average life = 90 hours s = 4.8 hours C p = 1.39 C pk = Minimum of Upper specification - x 3s x - Lower specification 3sProcessCapabilityIndex,

69 Process Capability Light-bulb Production Upper specification = 120 hours Lower specification = 80 hours Average life = 90 hours s = 4.8 hours C p = 1.39 C pk = Minimum of 120 - 90 3(4.8) 90 - 80 3(4.8) ProcessCapabilityIndex,

70 Process Capability Light-bulb Production Upper specification = 120 hours Lower specification = 80 hours Average life = 90 hours s = 4.8 hours C p = 1.39 C pk = Minimum of [ 0.69, 2.08 ] ProcessCapabilityIndex

71 Process Capability Light-bulb Production Upper specification = 120 hours Lower specification = 80 hours Average life = 90 hours s = 4.8 hours C p = 1.39C pk = 0.69 ProcessCapabilityIndexProcessCapabilityRatio

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