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Statistical Process Control Dr. Mohamed Riyazh Khan DoMS.

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2 Statistical Process Control Dr. Mohamed Riyazh Khan DoMS

3 SQC S.Q.C. means planned collection and effective use of data for studying causes of variations in quality either as between processes, procedures, materials, machines, etc., or over periods of time. The main purpose of Statistical Quality control is to determine statistical techniques which would help us in separating the assignable causes from the chance causes, thus enabling us to take immediate remedial action whenever assignable causes are present A production process is said to be in a state of statistical control, if it is governed by chance causes alone, in the absence of assignable causes of variation.

4 Two Primary Topics in Statistical Quality Control 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.

5 Two Primary Topics in Statistical Quality Control 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 ?

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

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

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

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

10 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)

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

12 Variation & Process Control Charts Variation always exists 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. Process control charts are designed to detect causal variations

13 Variation in the quality of manufactured product in the repetitive process in industry is inevitable. The variations may be classified as being due to two causes: Chance Causes Assignable causes

14 Chance Causes Some “stable pattern of variation” or “ a constant cause system” is inherent in any particular scheme of production and inspection. The variation due to these causes is beyond the circumstances.

15 Assignable Causes This type of variation is attributed to any production process is due to non-random or assignable causes and is termed as preventive variation.. These causes may be the result of multiplicity of factors such as defective or substandard raw material, new operation, improper setting and wrong handling of machine, mechanical defects etc. These causes can be identified and eliminated and are to be discovered in a production process before it goes wrong.

16 Advantages of quality control in industry Planned collection of data, analysis and interpretation Improvement in quality Reduction in cost per unit Reduction in scrap Saving in excess use of materials Removing production bottlenecks Reduction in inspection Evaluation of scientific tolerances Maintenance of operating efficiency Quality consciousness Greater customer satisfaction Enhanced productivity

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

18 Control Chart Control Chart for Variables Control Chart for Attributes

19 Control Chart for Variables For a characteristic which can be measured quantitatively. Many quality characteristics of a product are measurable and can be expressed in specific units of measurement such as diameter of a screw, tensile strength of steel pipe, specific resistance of a wire, life of an electric bulb, etc.

20 Control Chart for Variables Chart for X and σ (S.D) Charts for X (Mean) and R (Range)

21 Control Chart for Attributes Control Chart for Number of Defects (c– chart) Control Chart for Fraction Defective (p – chart)

22 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.

23 Basis of Control Charts 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) Historical Data Control Charts – Process Average, upper & lower control limits: based on historical measurements – Often used in well established processes

24 Common Causes 425 Grams

25 Assignable Causes (a) Location Grams Average

26 Assignable Causes (b) Spread Grams Average

27 Assignable Causes (b) Spread Grams Average

28 Assignable Causes (c) Shape Grams Average

29 Effects of Assignable Causes on Process ControlAssignable causes present

30 Effects of Assignable Causes on Process ControlNo assignable causes

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

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

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

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

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

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

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

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

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

40 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

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

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

43 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

44 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

45 Control Charts for Variables Mandara Industries

46 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

47 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

48 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

49 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

50 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

51 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

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

53 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

54 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

55 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

56 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

57 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.

58 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.

59 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

60 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

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

62 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

63 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

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

65 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

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

67 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

68 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

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

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

71 Process Capability Lower specification Mean Upper specification Two sigma

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

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

74 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

75 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

76 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

77 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,

78 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,

79 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

80 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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