1. 1 Chapter 9 Managing Flow Variability  Managing Flow Variability: Process Control and Capability Managing Business Process Flows:

2. 2 Chapter 9 Managing Flow Variability Managing Flow Variability  9.1 Performance Variability  9.2 Analysis of Variability  9.3 Process Control  9.4 Process Capability  9.5 Process Capability Improvement  9.6 Product and Process Design

3. 3 Chapter 9 Managing Flow Variability Managing Business Process Flows: Great year……. Great Products! Service! Reputation! Congratulations!! Good Job everyone! Sorry to burst the bubble... But we are not doing well. You’re Fired I heard customers are not satisfied with our products and services Hhhmmm… we need hard data. We need to identify, correct and prevent future problems! Yikes…mor e work

4. 4 Chapter 9 Managing Flow Variability All Products & Services VARY in Terms Of Managing Business Process Flows: CostQuality Availability FlowTimes Variability often leads to Customer Dissatisfaction Chapter covers some geographical/statistical methods for measuring, analyzing, controlling & reducing variability in product & process performance to improve customer satisfaction

5. 5 Chapter 9 Managing Flow Variability § 9.1 Performance Variability  All measures of product & process performance (external & internal) display Variability.  External Measurements - customer satisfaction, relative product rankings, customer complaints (vary from one market survey to the next)  Possible sources: supplier delivery delays or changing tastes  Internally - flow units in all business processes vary with respect to cost, quality & flow times  Possible sources: untrained workers or imprecise equipment Example 1 ~ No two cars rolling off an assembly line are identical. Even under identical circumstances, the time & cost required to produce the same product could be quite different. Example 2 ~ Cost of operating a department within a company can vary from one quarter to the next.

6. 6 Chapter 9 Managing Flow Variability § 9.1 Performance Variability  Variability refers to a discrepancy between the actual and the expected performance.  Can be due to gap between the following:  What customer wants and what product is designed for  What product design calls for and what process for making it is capable of producing  What process is capable of producing and what it actually produces  How the produced product is expected to perform and how it actually performs  How the product actually performs and how the customer perceives it  This often leads to:  higher costs, longer flow times, lower quality & DISSATISFIED CUSTOMERS

7. 7 Chapter 9 Managing Flow Variability § 9.1 Performance Variability  Processes with greater performance variability are generally judged LESS satisfactory than those with consistent, predictable performance.  Variability in product & process performance, not just its average, Matters to consumers!  Customers perceive any variation in their product or service from what they expected as a LOSS IN VALUE.  In general, a product is classified as defective if its cost, quality, availability or flow time differ significantly from their expected values, leading to dissatisfied customers.

8. 8 Chapter 9 Managing Flow Variability Quality Management Terms BOOK COVERS A FEW QUALITY MANAGEMENT TERMS:  Quality of Design: how well product specifications aim to meet customer requirements (what we promise consumers ~ in terms of what the product can do)  Quality Function Deployment (QFD): conceptual framework for translating customers’ functional requirements (such as ease of operation of a door or its durability) into concrete design specifications (such as the door weight should be between 75 and 85 kg.)  Quality of conformance: how closely the actual product conforms to the chosen design specifications (how well we keep our promise in terms of how it actually performs)  Measures: fraction of output that meets specifications, # defects per car, percentage of flights delayed for more than 15 minutes OR the number of reservation errors made in a specific period of time.

9. 9 Chapter 9 Managing Flow Variability § 9.2 Analysis of Variability  To analyze and improve variability there are diagnostic tools to help us:  Monitor the actual process performance over time  Analyze variability in the process  Uncover root causes  Eliminate those causes  Prevent them from recurring in the future  Again we will use MBPF Inc. as an example and look at how their customers perceive the experience of doing business with the company & how it can be improved. –Need to present raw data in a way to make sense of the numbers, track change over time, or identify key characteristics of the data set.

10. 10 Chapter 9 Managing Flow Variability § 9.2.1 Check Sheets  A check sheet is simply a tally of the types and frequency of problems with a product or a service experienced by customers.

11. 11 Chapter 9 Managing Flow Variability Example 9.1 Type of ComplaintNumber of Complaints CostIIII Response TimeIIII CustomizationIIII Service QualityIIII IIII IIII Door QualityIIII IIII IIII IIII IIII

12. 12 Chapter 9 Managing Flow Variability Check Sheets Pros  Easy to collect data Cons  Not very enlightening  No numerical characteristics

13. 13 Chapter 9 Managing Flow Variability § 9.2.2 Pareto Charts  A Pareto chart is simply a bar chart that plots frequencies of occurrences of problem types in decreasing order.  The 80-20 Pareto principle states that 20% of problem types account for 80% of all occurrences.

14. 14 Chapter 9 Managing Flow Variability Example 9.2

15. 15 Chapter 9 Managing Flow Variability Pareto Charts Pros  Ranks problems  Shows relative size of quantities Cons  No numerical characteristics  Only categorizes data  No comparison process information

16. 16 Chapter 9 Managing Flow Variability § 9.2.3 Histograms  A histogram is a bar plot that displays the frequency distribution of an observed performance characteristic.

17. 17 Chapter 9 Managing Flow Variability Example 9.3

18. 18 Chapter 9 Managing Flow Variability Histograms Pros  Visualizes data distribution  Shows relative size of quantities Cons  No numerical characteristics  Dependant on category size  No focus on change over time

19. 19 Chapter 9 Managing Flow Variability Table 9.1 Day Time12345678910 9:00 AM81828074758183868882 11:00 AM7387838186 82837984 1:00 PM85887691828376828689 3:00 PM907884758488777984 5:00 PM8084828375817885 80 Day Time11121314151617181920 9:00 AM86 8872847674858289 11:00 AM84837986858286858480 1:00 PM817883808183 828390 3:00 PM81808379888489779283 5:00 PM87838287817983778477

20. 20 Chapter 9 Managing Flow Variability Raw Data Pros  Actual information  Specific numbers Cons  Not intuitive  Does not help with understanding of relationships

21. 21 Chapter 9 Managing Flow Variability § 9.2.4 Run Charts  A run chart is a plot of some measure of process performance monitored over time  Advantage is that it is dynamic

22. 22 Chapter 9 Managing Flow Variability Example 9.4

23. 23 Chapter 9 Managing Flow Variability Run Charts Pros  Shows data in chronological order  Displays relative change over time (trends, seasonality) Cons  Erratic graph  No numerical characteristics

24. 24 Chapter 9 Managing Flow Variability § 9.2.5 Multi-Vari Charts  A multi-vari chart is a plot of high-average-low values of performance measurement sampled over time.

25. 25 Chapter 9 Managing Flow Variability Example 9.5

26. 26 Chapter 9 Managing Flow Variability Table 9.2 Day 12345678910 High90888491868883868889 Low7378767475817679 80 Average81.883.881.080.880.483.879.283.084.483.8 Day 11121314151617181920 High87868887888489859290 Low81787972817674778277 Average83.882.083.080.883.880.883.081.285.083.8

27. 27 Chapter 9 Managing Flow Variability Multi-Vari Charts Pros  Shows numerical range and average  Displays relative change over time Cons  Erratic graph  No numerical characteristics  Lacks distribution information  Does not provide guidance for taking actions

28. 28 Chapter 9 Managing Flow Variability § 9.3 Process Control  Goal  Actual Performance vs. Planned Performance  Involves   Tracking Deviations  Taking Corrective Actions  Principle of feedback control of dynamical systems

29. 29 Chapter 9 Managing Flow Variability Plan-Do-Check-Act (PDCA)  Process planning and process control are similar to the Plan-Do- Check-Act (PDCA) cycle.  PDCA cycle…  “involves planning the process, operating it, inspecting its output, and adjusting it in light of the observation.”  Performed continuously to monitor and improve the process performance  Main Problems  When to Act ….  Variances beyond control …

30. 30 Chapter 9 Managing Flow Variability Process Control  Two types of variability 1.Normal variability –Statistically predictable –Structural variability and stochastic variability –Variations due to random causes only (worker cannot control) –PROCESS IS IN CONTROL –Process design improvement 2. Abnormal variability –Unpredictable –Disturbs state of statistical equilibrium of the process –Identifiable and can be removed (worker can control) –Abnormal - due to assignable causes –PROCESS IS OUT OF CONTROL

31. 31 Chapter 9 Managing Flow Variability Process Control  The short run goal is:  Estimate normal stochastic variability.  Accept it as an inevitable and avoid tampering  Detect presence of abnormal variability  Identify and eliminate its sources  The long run goal is to reduce normal variability by improving process. When is observed variability normal and abnormal???

32. 32 Chapter 9 Managing Flow Variability § 9.3.3 Control Limit Policy  Control Limit Policy  Control band  Range within variation in performance  normal  Due to causes that cannot be identified or eliminated in short run  Leave alone and do not tamper  Variability outside this range is abnormal  Due to assignable causes  Investigate and correct  Applications  Inventory, Process Flow  Cash management  Stock trading

33. 33 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued LCL =  - z  UCL =  + z  The smaller the value of “z”, the tighter the control   - expected value of the performance  UCL and LCL  Standard Deviation   Assign z Process Control Chart:

34. 34 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued  Within the control band  Performance variability is normal  Outside the control band  Process is “out of control”  Data Misinterpretation Type I error,  : Process is “in control”, but data outside the Control Band Type II error,  : Process is “out of control”, but data inside the Control Band

35. 35 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued Acceptable Frequency “z” too small  unnecessary investigation; additional cost “z” to large  accept more variations, less costly Optimal Degree of Control In practice, a value of z = 3 is used 99.73% of all measurements will fall within the “normal” range

36. 36 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued  Average and Variation Control Charts -To calculate: Calculate the average value, A 1, A 2 ….A N Calculate the variance of each sample, V 1, V 2 ….V N  A =  /  n (n = sample size) LCL =  - z  /  n and UCL =  + z  /  n Take it one step further: Estimate  by the overall average of all the sample averages, A A = (A 1 + A 2 +…+A N ) / N (N = # of samples) Also estimate  by the standard deviation of all N x n observations, S

37. 37 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued New, Improved equations for UCL and LCL are: LCL =  A - zs/  n and UCL =  A + zs/  n Calculate  V -- the average variance of the sample variances  V = (V 1 + V 2 +…+V N ) / N (N = # of samples) Also calculate S V -- the standard deviation of the variances Sample Variances LCL =  V - z s V and UCL =  V + z s V If fall within this range  Process Variability is stable If not within this range  Investigate cause of abnormal variations Average and Variation Control Charts Variance Control Limits

38. 38 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued  Average and Variation Control Charts Garage Door Example revisited… Ex: A 1 = (81 + 73 + 85 + 90 + 80) / 5 = 81.8 kg Ex: V 1 = (90 - 73) = 17 kg

39. 39 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued  Average and Variation Control Charts Average Weights of Garage Door Samples: A = 82.5 kg V = 10.1 kg Std. Dev. of Door Weights: s = 4.2 kg Std. Dev. of Sample Variances:sV = 3.5 kg

40. 40 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued  Average and Variation Control Charts Let z = 3 Sample Averages UCL =  A + zs/  n = 82.5 + 3 (4.2) /  5 = 88.13 LCL =  A - zs/  n = 82.5 – 3 (4.2) /  5 = 76.87 Process is Stable!

41. 41 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued  Average and Variation Control Charts Let z = 3Sample Variances UCL =  V + z s V = 10.1 + 3 (3.5) = 20.6 LCL =  V - zs s V = 10.1 – 3 (3.5) = - 0.4

42. 42 Chapter 9 Managing Flow Variability 9.3.4 Control Charts … Continued  Extensions Continuous Variables - Garage Door Weights, Processing Costs, Customer Waiting Time Discrete Variables - Number of Customer Complaints, Whether a Flow Unit is Defective, Number of Defects per Flow Unit Produced Use Normal distribution Use Binomial or Poisson distribution Control Limit formula differs, but basic principles is same.

43. 43 Chapter 9 Managing Flow Variability 9.3.5 Cause-Effect Diagrams  Cause-Effect Diagrams Now what?!! Answer 5 “WHY” Questions ! Sample Observations Plot Control Charts Abnormal Variability !! Brainstorm Session!!

44. 44 Chapter 9 Managing Flow Variability 9.3.5 Cause-Effect Diagrams … Continued  Why…? Why…? Why…? Our famous “Garage Door” Example: 1. Why are these doors so heavy? Because the Sheet Metal was too ‘thick’. 2. Why was the sheet metal too thick? Because the rollers at the steel mill were set incorrectly. 3. Why were the rollers set incorrectly? Because the supplier is not able to meet our specifications. 4. Why did we select this supplier? Because our Project Supervisor was too busy getting the product out – didn’t have time to research other vendors. 5. Why did he get himself in this situation? Because he gets paid by meeting the production quotas.

45. 45 Chapter 9 Managing Flow Variability 9.3.5 Cause-Effect Diagrams … Continued  Fishbone Diagram

46. 46 Chapter 9 Managing Flow Variability 9.3.6 Scatter Plots  The Thickness of the Sheet Metals Change Settings on Rollers Measure the Weight of the Garage Doors Determine Relationship between the two Plot the results on a graph: Scatter Plot

47. 47 Chapter 9 Managing Flow Variability 9.3 Section Summary  Process Control involves –Dynamic Monitoring –Ensure variability in performance is due to normal random causes only –Detect abnormal variability and eliminate root causes

48. 48 Chapter 9 Managing Flow Variability 9.4 Process Capability  Ease of external product measures (door operations and durability) and internal measures (door weight)  Product specification limits vs. process control limits  Individual units, NOT sample averages - must meet customer specifications.  Once process is in control, then the estimates of μ (82.5kg) and σ (4.2k) are reliable. Hence we can estimate the process capabilities.  Process capabilities - the ability of the process to meet customer specifications  Three measures of process capabilities:  9.4.1 Fraction of Output within Specifications  9.4.2 Process Capability Ratios (Cpk and Cp)  9.4.3 Six-Sigma Capability

49. 49 Chapter 9 Managing Flow Variability 9.4.1 Fraction of Output within Specifications  To compute for fraction of process that meets customer specs:  Actual observation (see Histogram, Fig 9.3)  Using theoretical probability distribution Ex. 9.7:  US: 85kg; LS: 75 kg (the range of performance variation that customer is willing to accept) See figure 9.3 Histogram: In an observation of 100 samples, the process is 74% capable of meeting customer requirements, and 26% defectives!!! OR:  Let W (door weight): normal random variable with mean = 82.5 kg and standard deviation at 4.2 kg, Then the proportion of door falling within the specified limits is: Prob (75 ≤ W ≤ 85) = Prob (W ≤ 85) - Prob (W ≤ 75)

50. 50 Chapter 9 Managing Flow Variability 9.4.1 Fraction of Output within Specifications cont…  Let Z = standard normal variable with μ = 0 and σ = 1, we can use the standard normal table in Appendix II to compute: AT US: Prob (W≤ 85) in terms of: Z = (W-μ)/ σ As Prob [Z≤ (85-82.5)/4.2] = Prob (Z≤.5952) =.724 (see Appendix II) (In Excel: Prob (W ≤ 85) = NORMDIST (85,82.5,4.2,True) =.724158) AT LS: Prob (W ≤ 75) = Prob (Z≤ (75-82.5)/4.2) = Prob (Z ≤ -1.79) =.0367 in Appendix II (In Excel: Prob (W ≤ 75) = NORMDIST(75,82.5,4.2,true) =.037073) THEN: Prob (75≤W≤85) =.724 -.0367 =.6873

51. 51 Chapter 9 Managing Flow Variability 9.4.1 Fraction of Output within Specifications cont… SO with normal approximation, the process is capable of producing 69% of doors within the specifications, or delivering 31% defective doors!!! Specifications refer to INDIVIDUAL doors, not AVERAGES. We cannot comfort customer that there is a 31% chance that they’ll get doors that are either TOO LIGHT or TOO HEAVY!!!

52. 52 Chapter 9 Managing Flow Variability 9.4.2 Process Capability Ratios (C pk and Cp)  2 nd measure of process capability that is easier to compute is the process capability ratio (Cpk)  If the mean is 3σ above the LS (or below the US), there is very little chance of a product falling below LS (or above US). So we use:  (US- μ)/3σ (.1984 as calculated later)  and (μ -LS)/3σ(.5952 as calculated later) as measures of how well process output would fall within our specifications.  The higher the value, the more capable the process is in meeting specifications.  OR take the smaller of the two ratios [aka (US- μ)/3σ =.1984] and define a single measure of process capabilities as: Cpk = min[(US-μ/)3σ, (μ -LS)/3σ] (.1984, as calculated later)

53. 53 Chapter 9 Managing Flow Variability 9.4.2 Process Capability Ratios (C pk and Cp)  Cpk of 1+- represents a capable process  Not too high (or too low)  Lower values = only better than expected quality Ex: processing cost, delivery time delay, or # of error per transaction process  If the process is properly centered –Cpk is then either: (US- μ)/3σ or (μ -LS)/3σ As both are equal for a centered process.

54. 54 Chapter 9 Managing Flow Variability 9.4.2 Process Capability Ratios (C pk and Cp) cont…  Therefore, for a correctly centered process, we may simply define the process capability ratio as: –Cp = (US-LS)/6σ (.3968, as calculated later) Numerator = voice of the customer / denominator = the voice of the process  Recall: with normal distribution: Most process output is 99.73% falls within +-3σ from the μ.  Consequently, 6σ is sometimes referred to as the natural tolerance of the process. Ex: 9.8 Cpk = min[(US- μ)/3σ, (μ -LS)/3σ ] = min {(85-82.5)/(3)(4.2)], (82.5-75)/(3)(4.2)]} = min {.1984,.5952} =.1984

55. 55 Chapter 9 Managing Flow Variability 9.4.2 Process Capability Ratios (C pk and Cp)  If the process is correctly centered at μ = 80kg (between 75 and 85kg), we compute the process capability ratio as Cp = (US-LS)/6σ = (85-75)/[(6)(4.2)] =.3968  NOTE: Cpk =.1984 (or Cp =.3968) does not mean that the process is capable of meeting customer requirements by 19.84% (or 39.68%), of the time. It’s about 69%.  Defects are counted in parts per million (ppm) or ppb, and the process is assumed to be properly centered. IN THIS CASE, If we want no more than 100 defects per million (.01% defectives), we SHOULD HAVE the probability distribution of door weighs so closely concentrated around the mean that the standard deviation is 1.282 kg, or Cp=1.3 (see Table 9.4) Test: σ = (85-75)/(6)(1.282)] = 1.300kg

56. 56 Chapter 9 Managing Flow Variability Table 9.4

57. 57 Chapter 9 Managing Flow Variability 9.4.3 Six-Sigma Capability  Sigma measure S = min[(US- μ /σ), (μ -LS)/σ] (= min(.5152,1.7857) =.5152 to be calculated later)  S-Sigma process If process is correctly centered at the middle of the specifications, S = [(US-LS)/2σ] Ex: 9.9 Currently the sigma capability of door making process is S=min[(85-82.5)/(4.2), (82.5-75)/4.2] =.5952 By centering the process correctly, its sigma capability increases to S=min(85-75)/[(2)(4.2)] = 1.19 THUS, with a 3σ that is correctly centered, the US and LS are 3σ away from the mean, which corresponds to Cp=1, and 99.73% of the output will meet the specifications.

58. 58 Chapter 9 Managing Flow Variability 9.4.3 Six-Sigma Capability cont…  Correctly centered six-sigma process has a standard deviation so small that the US and LS limits are 6σ from the mean each.  Extraordinary high degree of precision. Corresponds to Cp=2 or 2 defective units per billion produced!!! (see Table 9.5)  In order for door making process to be a six-sigma process, its standard deviation must be: σ = (85-75)/(2)(6)] =.833kg  Adjusting for Mean Shifts - +-1.5 standard deviation from the center of specifications. - Producing an average of 3.4 defective units per million. (see table 9.5)

59. 59 Chapter 9 Managing Flow Variability Table 9.5

60. 60 Chapter 9 Managing Flow Variability 9.4.3 Six-Sigma Capability cont…  Why Six-Sigma? –See table 9.5 –Improvement in process capabilities from a 3-sigma to 4-sigma = 10-fold reduction in the fraction defective (66810 to 6210 defects) –While 4-sigma to 5-sigma = 30-fold improvement (6210 to 232 defects) –While 5-sigma to 6-sigma = 70-fold improvement (232 to 3.4 defects, per million!!!).  Average companies deliver about 4-sigma quality, where best-in-class companies aim for six-sigma.

61. 61 Chapter 9 Managing Flow Variability 9.4.3 Six-Sigma Capability cont…  Why High Standards?  The overall quality of the entire product/process that requires ALL of them to work satisfactorily will be significantly lower. Ex: If product contains 100 parts and each part is 99% reliable, the chance that the product (all its parts) will work is only (.99)100 =.366, or 36.6%!!!  Also, costs associated with each defects may be high  Expectations keep rising

62. 62 Chapter 9 Managing Flow Variability 9.4.3 Six-Sigma Capability cont…  Safety capability  We may also express process capabilities in terms of the desired margin [(US-LS)-zσ] as safety capability  It represents an allowance planned for variability in supply and/or demand  Greater process capability means less variability  If process output is closely clustered around its mean, most of the output will fall within the specifications  Higher capability thus means less chance of producing defectives  Higher capability = robustness

63. 63 Chapter 9 Managing Flow Variability 9.4.4 Capability and Control  In Ex. 9.7: the production process is not performing well in terms of MEETING THE CUSTOMER SPECIFICATIONS. Only 69% meets output specifications!!! (See 9.4.1: Fraction of Output within Specifications)  Yet in example 9.6, “the process was in control!!!”, or within us & ls limits.  Being in control and meeting specifications are two different measures of performance. The former indicates internal stability, the latter indicates the ability to meet the customers specifications.  Observation of a process in control ensures that the resulting estimates of the process mean and standard deviation are reliable so that our measurement of the process capability is accurate.  The final step is to improve process capability, so it is satisfactory from the customers viewpoint as well.

64. 64 Chapter 9 Managing Flow Variability 9.5 Process Capability Improvement  How do we improve the process capability?  Shift the process mean  Reduce the variability  Both

65. 65 Chapter 9 Managing Flow Variability 9.5.1 Mean Shift  Examine where the current process mean lies in comparison to the specification range (i.e. closer to the LS or the US)  Alter the process to bring the process mean to the center of the specification range in order to increase the proportion of outputs that fall within specification

66. 66 Chapter 9 Managing Flow Variability Ex 9.10  MBPF garage doors (currently)  specification range: 75 to 85 kgs  process mean: 82.5 kgs  proportion of output falling within specifications:.6873  The process mean of 82.5 kgs was very close to the US of 85 kgs (i.e. too thick/heavy)  To lower the process mean towards the center of the specification range the supplier could change the thickness setting on their rolling machine.

67. 67 Chapter 9 Managing Flow Variability Ex 9.10 Continued  Center of the specification range: (75 + 85)/2 = 80 kgs  New process mean: 80 kgs  If the door weight (W) is a normal random variable, then the proportion of doors falling within specifications is: Prob (75 =< W =< 85)  Prob (W =< 85) – Prob (W =< 75)  Z = (weight – process mean)/standard deviation  Z = (85 – 80)/4.2 = 1.19  Z = (75 – 80)/4.2 = -1.19

68. 68 Chapter 9 Managing Flow Variability Ex 9.10 Continued  [from table A2.1 on page 319] Z = 1.19.8830 Z = -1.19 (1 -.8830).1170  Prob (W =< 85) – Prob (W =< 75) =.8830 -.1170 =.7660  By shifting the process mean from 82.5 kgs to 80 kgs, the proportion of garage doors that falls within specifications increases from.6873 to.7660

69. 69 Chapter 9 Managing Flow Variability 9.5.2 Variability Reduction  Measured by standard deviation  A higher standard deviation value means higher variability amongst outputs  Lowering the standard deviation value would ultimately lead to a greater proportion of output that falls within the specification range

70. 70 Chapter 9 Managing Flow Variability 9.5.2 Variability Reduction Continued  Possible causes for the variability MBPF experienced are:  old equipment  poorly maintained equipment  improperly trained employees  Investments to correct these problems would decrease variability however doing so is usually time consuming and requires a lot of effort

71. 71 Chapter 9 Managing Flow Variability Ex 9.11  Assume investments are made to decrease the standard deviation from 4.2 to 2.5 kgs  The proportion of doors falling within specifications: Prob (75 =< W =< 85)  Prob (W =< 85) – Prob (W =< 75)  Z = (weight – process mean)/standard deviation  Z = (85 – 80)/2.5 = 2.0  Z = (75 – 80)/2.5 = -2.0

72. 72 Chapter 9 Managing Flow Variability Ex 9.11 Continued  [from table A2.1 on page 319] Z = 2.0.9772 Z = -2.0 (1 -.9772).0228  Prob (W =< 85) – Prob (W =< 75) =.9772 -.0228 =.9544  By shifting the standard deviation from 4.2 kgs to 2.5 kgs and the process mean from 82.5 kgs to 80 kgs, the proportion of garage doors that falls within specifications increases from.6873 to.9544

73. 73 Chapter 9 Managing Flow Variability 9.5.3 Effect of Process Improvement on Process Control  Changing the process mean or variability requires re-calculating the control limits  This is required because changing the process mean or variability will also change what is considered abnormal variability and when to look for an assignable cause

74. 74 Chapter 9 Managing Flow Variability 9.6 Product and Process Design  Reducing the variability from product and process design  simplification  standardization  mistake proofing

75. 75 Chapter 9 Managing Flow Variability Simplification  Reduce the number of parts (or stages) in a product (or process)  less chance of confusion and error  Use interchangeable parts and a modular design  simplifies materials handling and inventory control  Eliminate non-value adding steps  reduces the opportunity for making mistakes

76. 76 Chapter 9 Managing Flow Variability Standardization  Use standard parts and procedures  reduces operator discretion, ambiguity, and opportunity for making mistakes

77. 77 Chapter 9 Managing Flow Variability Mistake Proofing  Designing a product/process to eliminate the chance of human error  ex. color coding parts to make assembly easier  ex. designing parts that need to be connected with perfect symmetry or with obvious asymmetry to prevent assembly errors

78. 78 Chapter 9 Managing Flow Variability 9.6.2 Robust Design  Designing the product in a way so its actual performance will not be affected by variability in the production process or the customer’s operating environment  The designer must identify a combination of design parameters that protect the product from the process related and environment related factors that determine product performance

79. 79 Chapter 9 Managing Flow Variability 9.6 Product and Process Design  Summary  Variability is inevitable. It is a problem when it creates process instability, lower capability, and customer dissatisfaction.  The goal of this chapter has been to study how to measure, analyze, and minimize sources of this variability.  The point of this it to improve consistency in product process and performance, which will hopefully lead to…  Total customer satisfaction, and..  A better competitive position.