Chapter 9 Managing Flow Variability Managing Business Process

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

Chapter 9 Managing Flow Variability 2 Ø 9. 1 Performance Variability Ø 9. 2 Analysis of Variability Ø 9. 3 Process Control Ø 9. 4 Process Capability Ø 9. 5 Process Capability Improvement Ø 9. 6 Product and Process Design

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

Chapter 9 Managing Flow Variability Managing Business Process Flows: 4 All Products & Services VARY in Terms Of Cost Quality Availability Flow Times 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

Chapter 9 Managing Flow Variability § 9. 1 Performance Variability 5 q All measures of product & process performance (external & internal) display Variability. Ø External Measurements - customer satisfaction, relative product rankings, customer complaints (vary from one market survey to the next) Ø Possible sources: supplier delivery delays or changing tastes Ø Internally - flow units in all business processes vary with respect to cost, quality & flow times Ø 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.

Chapter 9 Managing Flow Variability § 9. 1 Performance Variability 6 q Variability refers to a discrepancy between the actual and the expected performance. q Can be due to gap between the following: Ø What customer wants and what product is designed for Ø What product design calls for and what process for making it is capable of producing Ø What process is capable of producing and what it actually produces Ø How the produced product is expected to perform and how it actually performs Ø How the product actually performs and how the customer perceives it q This often leads to: Ø higher costs, longer flow times, lower quality & DISSATISFIED CUSTOMERS

Chapter 9 Managing Flow Variability § 9. 1 Performance Variability 7 q Processes with greater performance variability are generally judged LESS satisfactory than those with consistent, predictable performance. q Variability in product & process performance, not just its average, Matters to consumers! q Customers perceive any variation in their product or service from what they expected as a LOSS IN VALUE. q 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.

Chapter 9 Managing Flow Variability Quality Management Terms 8 BOOK COVERS A FEW QUALITY MANAGEMENT TERMS: q Quality of Design: how well product specifications aim to meet customer requirements (what we promise consumers ~ in terms of what the product can do) q 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. ) q 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) Ø 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.

Chapter 9 Managing Flow Variability § 9. 2 Analysis of Variability 9 q q To analyze and improve variability there are diagnostic tools to help us: Ø Monitor the actual process performance over time Ø Analyze variability in the process Ø Uncover root causes Ø Eliminate those causes Ø 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.

Chapter 9 Managing Flow Variability § 9. 2. 1 Check Sheets 10 q A check sheet is simply a tally of the types and frequency of problems with a product or a service experienced by customers.

Chapter 9 Managing Flow Variability Example 9. 1 11 Type of Complaint Number of Complaints Cost IIII Response Time IIII Customization IIII Service Quality IIII Door Quality IIII IIII

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

Chapter 9 Managing Flow Variability § 9. 2. 2 Pareto Charts 13 q A Pareto chart is simply a bar chart that plots frequencies of occurrences of problem types in decreasing order. q The 80 -20 Pareto principle states that 20% of problem types account for 80% of all occurrences.

Chapter 9 Managing Flow Variability Example 9. 2 14

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

Chapter 9 Managing Flow Variability § 9. 2. 3 Histograms 16 q A histogram is a bar plot that displays the frequency distribution of an observed performance characteristic.

Chapter 9 Managing Flow Variability Example 9. 3 17

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

Chapter 9 Managing Flow Variability Table 9. 1 19 Day Time 1 2 3 4 5 6 7 8 9 10 9: 00 AM 81 82 80 74 75 81 83 86 88 82 11: 00 AM 73 87 83 81 86 86 82 83 79 84 1: 00 PM 85 88 76 91 82 83 76 82 86 89 3: 00 PM 90 78 84 75 84 88 77 79 84 84 5: 00 PM 80 84 82 83 75 81 78 85 85 80 Day Time 11 12 13 14 15 16 17 18 19 20 9: 00 AM 86 86 88 72 84 76 74 85 82 89 11: 00 AM 84 83 79 86 85 82 86 85 84 80 1: 00 PM 81 78 83 80 81 83 83 82 83 90 3: 00 PM 81 80 83 79 88 84 89 77 92 83 5: 00 PM 87 83 82 87 81 79 83 77 84 77

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

Chapter 9 Managing Flow Variability § 9. 2. 4 Run Charts 21 q A run chart is a plot of some measure of process performance monitored over time q Advantage is that it is dynamic

Chapter 9 Managing Flow Variability Example 9. 4 22

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

Chapter 9 Managing Flow Variability § 9. 2. 5 Multi-Vari Charts 24 q A multi-vari chart is a plot of high-average-low values of performance measurement sampled over time.

Chapter 9 Managing Flow Variability Example 9. 5 25

Chapter 9 Managing Flow Variability Table 9. 2 26 Day 1 2 3 4 5 6 7 8 9 10 High 90 88 84 91 86 88 83 86 88 89 Low 73 78 76 74 75 81 76 79 79 80 81. 8 83. 8 81. 0 80. 8 80. 4 83. 8 79. 2 83. 0 84. 4 83. 8 Average Day 11 12 13 14 15 16 17 18 19 20 High 87 86 88 87 88 84 89 85 92 90 Low 81 78 79 72 81 76 74 77 82 77 83. 8 82. 0 83. 0 80. 8 83. 8 80. 8 83. 0 81. 2 85. 0 83. 8 Average

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

Chapter 9 Managing Flow Variability § 9. 3 Process Control 28 q Goal Actual Performance vs. Planned Performance q Involves Ø Tracking Deviations Ø Taking Corrective Actions q Principle of feedback control of dynamical systems

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

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

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

Chapter 9 Managing Flow Variability § 9. 3. 3 Control Limit Policy 32 q Control Limit Policy Ø Control band Ø Range within variation in performance normal Ø Due to causes that cannot be identified or eliminated in short run Ø Leave alone and do not tamper Ø Variability outside this range is abnormal Ø Due to assignable causes Ø Investigate and correct Ø Applications Ø Inventory, Process Flow Ø Cash management Ø Stock trading

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 33 Process Control Chart: q - expected value of the performance q UCL and LCL q Standard Deviation q LCL = - z UCL = + z The smaller the value of “z”, the tighter the control Assign z

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 34 q Within the control band Performance variability is normal q Outside the control band Process is “out of control” q 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

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 35 Optimal Degree of Control Acceptable Frequency “z” too small unnecessary investigation; additional cost “z” to large accept more variations, less costly In practice, a value of z = 3 is used 99. 73% of all measurements will fall within the “normal” range

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 36 q Average and Variation Control Charts - To calculate: Calculate the average value, A 1, A 2…. AN Calculate the variance of each sample, V 1, V 2…. VN 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+…+AN) / N (N = # of samples) Also estimate by the standard deviation of all N x n observations, S

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 37 New, Improved equations for UCL and LCL are: LCL = A - zs/ n and UCL = A + zs/ n Average and Variation Control Charts Calculate V -- the average variance of the sample variances V = (V 1+ V 2+…+VN) / N Sample Variances (N = # of samples) Also calculate SV -- the standard deviation of the 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 Variance Control Limits

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 38 q 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

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 39 q Average and Variation Control Charts Average Weights of Garage Door Samples: A = 82. 5 kg V = 10. 1 kg Std. Dev. of Door Weights: Std. Dev. of Sample Variances: s = 4. 2 kg s. V = 3. 5 kg

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 40 q 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!

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 41 q Average and Variation Control Charts Let z = 3 UCL = V + z s. V = 10. 1 + 3 (3. 5) = 20. 6 LCL = V - zs s. V = 10. 1 – 3 (3. 5) = - 0. 4 Sample Variances

Chapter 9 Managing Flow Variability 9. 3. 4 Control Charts … Continued 42 q Extensions Continuous Variables - Garage Door Weights, Processing Costs, Customer Waiting Time Use Normal distribution Discrete Variables - Number of Customer Complaints, Whether a Flow Unit is Defective, Number of Defects per Flow Unit Produced Use Binomial or Poisson distribution Control Limit formula differs, but basic principles is same.

Chapter 9 Managing Flow Variability 9. 3. 5 Cause-Effect Diagrams 43 q Cause-Effect Diagrams Sample Plot Abnormal Observations Control Charts Variability !! Now what? !! Brainstorm Session!! Answer 5 “WHY” Questions !

Chapter 9 Managing Flow Variability 9. 3. 5 Cause-Effect Diagrams … Continued 44 q 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 Because the supplier is not able to meet incorrectly? 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 Because he gets paid by meeting the situation? production quotas.

Chapter 9 Managing Flow Variability 9. 3. 5 Cause-Effect Diagrams … Continued 45 q Fishbone Diagram

Chapter 9 Managing Flow Variability 9. 3. 6 Scatter Plots 46 q 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

Chapter 9 Managing Flow Variability 9. 3 Section Summary 47 q Process Control involves – Dynamic Monitoring – Ensure variability in performance is due to normal random causes only – Detect abnormal variability and eliminate root causes

Chapter 9 Managing Flow Variability 9. 4 Process Capability 48 q Ease of external product measures (door operations and durability) and internal measures (door weight) q Product specification limits vs. process control limits q Individual units, NOT sample averages - must meet customer specifications. q Once process is in control, then the estimates of μ (82. 5 kg) and σ (4. 2 k) are reliable. Hence we can estimate the process capabilities. q Process capabilities - the ability of the process to meet customer specifications q Three measures of process capabilities: Ø 9. 4. 1 Fraction of Output within Specifications Ø 9. 4. 2 Process Capability Ratios (Cpk and Cp) Ø 9. 4. 3 Six-Sigma Capability

Chapter 9 Managing Flow Variability 9. 4. 1 Fraction of Output within Specifications 49 q To compute for fraction of process that meets customer specs: Ø Actual observation (see Histogram, Fig 9. 3) Ø Using theoretical probability distribution Ex. 9. 7: Ø US: 85 kg; 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: Ø 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)

Chapter 9 Managing Flow Variability 9. 4. 1 Fraction of Output within Specifications cont… 50 q 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

Chapter 9 Managing Flow Variability 9. 4. 1 Fraction of Output within Specifications cont… 51 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!!!

Chapter 9 Managing Flow Variability 9. 4. 2 Process Capability Ratios (C pk and Cp) 52 q 2 nd measure of process capability that is easier to compute is the process capability ratio (Cpk) q 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: q (US- μ)/3σ (. 1984 as calculated later) q and (μ -LS)/3σ (. 5952 as calculated later) as measures of how well process output would fall within our specifications. q The higher the value, the more capable the process is in meeting specifications. q 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)

Chapter 9 Managing Flow Variability 9. 4. 2 Process Capability Ratios (C pk and Cp) 53 q Cpk of 1+- represents a capable process q Not too high (or too low) q Lower values = only better than expected quality Ex: processing cost, delivery time delay, or # of error per transaction process q 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.

Chapter 9 Managing Flow Variability 9. 4. 2 Process Capability Ratios (C pk and Cp) cont… 54 q 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 q Recall: with normal distribution: Most process output is 99. 73% falls within +-3σ from the μ. q 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

Chapter 9 Managing Flow Variability 9. 4. 2 Process Capability Ratios (C pk and Cp) 55 q If the process is correctly centered at μ = 80 kg (between 75 and 85 kg), we compute the process capability ratio as Cp = (US-LS)/6σ = (85 -75)/[(6)(4. 2)] =. 3968 q 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%. q 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. 300 kg

Chapter 9 Managing Flow Variability Table 9. 4 56

Chapter 9 Managing Flow Variability 9. 4. 3 Six-Sigma Capability 57 q Sigma measure S = min[(US- μ /σ), (μ -LS)/σ] (= min(. 5152, 1. 7857) =. 5152 to be calculated later) q 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.

Chapter 9 Managing Flow Variability 9. 4. 3 Six-Sigma Capability cont… 58 q Correctly centered six-sigma process has a standard deviation so small that the US and LS limits are 6σ from the mean each. q Extraordinary high degree of precision. Corresponds to Cp=2 or 2 defective units per billion produced!!! (see Table 9. 5) q In order for door making process to be a six-sigma process, its standard deviation must be: σ = (85 -75)/(2)(6)] =. 833 kg q 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)

Chapter 9 Managing Flow Variability Table 9. 5 59

Chapter 9 Managing Flow Variability 9. 4. 3 Six-Sigma Capability cont… 60 q 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!!!). q Average companies deliver about 4 -sigma quality, where best-in-class companies aim for six-sigma.

Chapter 9 Managing Flow Variability 9. 4. 3 Six-Sigma Capability cont… 61 q Why High Standards? Ø 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%!!! Ø Also, costs associated with each defects may be high Ø Expectations keep rising

Chapter 9 Managing Flow Variability 9. 4. 3 Six-Sigma Capability cont… 62 q Ø Safety capability We may also express process capabilities in terms of the desired margin [(US-LS)-zσ] as safety capability Ø It represents an allowance planned for variability in supply and/or demand Ø Greater process capability means less variability Ø If process output is closely clustered around its mean, most of the output will fall within the specifications Ø Higher capability thus means less chance of producing defectives Ø Higher capability = robustness

Chapter 9 Managing Flow Variability 9. 4. 4 Capability and Control 63 q 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) q Yet in example 9. 6, “the process was in control!!!”, or within us & ls limits. q 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. q 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. q The final step is to improve process capability, so it is satisfactory from the customers viewpoint as well.

Chapter 9 Managing Flow Variability 9. 5 Process Capability Improvement 64 q How do we improve the process capability? Ø Shift the process mean Ø Reduce the variability Ø Both

Chapter 9 Managing Flow Variability 9. 5. 1 Mean Shift 65 q Examine where the current process mean lies in comparison to the specification range (i. e. closer to the LS or the US) q 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

Chapter 9 Managing Flow Variability Ex 9. 10 66 q MBPF garage doors (currently) Ø specification range: 75 to 85 kgs Ø process mean: 82. 5 kgs Ø proportion of output falling within specifications: . 6873 q The process mean of 82. 5 kgs was very close to the US of 85 kgs (i. e. too thick/heavy) q To lower the process mean towards the center of the specification range the supplier could change thickness setting on their rolling machine.

Chapter 9 Managing Flow Variability Ex 9. 10 Continued 67 q Center of the specification range: (75 + 85)/2 = 80 kgs q New process mean: 80 kgs q If the door weight (W) is a normal random variable, then the proportion of doors falling within specifications is: Prob (75 =< W =< 85) q Prob (W =< 85) – Prob (W =< 75) q Z = (weight – process mean)/standard deviation q Z = (85 – 80)/4. 2 = 1. 19 q Z = (75 – 80)/4. 2 = -1. 19

Chapter 9 Managing Flow Variability Ex 9. 10 Continued 68 q [from table A 2. 1 on page 319] Z = 1. 19 Z = -1. 19 q . 8830 (1 -. 8830) . 1170 Prob (W =< 85) – Prob (W =< 75) =. 8830 -. 1170 =. 7660 q 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

Chapter 9 Managing Flow Variability 9. 5. 2 Variability Reduction 69 q Measured by standard deviation q A higher standard deviation value means higher variability amongst outputs q Lowering the standard deviation value would ultimately lead to a greater proportion of output that falls within the specification range

Chapter 9 Managing Flow Variability 9. 5. 2 Variability Reduction Continued 70 q Possible causes for the variability MBPF experienced are: Ø old equipment Ø poorly maintained equipment Ø improperly trained employees q Investments to correct these problems would decrease variability however doing so is usually time consuming and requires a lot of effort

Chapter 9 Managing Flow Variability Ex 9. 11 71 q Assume investments are made to decrease the standard deviation from 4. 2 to 2. 5 kgs q The proportion of doors falling within specifications: 85) q Prob (W =< 85) – Prob (W =< 75) q Z = (weight – process mean)/standard deviation q Z = (85 – 80)/2. 5 = 2. 0 q Z = (75 – 80)/2. 5 = -2. 0 Prob (75 =< W =<

Chapter 9 Managing Flow Variability Ex 9. 11 Continued 72 q [from table A 2. 1 on page 319] Z = 2. 0 Z = -2. 0 q . 9772 (1 -. 9772) . 0228 Prob (W =< 85) – Prob (W =< 75) =. 9772 -. 0228 =. 9544 q 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

Chapter 9 Managing Flow Variability 9. 5. 3 Effect of Process Improvement on Process Control 73 q Changing the process mean or variability requires re-calculating the control limits q 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

Chapter 9 Managing Flow Variability 9. 6 Product and Process Design 74 q Reducing the variability from product and process design Ø simplification Ø standardization Ø mistake proofing

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

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

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

Chapter 9 Managing Flow Variability 9. 6. 2 Robust Design 78 q 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 q 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

Chapter 9 Managing Flow Variability 9. 6 Product and Process Design 79 q Summary Ø Variability is inevitable. It is a problem when it creates process instability, lower capability, and customer dissatisfaction. Ø The goal of this chapter has been to study how to measure, analyze, and minimize sources of this variability. Ø The point of this it to improve consistency in product process and performance, which will hopefully lead to… Ø Total customer satisfaction, and. . Ø A better competitive position.