Systems Thinking and the Theory of Constraints A Statement for Quality Goes Here These sides and note were prepared using 1. Managing Business Flow processes. Anupindi, Chopra, Deshmukh, Van Mieghem, and Zemel.Pearson Prentice Hall. 2. Few of the graphs of the slides of Prentice Hall for this book, originally prepared by professor Deshmukh. Introduction ~ The Garage Door Manufacturer According to the sales manager of a high-tech manufacturer of garage doors, while the company has 15% of market share, customers are not satisfied Door Quality in terms of safety, durability, and ease of use High Price compared competitors process Not on-time orders Poor After Sales Service We can not rely of subjective statements and opinions Collect and analyze concrete data facts- on performance measures that drive customer satisfaction Identify, correct, and prevent sources of future problems Quality Process Control
Ardavan Asef-Vaziri Jan-2012 2 9.1 Performance Variability All internal and external performance measures display vary from tome to time. External Measurements - customer satisfaction, product rankings, customer complaints. Internal Measurements - flow units cost, quality, and time. No two cars rolling off an assembly line have identical cost. No two customers for identical transaction spend the same time in a bank. The same meal you have had in two different occasions in a restaurant do not taste exactly the same. Sources of Variability Internal: imprecise equipment, untrained workers, and lack of standard operating procedures. External: inconsistent raw materials, supplier delays, Quality Process Control Ardavan Asef-Vaziri
Jan-2012 3 9.1 Performance Variability A discrepancy between the actual and the expected performance often leads to cost, flow time, quality dissatisfied customers. Processes with greater variability are judged less satisfactory than those with consistent, predictable performance. What is the base of the customer judgment the exact unit of product or service s/he gets, not how the average product performs. 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. Quality Process Control Ardavan Asef-Vaziri Jan-2012 4 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) is a 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. Ex. # defects per car, fraction of output that meets specifications. Ex. irline conformance can be measured in terms of the percentage of flights delayed for more than 15 minutes OR the number of reservation errors Quality Process Control Ardavan Asef-Vaziri Jan-2012 5 9.2 Analysis of Variability To analyze and improve variability there are diagnostic tools to help us: 1. 2. 3. 4. 5. 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
Quality Process Control Ardavan Asef-Vaziri Jan-2012 6 9.2.1 Check Sheets check Sheet is simply a tally of the types and frequency of problems with a product or a service experienced by customers. Pareto Chart is a bar chart of frequencies of occurrences in non-increasing order. The 80-20 Pareto principle states that 20% of problem types account for 80% of all occurrences. 25 20 15 Type of Complaint Number of Complaints Cost IIII IIII Response Time Customization IIII IIII IIII IIII IIII
Service Quality Door Quality Quality Process Control IIII IIII IIII IIII IIII 10 5 0 Door Quality Service Quality Ardavan Asef-Vaziri Cost Jan-2012 Response Time Customization 7 9.2.3 Histograms Collect data on door weight Ex. one door, five times a day, 20 days, total of 100 door weight. Time\ Day 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 9 a.m. 11 a.m. 1 p.m. 3 p.m. 5 p.m. 81 73 85 90 80 82 87 88 78 84
80 83 76 84 82 74 81 91 75 83 75 86 82 84 75 81 86 83 88 81 83 82 76 77 78 86 83 82 79
85 88 79 86 84 85 82 84 89 84 80 86 84 81 81 87 72 74 76 Histogram is a bar plot 88 79 83 83 82 72
86 80 79 87 84 85 81 88 81 76 82 83 84 79 74 86 83 89 83 85 85 82 77 77 82 84 83 92 84
89 80 90 83 77 14 12 10 Frequency that displays the frequency distribution of an observed performance characteristic. Ex. 14% of the doors weighed about 83 kg, 8% weighed about 81 kg, and so forth. Quality Process Control 86 83 78 80 83 8 6 4 2 0 Ardavan Asef-Vaziri
78 80 82 84 Weight (kg) Jan-2012 86 88 90 92 8 9.2.4 Run Charts Run chart is a plot of some measure of process performance monitored over time. 95 90 85 80 75
70 1 4 7 10 13 16 19 Quality Process Control 22 25 28 31 34 37 40 43 46
49 52 55 58 61 64 67 Ardavan Asef-Vaziri 70 73 76 79 82 Jan-2012 85 88 91
94 97 100 9 9.2.5 Multi-Vari Charts Multi-vari chart is a plot of high-average-low values of performance measurement sampled over time. Time\ Day 9 a.m. 11 a.m. 1 p.m. 3 p.m. 5 p.m. Average High Low Range 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20 81 73 85 90 80 82 87 88 78
84 80 83 76 84 82 74 81 91 75 83 75 86 82 84 75 81 86 83 88 81 83 82 76 77 78 86 83 82
79 85 88 79 86 84 85 82 84 89 84 80 86 84 81 81 87 86 83 78 80 83 88 79 83 83 82 72 86
80 79 87 84 85 81 88 81 76 82 83 84 79 74 86 83 89 83 85 85 82 77 77 82 84 83 92 84 89
80 90 83 77 81.8 83.8 81.0 80.8 80.4 83.8 79.2 83.0 84.4 83.8 83.8 82.0 83.0 80.8 83.8 80.8 83.0 81.2 85.0 83.8 90 73 88 78 84 76 91 74 86 75 88 81 83 76 86 79 88 79 89 80
87 81 86 78 88 79 87 72 88 81 84 76 89 74 85 77 92 82 90 77 17 10
8 17 11 7 7 7 9 9 6 8 9 15 7 8 15 8 10 13
95 90 85 80 75 70 1 Quality Process Control 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 Ardavan Asef-Vaziri 18 19 20 Jan-2012 10 Comparison Pareto Chart. The importance of each item. Quality was the most important item. Quality was then defined as finish, ease of use, and durability. Ease of use and durability which are subjective, must be translated into some thing measurable. We translate them into weight. If weight is high, it cannot operate easily, if weight is low, it will not be durable. A high quality door, based on engineering design must weight 82.5 lbs.
Histogram. Shows the tendency (mean) and the standard deviation. Ex. For door weight. Run Chart. Can show trend. Multi-Vari Chart. Shows average and variability inside the samples and among the samples. Quality Process Control Ardavan Asef-Vaziri Jan-2012 11 Process Management Two aspects to process management; Process plannings goal is to produce and deliver products that satisfy targeted customer needs. Structuring the process Designing operating procedures Developing key competencies such as process capability, flexibility, capacity, and cost efficiency Process controls goal is to ensure that actual performance conforms to the planned performance. Tracking deviations between the actual and the planned performance and taking corrective actions to identify and
eliminate sources of these variations. There could be various reasons behind variation in performance. Quality Process Control Ardavan Asef-Vaziri Jan-2012 12 9.3.1 The Feedback Control Principle Process performance management is based on the general principle of feedback control of dynamical systems. Applying the feedback control principle to process control. involves periodically monitoring the actual process performance (in terms of cost, quality, availability, and response time), comparing it to the planned levels of performance, identifying causes of the observed discrepancy between the two, and taking corrective actions to eliminate those Ardavan causes. Quality Process Control Asef-Vaziri Jan-2012 13 Plan-Do-Check-Act (PDCA) Process planning and process control are similar
to the Plan-Do-Check-Act (PDCA) cycle. Performed continuously to monitor and improve the process performance. Problems in Process Control Performance variances are determined by comparison of the current and previous periods performances. Decisions are based on results of this comparison. Some variances may be due to factors beyond a workers control. According to W. Edward Deming, incentives based on factors that are beyond a workers control is like rewarding or punishing workers according to a lottery. Quality Process Control Ardavan Asef-Vaziri Jan-2012 14 Two categories of performance variability Normal Variability. Is statistically predictable and includes both structural variability and stochastic variability. Cannot be removed easily. Is not in workers control. Can be removed only by process re-design, more precise equipment,
skilled workers, better material, etc. Abnormal variability. Unpredictable and disturbs the state of statistical equilibrium of the process by changing parameters of its distribution in an unexpected way. Implies that one or more performance affecting factors may have changed due to external causes or process tampering. Can be identified and removed easily therefore is workers responsibility. Quality Process Control Ardavan Asef-Vaziri Jan-2012 15 Process Control If observed performance variability is Normal - due to random causes - process is in control Abnormal - due to assignable causes - process is out of control The short run goal is: 1. Estimate normal stochastic variability. 2. Accept it as an inevitable and avoid tampering 3. Detect presence of abnormal variability 4. Identify and eliminate its sources The long run goal is to reduce normal variability by improving process. Quality Process Control Ardavan Asef-Vaziri
Jan-2012 16 9.3.3 Control Limit Policy How to decide whether observed variability is normal or abnormal? Control Limit Policy Control band - A range within which any variation in performance is interpreted as normal due to causes that cannot be identified or eliminated in short run. Variability outside this range is abnormal. Lower limit of acceptable mileage, control band for house temperature. Quality Process Control Ardavan Asef-Vaziri Jan-2012 17 Process Control Process control is useful to control any type of process. Application of control limit policy
Managing inventory, process capacity and flow time. Cash management - liquidate some assets if cash falls below a certain level. Stock trading - purchase a stock if and when its price drops to a specific level. Control limit policy has usage in a wide variety of business in form of critical threshold for taking action Quality Process Control Ardavan Asef-Vaziri Jan-2012 18 9.3.4 Statistical Process Control Statistical process control involves setting a range of acceptable variations in the performance of the process, around its mean. If the observed values are within this range: Accept the variations as normal Dont make any adjustments to the process If the observed values are outside this range: The process is out of control
Need to investigate whats causing the problems the assignable cause Quality Process Control Ardavan Asef-Vaziri Jan-2012 19 9.3.4 Process Control Charts Let be the expected value and be the standard deviation of the performance. Set up an Upper Control Limit (UCL) and a Lower Control Limit (LCL). LCL = - z UCL = + z Decide how tightly to monitor and control the process. The smaller the z, the tighter the control Quality Process Control Ardavan Asef-Vaziri Jan-2012 20 9.3.4 Process Control Charts If observed data within the control limits and does not show any systematic pattern Performance
variability is normal . Otherwise Process is out of control Type I error ( error). Process is in control, its statistical parameters have not changed, but data falls outside the limits. Type II error ( error) Process is out of control, its statistical parameters have changed, but data falls inside the limits. Quality Process Control Ardavan Asef-Vaziri Jan-2012 21 9.3.4 Control Charts Continued Optimal Degree of Control depends on 2 things: How much variability in the performance measure we consider acceptable How frequently we monitor the process performance. Optimal frequency of monitoring is a balance between the costs and benefits If we set z to be too small: Well end up doing unnecessary investigation. Incur additional costs. If we set z to be too large: Well accept a lot more variations as normal. We wouldnt look for problems in the process less costly Quality Process Control
Ardavan Asef-Vaziri Jan-2012 22 9.3.4 Control Charts Continued In practice, a value of z = 3 is used. 99.73% of all measurements will fall within the normal range Quality Process Control Ardavan Asef-Vaziri Jan-2012 23 We have collected 20 samples, each of size 5, n=5, of our variable of interest X the door weight in our example. We have 100 pieces of data. We can simple use excel to compute the average and standard deviation of this data. Overall average X 82 .5 weight Standard deviation s 4 .2 Variance s 2 17 .64 A higher value of the average indicates a shift in the entire distribution to the right, so that all doors produced are consistently heavier. An increase in the value of the
standard deviation means a wider spread of the distribution around the mean, implying that many doors are much heavier or lighter than the overall average weight. Quality Process Control Ardavan Asef-Vaziri Jan-2012 24 X Bar Chart If we compute the average of the random variable X, in each sample of n, in our example 5, and show it by X Average Door Weigh t in each sample : X n X has any dostribution with Mean and Standard Deviation of X has Normal dostribution with Mean and Standard Deviation of n Average of Average Door Weigh t : X 82.5 s 4.2 Standard Deviation of Average Door Weight : s X 1.88 n 5 Quality
Process Copyright 2013 PearsonControl Education Inc. publishing as Ardavan Asef-Vaziri Jan-2012 25 X Bar Chart Therefore, if we compute the average weight door 68.26% of all doors will weigh within 82.5 + (1) (1.88), 95.44% of doors will weight within 82.5 + (2)(1.88), and 99.73% of door weights will be within 82.5 + (3)(1.88), or between and 76.86 and 88.14 . A v e ra g e UCL 86 84 82 80 78 LCL 76 1 3
5 7 9 11 13 15 17 19 Day Quality Process Copyright 2013 PearsonControl Education Inc. publishing as Ardavan Asef-Vaziri Jan-2012 26 Process Control and Improvement Out of Control In Control Improved UCL LCL Quality Process Copyright 2013
PearsonControl Education Inc. publishing as Ardavan Asef-Vaziri Jan-2012 27 R Chart Range in a Sample of Size n : R Time\ Day Range 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 17 10 8 17 11 7 7 7
9 9 6 8 9 15 7 8 15 8 10 13 Average Range in a Sample of Size n : R Standard Deviation of R : s R R 10.1 s R 3.5 Range UCL = 10.1+3(3.5) = 20.6 , LCL = 10.1-3(3.5) = -0.4 = 0 20 15
10 5 0 UCL LCL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Day Process Is In Control (i.e., variation is stable) Quality Process Copyright 2013 PearsonControl Education Inc. publishing as Ardavan Asef-Vaziri Jan-2012 28 Number of Defects (c) Chart Discrete Quality Measurement: D = Number of defects (errors) per unit of work Examples: Number of typos/page, errors/thousand transactions, equipment breakdowns/shift, bags lost/thousand flown, power outages/year, customer complaints/month, defects/car....... If n = No. of opportunities for defects to occur, and p = Probability of a defect/error occurrence in each then D ~ Binomial (n, p) with mean np, variance np(1-p)
Poisson (m) with m = mean = variance = np , if n is large ( 20) and p is small ( 0.05) With m = np = average number of defects per unit, Control limits = m + 3 m Quality Process Copyright 2013 PearsonControl Education Inc. publishing as Ardavan Asef-Vaziri Jan-2012 29 Performance Variation Stable Unstable Trend Cyclical Shift Quality Process Copyright 2013 PearsonControl Education Inc. publishing as Ardavan Asef-Vaziri Jan-2012 30
Performance Variation Stable Unstabl e Trend Cyclical Quality Process Copyright 2013 PearsonControl Education Inc. publishing as Shift Ardavan Asef-Vaziri Jan-2012 31 Performance Variation Stable Unstabl e Trend Cyclical Quality Process Copyright 2013 PearsonControl Education Inc. publishing as Shift
Ardavan Asef-Vaziri Jan-2012 32 Performance Variation Stable Unstabl e Trend Cyclical Quality Process Copyright 2013 PearsonControl Education Inc. publishing as Shift Ardavan Asef-Vaziri Jan-2012 33 Performance Variation Stable Unstabl e Trend Cyclical Quality Process Copyright 2013
PearsonControl Education Inc. publishing as Shift Ardavan Asef-Vaziri Jan-2012 34 X Bar Chart If the door weight distribution was Normal, 68.26% of all doors will weigh within 82.5 + (1) (4.2), 95.44% of doors will weight within 82.5 + (2)(4.2), and 99.73% of door weights will be within 82.5 + (3)(4.2). This would be the distribution of the weight of each individual door. Quality Process Copyright 2013 PearsonControl Education Inc. publishing as Ardavan Asef-Vaziri Jan-2012 35 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 Average Weight Control Chart 90 Average Wt. (Kg) 88 UCL = 88.13 86 84 82 ` 80 78 LCL = 76.87 76 74 1 2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Days Quality Process Control Ardavan Asef-Vaziri Jan-2012 36 9.3.4 Control Charts Continued Average and Variation Control Charts Let z = 3 Sample Variances UCL = V + z sV = 10.1 + 3 (3.5) = 20.6 LCL = V - zs sV = 10.1 3 (3.5) = - 0.4 Variance (range) of Wt. (Kg) Variance Control Chart 25 UCL = 20.6 20 15
10 5 LCL = 0 0 1 Quality Process Control 2 3 4 5 6 7 8 9 10 11 Days 12 13 14 Ardavan Asef-Vaziri 15 16 17 Jan-2012
18 19 20 37 9.3.4 Control Charts Continued 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 38 9.3.5 Cause-Effect Diagrams Cause-Effect Diagrams
Sample Plot Abnormal Observation s Control Charts Variability !! Now what?!! Brainstorm Session!! Answer 5 WHY Questions ! Quality Process Control Ardavan Asef-Vaziri Jan-2012 39 9.3.5 Cause-Effect Diagrams Why? Why? Why? Continued (+2)
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 didnt have time to research other vendors. 5. Why did he get himself in this situation? Because he gets paid by meeting the production quotas. Quality Process Control Ardavan Asef-Vaziri Jan-2012 40 9.3.5 Cause-Effect Diagrams
Continued Fishbone Diagram Quality Process Control Ardavan Asef-Vaziri Jan-2012 41 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 Roller Settings & Garage Door Weights Plot the results on a graph: Door Weight (Kg) Scatter Plot 20 15 10 5 0 0 1
2 3 4 5 6 7 8 9 10 11 12 13 Roller Setting (m m ) Quality Process Control Ardavan Asef-Vaziri Jan-2012 42 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 (82.5kg) and (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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 43 9.4.1 Fraction of Output within Specifications The fraction of the process output that meets customer specifications. We can compute this fraction by: - 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) Quality Process Control Ardavan Asef-Vaziri Jan-2012 44 9.4.1 Fraction of Output within Specifications cont Let Z = standard normal variable with = 0 and = 1, we can use the standard normal table in Appendix II to compute: AT US: Prob (W 85) in terms of: Z = (W-)/ 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 (75W85) = .724 - .0367 = .6873
Quality Process Control Ardavan Asef-Vaziri Jan-2012 45 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 30% chance that theyll get doors that is either TOO LIGHT or TOO HEAVY!!! Quality Process Control Ardavan Asef-Vaziri Jan-2012 46 9.4.2 Process Capability Ratios (C pk and Cp) 2nd measure of process capability that is easier to compute is the
process capability ratio (Cpk) If the mean is 3 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- )/3 (.1984 as calculated later) and ( -LS)/3 (.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- )/3 =.1984] and define a single measure of process capabilities as: Cpk = min[(US-/)3, ( -LS)/3] (.1984, as calculated later) Quality Process Control Ardavan Asef-Vaziri Jan-2012 47 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- )/3 or ( -LS)/3 As both are equal for a centered process. Quality Process Control Ardavan Asef-Vaziri Jan-2012 48 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)/6 (.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 +-3 from the . Consequently, 6 is sometimes referred to as the natural tolerance of the process. Ex: 9.8 Cpk = min[(US- )/3 , ( -LS)/3 ] = min {(85-82.5)/(3)(4.2)], (82.5-75)/(3)(4.2)]} = min {.1984, .5952} =.1984
Quality Process Control Ardavan Asef-Vaziri Jan-2012 49 9.4.2 Process Capability Ratios (C pk and Cp) If the process is correctly centered at = 80kg (between 75 and 85kg), we compute the process capability ratio as Cp = (US-LS)/6 = (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. Its 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 like 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: = (85-75)/(6)(1.282)] = 1.300kg Quality Process Control Ardavan Asef-Vaziri Jan-2012 50
Table 9.4 Table9.4RelationshipBetweenProcess Capability Ratio and ProportionDefective Defects (ppm) 10000 1000 100 10 1 2ppb Cp 0.86 1 1.3 1.47 1.63 2 Quality Process Control Ardavan Asef-Vaziri Jan-2012 51 9.4.3 Six-Sigma Capability The 3rd process capability Known as Sigma measure, which is computed as S = min[(US- /), ( -LS)/] (= 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)/2] Ex: 9.9 Currently the sigma capability of door making process is S=min(85-82.5)/[(2)(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 3 that is correctly centered, the US and LS are 3 away from the mean, which corresponds to Cp=1, and 99.73% of the output will meet the specifications. Quality Process Control Ardavan Asef-Vaziri Jan-2012 52 9.4.3 Six-Sigma Capability cont SIMILARLY, a correctly centered six-sigma process has a standard deviation so small that the US and LS limits are 6 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: = (85-75)/(2)(6)] = .833kg Adjusting for Mean Shifts Allowing for a shift in the mean of +-1.5 standard deviation from the center of specifications. Allowing for this shift, a six-sigma process amounts to producing an average of 3.4 defective units per million. (see table 9.5)
Quality Process Control Ardavan Asef-Vaziri Jan-2012 53 Table 9.5 Table9.5FractionDefectiveand SigmaMeasure SigmaS 3 4 5 CapabilityRatio Cp 1 1.33 1.667 Defects (ppm) 66810 6210 233 Quality Process Control Ardavan Asef-Vaziri Jan-2012 6 2 3.4
54 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 = 10fold 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. Quality Process Control Ardavan Asef-Vaziri Jan-2012 55 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 56 9.4.3 Six-Sigma Capability cont Safety capability - We may also express process capabilities in terms of the desired margin [(US-LS)-z] 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 Quality Process Control Ardavan Asef-Vaziri
Jan-2012 57 9.4.4 Capability and Control So 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. Meeting customer specifics: indicates internal stability and statistical predictability of the process performance. In control (aka within LS and US range): ability to meet external customers requirements. 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. Quality Process Control Ardavan Asef-Vaziri Jan-2012 58 9.5 Process Capability Improvement
Shift the process mean Reduce the variability Both Quality Process Control Ardavan Asef-Vaziri Jan-2012 59 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 60 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 61 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 62
Ex 9.10 Continued [from table A2.1 on page 319] Z = 1.19 Z = -1.19 (1 - .8830) .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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 63 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 Quality Process Control
Ardavan Asef-Vaziri Jan-2012 64 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 65 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: =< 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 Prob (75 =< W 66 Ex 9.11 Continued [from table A2.1 on page 319] Z = 2.0 Z = -2.0 .9772 .0228 (1 - .9772) 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 Quality Process Control
Ardavan Asef-Vaziri Jan-2012 67 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 68 9.6 Product and Process Design Reducing the variability from product and process design -simplification -standardization -mistake proofing Quality Process Control Ardavan Asef-Vaziri
Jan-2012 69 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 70 Standardization Use standard parts and procedures -reduces operator discretion, ambiguity, and opportunity for making mistakes Quality Process Control Ardavan Asef-Vaziri Jan-2012 71
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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 72 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 customers 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 Quality Process Control Ardavan Asef-Vaziri Jan-2012 73 QUESTIONS ???
Quality Process Control Ardavan Asef-Vaziri Jan-2012 74
FLORIDA ELEVATOR ASSOCIATION Alteration/Modernization Inspection Criteria by: John
4/17/2010 www.CodeDataPlate.com * From Code Data Plate to Acceptance Inspection Tag From Code Data Plate to Acceptance Inspection Tag Scope of a Modernization What is Retained What is New What is Altered Scope of Acceptance Inspection What was Retained What...