SCM – 302 OPERATIONS MANAGEMENT
06 – Quality Management SCM 302 - Quality & SPC
Ratcliffe 2 Learning Objectives
1. Explain different definitions of quality. 2. Describe two ways that quality improves profitability. 3. What are 4 types of quality-associated costs and the relationship between them? 4. Discuss examples of how firms applied PDCA cycle and utilized various TQM tools to improve their processes. 5. What are the 7 concepts of Total Quality Management? 6. What is Six Sigma? 7. Describe how to use the 7 TQM tools to analyze a quality problem. 8. Explain unique challenges for managing quality in services.
A. Construct 푥 -charts, 푅-charts, p-charts B. Explain five steps for building control charts C. Compute 퐶푝 and 퐶푝푘 and explain process capability SCM 302 - Quality & SPC
Ratcliffe 3 SCM 302 - Quality & SPC
Ratcliffe 4 Toyota Issues Sweeping Global Recall Over Fire Hazard • Toyota recalled 7.4 million vehicles to repair faulty power- window switches that pose a fire risk. • Toyota’s largest recall for a single part • Set back its efforts to recover from previous safety issues and Japan tsunami. • In 2009-2010, Toyota recalled more than 11 million vehicles worldwide to replace floor mats and sticky accelerator pedals. • The automaker has been seeking to reassure consumers about the quality of its vehicles since then. • Toyota’s report to National Highway Traffic Safety Association • Originally wanted to conduct a “customer satisfaction campaign” but decided to pursue the recall after discussions with the agency. • Voluntary recall, but federal regulations require a manufacturer learns to notify NHTSA of plans for a recall within 5 business days • Notify owners by mail. Technicians will inspect & repair switch free of charge.
• What are the negative impacts of poor “quality” for Toyota? • What are the costs associated with a recall? • What is Toyota doing to rebuild its image as a quality leader? SCM 302 - Quality & SPC
Ratcliffe 5 Test Your IQ. What is Quality?
• If you plan to buy a car, what is your key criterion? • Speed/acceleration • Design/appearance • Reliability • Others
• How would you measure the quality of the vehicle? SCM 302 - Quality & SPC
Ratcliffe 6 What is Quality?
A high-performance or e.g. high-end product like a Rolls Royce luxury product ? • But is a Toyota or Honda not high quality?
Conformance to i.e. does the product do what it was designed to do Specification ? • But what if the design was bad?
Conformance to Customer i.e. does the product do what the customer wants it to do Needs ? • In other words does it meet the customer’s needs SCM 302 - Quality & SPC
Ratcliffe 7 What is Quality?
• “Consistently meeting customers’ expectations” 3M Corporation
• “Providing our external and internal customers with innovative products and services that fully satisfy their requirements” Xerox Corporation
• “100% customer satisfaction, by performing 100% to our standards, as perceived by the customer” Federal Express
• “Meeting the requirements of our customers for defect-free products and services” IBM
• “Performance leadership in meeting customer requirements by doing the right things right the first time” Westinghouse Electric Corporation
• “The unyielding and continually improving effort by everyone in an organization to understand, meet, and exceed the expectations of customers” Procter and Gamble SCM 302 - Quality & SPC
Ratcliffe 8 What is Quality? The totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs American Society for Quality
• User-based: better performance, more features
• Manufacturing-based: conformance to standards, making it right the first time
• Product-based: specific and measurable attributes of the product SCM 302 - Quality & SPC
Ratcliffe 9 Why is Quality Important?
Managing quality supports all three strategies Sales Gains via • Differentiation • Improved response • Lower costs • Flexible pricing • Improved response • Improved reputation Improved Increased Other reasons quality is important: Quality Profits 1. Company reputation Reduced Costs via • Perception of new products, Employment practices, Supplier relations • Increased productivity 2. Product liability • Lower rework and scrap costs • Reduce risk • Lower warranty costs 3. Global implications • Improved ability to compete 4. Company Ethics • Must deliver healthy, safe, quality products and services • Poor quality risks injuries, lawsuits, recalls, and regulation • All stakeholders much be considered SCM 302 - Quality & SPC
Ratcliffe 10 Quality Awards & Standards
• Malcom Baldrige National Quality Award • Established in 1988 by the U.S. government • Designed to promote TQM practices • Recent winners include: Lockheed Martin Missiles and Fire Control, North Mississippi Health Services, City of Irving, Concordia Publishing House, Nestlé Purina PetCare Co. • Deming Prize in Japan • ISO 9000 • Set of quality standards developed by International Organization for Standardization • Encourages quality management procedures, detailed documentation, work instructions, and recordkeeping • Over one million certifications in 178 countries • Critical for global business SCM 302 - Quality & SPC
Ratcliffe 11 Four Classes of Quality Associated Costs
Prevention Appraisal • Costs of process of • Costs of process of preventing poor UNCOVERING quality defects • Planning, training, • Inspections, tests, Total Total Cost upfront design etc. audits etc. Cost External Failure
Internal Failure External Failure Internal Failure • Costs of discovering • Costs of product poor product quality quality problems that before it reaches the occur AFTER product Prevention customer reaches customer • Rework (fixing • Recall logistics, Appraisal defect), scrap, Repair, Brand loyalty, equipment downtime Litigation Quality Improvement etc. SCM 302 - Quality & SPC
Ratcliffe 12 Quality Involves Some Trade-Offs A Traditional View
Cost
Total Costs
Prevention and Appraisal Costs
Internal and External Failure Costs Quality
The cost of high quality may be as high as low quality. There is an optimal quality level. Good quality management programs figure out how to reduce the cost of achieving quality and then transfer this knowledge through the company SCM 302 - Quality & SPC
Ratcliffe 13 The Progression of Quality Management
(1952-1954) Joseph Juran (1961) Arnold Feigenbaum invited to Japan Total Quality Control • Top-management support • 40 steps to quality and involvement in quality improvement processes. Motorola developed effort. • Quality not set of tools but Six Sigma, extending World War I: • Teams continually seek to total field that integrates the concept of quality quality inspection raise quality standards. company processes management from was introduced to • Customer focused - define • Learn from each other’s product level to minimize failures quality as fitness for use, successes, cross-functional business process and due to quality. not written specifications. teamwork. organizational level
1920s 1950s 1980s
W. Edwards (1929). (1950) Deming trains hundreds The U.S. companies Deming meets Walter of engineers, managers, were threaten by the (1979) Phillip Crosby A. Shewhart. Inspired scholars, and chief executives superior quality of Quality Is Free by his ideas of statistical on quality control Japanese products and • Cost of poor quality process control, control • Management accept TQM received great understated compared to cost chart, Shewhart Cycle responsibility for building attention. of improving quality. good systems. • Should include everything • The quality the process is involved in not doing job capable of producing limits right the first time. the employee • Coined term zero defects • 14 points for implementing • “There is absolutely no reason quality improvement for having errors or defects in any product or service.” SCM 302 - Quality & SPC
Ratcliffe 14 Total Quality Management
• Management of entire organization so that it excels in all aspects of products and services important to the customer • Continuous companywide drive
• Seven Key Concepts 1. Continuous improvement TQM did not invent any 2. Six Sigma revolutionary quality techniques 3. Employee empowerment (i.e. the basic building blocks) 4. Benchmarking but rather packaged quality management as a strategic 5. Just-in-time (JIT) imperative 6. Taguchi concepts • Some companies had great 7. Knowledge of TQM tools success and others failed SCM 302 - Quality & SPC
Ratcliffe 15 TQM Concept #1: Continuous Improvement
PDCA Cycle • Kaizen: never-ending process of continual 4. Act 1. Plan Implement Identify the improvement the plan, pattern and • Covers people, document make a plan equipment, materials, procedures
3. Check 2. Do Is the plan Test the working? plan SCM 302 - Quality & SPC
Ratcliffe 16 TQM Concept #2: Six Sigma
• Two meanings: 2,700 defects/million 1. Process 99.9997% capable, 3.4 defects per million 3.4 defects/million 2. Program designed to reduce defects, lower costs, save time, and improve customer satisfaction
Mean • Key Concepts ±3 • Customer perception of quality is not just driven by ±6 average quality but by variation in quality from interaction with the firm • Processes need to be designed to minimize variability, deliver what customer wants • Cannot be accomplished without a major commitment from top level management
• Implementing • Emphasize defects per million as standard metric • Provide extensive training • Create qualified process improvement experts (Black Belts, Green Belts, etc.) • Set stretch objectives SCM 302 - Quality & SPC
Ratcliffe 17 TQM Concept #3 Employee Empowerment • Enlarge employee jobs so that the added responsibility and authority are moved to the lowest level possible in the organization • 85% of quality problems are due to process and material not employees • Techniques • Build communication networks that include employees • Develop open, supportive supervisors • Build a high-morale organization • Create formal team structures SCM 302 - Quality & SPC
Ratcliffe 18 TQM Concept #4: Benchmarking • Selecting a demonstrated standard of performance that represents the very best performance for a process or an activity. 1. Determine what to benchmark 2. Form a benchmark team 3. Identify benchmarking partners 4. Collect and analyze benchmarking information 5. Take action to match or exceed the benchmark SCM 302 - Quality & SPC
Ratcliffe 19 TQM Concept #5: Just-in-Time (JIT)
• JIT cuts the cost of quality • ‘Pull’ system of production • JIT improves quality scheduling including supply management • Better quality means less inventory and better, easier-to-employ JIT • Production only when signaled system • Allows reduced inventory levels • Inventory costs money and hides process and material problems • Encourages improved process and product quality SCM 302 - Quality & SPC
Ratcliffe 20 TQM Concepts #6: Taguchi Concepts
• Most quality problems are the result of poor product and process design • Quality robustness: Products should be produced uniformly and consistently even in adverse manufacturing and environmental conditions. • Quality loss function: mathematical function identifies all costs connected with poor quality, shows how these costs increase as product quality moves from what customer wants: 퐿 = 퐷2퐶 • Target-oriented quality: a philosophy of continuous improvement to bring the product exactly on target SCM 302 - Quality & SPC
Ratcliffe 21 TQM Concepts #7: TQM Tools
• Tools for Generating Ideas 1. Check Sheet 2. Scatter Diagram 3. Cause-and-Effect Diagram • Tools to Organize the Data 4. Pareto Chart 5. Flowchart (Process Diagram) • Tools for Identifying Problems 6. Histogram 7. Statistical Process Control Chart SCM 302 - Quality & SPC
Ratcliffe 22 TQM Tools: 1. Check Sheet An organized method of recording data
Hour
Defect 1 2 3 4 5 6 7 8 A /// / / / / /// / B // / / / // /// C / // // //// SCM 302 - Quality & SPC
Ratcliffe 23 TQM Tools #2: Scatter Diagram A graph of the value of one variable
vs. another variable Productivity
Absenteeism Figure 6.6 SCM 302 - Quality & SPC
Ratcliffe 24 TQM Tools #3: Cause-and-Effect Diagrams (Fishbone)
Material Method (ball) (shooting process) Grain/Feel Aiming point (grip) Size of ball Air pressure Bend knees Hand position Balance Lopsidedness Follow-through Missed free-throws Training Rim size
Conditioning Motivation Rim height
Consistency Rim alignment Backboard stability Concentration
Machine Manpower (hoop & Figure 6.7 (shooter) backboard) SCM 302 - Quality & SPC
Ratcliffe 25 TQM Tools #4: Pareto Charts Data for October – 100 70 – – 93 – 88 60 – 54 50 – – 72 40 – Number of 30 – occurrences 20 –
12
Frequency Frequency (number) Cumulativepercent 10 – 4 3 2 0 – Room svc Check-in Pool hours Minibar Misc. 72% 16% 5% 4% 3% Causes and percent of the total SCM 302 - Quality & SPC
Ratcliffe 26 TQM Tools #5: Histogram A distribution showing the frequency of occurrences of a variable
Distribution Frequency
Repair time (minutes) Figure 6.6 SCM 302 - Quality & SPC
Ratcliffe 27 TQM Tools #6: Flow Charts
MRI Flowchart 1. Physician schedules MRI 7. If unsatisfactory, repeat 2. Patient taken to MRI 8. Patient taken back to room 3. Patient signs in 9. MRI read by radiologist 4. Patient is prepped 10. MRI report transferred to 5. Technician carries out MRI physician 6. Technician inspects film 11. Patient and physician discuss
8 80% 1 2 3 4 5 6 7 11 9 10 20% SCM 302 - Quality & SPC
Ratcliffe 28 TQM Tool #7:Statistical Process Control (SPC)
Variability is inherent in every process Monitor the process; take • Natural variability (common causes) corrective action if things are • Assignable variability (special cause) “out-of-control.” • Detect and eliminate problems (negative assignable causes) • Verify and test process improvements Key Steps (positive assignable causes) 1. Collect data when process is in control 2. Construct charts using control data 3. Collect new data, plot on charts. 4. Assign causes for points or patterns that indicate process is out of control 5. Revalidate the control limits using the new data SCM 302 - Quality & SPC
Ratcliffe 29 Two types of variation
Natural Variations (Common Cause) Assignable Variations (Special Cause)
• Affects all production processes • Can be traced to a specific reason • Output measures follow a • Examples: a new supplier, a new, probability distribution with a a new technology or equipment, mean, 휇, and std. deviation, 휎. new manager • If the distribution of outputs falls • If the process is “out of control” within acceptable limits, the we need to assign a cause for process is said to be “in control” why this happened The objective of SPC is to provide a statistical signal when assignable causes of variation are present SCM 302 - Quality & SPC
Ratcliffe 30 Attributes vs. Variables
Measurements (Variables) Discrete Attributes • Output can be represented by a • Items are either good or bad, continuous number, e.g., acceptable or unacceptable • Height • Does not address degree of failure • Width • Output is represented by a • Weight discrete response, e.g., • Concentration • non-defective vs. defective • Processing time • Falls within an acceptable range
Must be used together SCM 302 - Quality & SPC
Ratcliffe 31 Sampling & Process Measurement Good sampling allows conclusions about population • 100% inspection is costly and unnecessary, especially if the tests are destructive
Samples averages form a distribution. Each Solid line represents • Samples of 5 boxes of cereal taken off the filling represents one sample of machine line, vary in average weight. distribution five boxes
• Distribution of sample means follows a normal Frequency distribution (Central Limit Theorem) regardless of the central tendency, variance, and shape of the underlying distribution Weight
Process forms a stable distribution over time if only natural causes of variation are present. Otherwise distribution is not stable. ??? ?? ?? ? ? ?? ?? ??? ???
Prediction Prediction
Frequency Frequency Weight Weight SCM 302 - Quality & SPC
Ratcliffe 32 The Central Limit Theorem Population Mean of sample means = 푥 distributions 휎 Standard deviation of =휎 = the sample means 푥 푛 Beta Distribution of sample means
Normal
Uniform
| | | | | | | = -3s x -2s x -1s x x +1s x +2s x +3s x
95.45% fall within ±2휎푥 Figure S6.3
99.73% fall within ±3휎푥 SCM 302 - Quality & SPC
Ratcliffe 33 Steps to Construct x-bar and R-charts
1. Collect samples from stable process. Compute means and ranges Often 푁 = 20 표푟 25 samples of 푛 = 4 or 5 observations each 2. Compute center lines (overall means, 푥 and 푅 ), and upper and lower control limits using factors from Table
푥 -Chart Limits 푥 = mean of sample means R-Chart Limits 푛 푅 푅 = 푖=1 푖 = avg. of sample 푈퐶퐿 = 푥 + 퐴2푅 푛 푈퐶퐿 = 퐷4푅 ranges 퐿퐶퐿 = 푥 − 퐴2푅 퐴2, 퐷4, 퐷3 are control chart factors 퐿퐶퐿 = 퐷3푅 found in Table S6.1 3. Collect new data. Graph sample means and ranges on control charts. 4. Investigate points or patterns that indicate process is out of control. Assign causes, address the causes, and then resume the process 5. Collect additional samples and, if necessary, revalidate the control limits using the new data
*If the process is not currently stable, use the desired mean, 휇, instead of 푥 **If true std. deviation of the process, 휎, is known, use a confidence intervals instead formulas above SCM 302 - Quality & SPC
Ratcliffe 34 Control Chart Factors
TABLE S6.1 Factors for Computing Control Chart Limits (3 sigma) SAMPLE SIZE, MEAN FACTOR, UPPER RANGE, LOWER RANGE,
n A2 D4 D3 2 1.880 3.268 0 3 1.023 2.574 0 4 .729 2.282 0 5 .577 2.115 0 6 .483 2.004 0 7 .419 1.924 0.076 8 .373 1.864 0.136 9 .337 1.816 0.184 10 .308 1.777 0.223 12 .266 1.716 0.284 SCM 302 - Quality & SPC
Ratcliffe 35 Calculating 푥 -chart limits Cereal boxes Process average = 16 ounces Labeled as “net weight 16 ounces” Average range = 1.733 ounce
Sample size = 5 푈퐶퐿푥 = 푥 + 퐴2푅 = 16 + 0.577 1.733 = 17 표푢푛푐푒푠 UCL = 17 From Table
퐿퐶퐿푥 = 푥 − 퐴2푅 Mean = 16 = 16 − 0.577 1.733 = 15 표푢푛푐푒푠 LCL = 15 SCM 302 - Quality & SPC
Ratcliffe 36 Calculating 푥 -chart limits
Control Chart Variation due for samples of Out of 5 boxes to assignable control causes
17 = UCL
Variation due to 16 = Mean natural causes
15 = LCL
Variation due | | | | | | | | | | | | to assignable 1 2 3 4 5 6 7 8 9 10 11 12 Out of causes Sample number control SCM 302 - Quality & SPC
Ratcliffe 37 Calculating 푅-chart limits Cereal boxes Process average = 16 ounces Labeled as “net weight 16 ounces” Average range = 1.733 ounce
Sample size = 5 푈퐶퐿푅 = 퐷4푅 = 2.115 1.733 = 3.665 표푢푛푐푒푠 UCL = 3.665 From Table
퐿퐶퐿푅 = 퐷3푅 Mean = 1.733 = 0 1.733 = 0 LCL = 0 SCM 302 - Quality & SPC
Ratcliffe 38 푥 -chart can indicate an out-of-control situation when R-chart does not. (a) These (Sampling mean is sampling shifting upward, but distributions range is consistent) result in the charts below
UCL (x-chart detects x-chart shift in central tendency) LCL UCL (R-chart does not R-chart detect change in mean) LCL Figure S6.5 SCM 302 - Quality & SPC
Ratcliffe 39 R-chart can indicate an out-of-control situation when 푥 -chart does not. (b) These sampling (Sampling mean distributions is constant, but result in the dispersion is charts below increasing)
UCL (x-chart indicates x-chart no change in central tendency) LCL UCL (R-chart detects R-chart increase in dispersion) LCL Figure S6.5 SCM 302 - Quality & SPC
Ratcliffe 40 Step 1: Collect Data. Samples of Smart Phone Battery Life in Hours Sample Measurement Mean Range 1 2 3 4 5 1 49.59 53.94 47.11 60.58 43.48 2 60.41 48.90 29.19 58.87 39.80 3 65.89 56.96 44.15 60.76 50.39 4 48.48 51.02 57.36 45.54 63.11 5 49.10 40.69 42.10 29.26 46.40 6 42.76 35.11 47.66 46.78 44.93 SCM 302 - Quality & SPC
Ratcliffe 41 Step 2: Calculate Overall Means. Compute UCL and LCL for 푥 -chart and R-chart
Sample Measurement Mean Range 1 2 3 4 5 1 49.59 53.94 47.11 60.58 43.48 50.94 17.10 2 60.41 48.90 29.19 58.87 39.80 47.44 31.22 3 65.89 56.96 44.15 60.76 50.39 55.63 21.74 4 48.48 51.02 57.36 45.54 63.11 53.10 17.56 5 49.10 40.69 42.10 29.26 46.40 41.51 19.84 6 42.76 35.11 47.66 46.78 44.93 43.45 12.55
50.94 + 47.44 + 55.63 + 53.10 + 41.51 + 43.45 푥 = = ퟒퟖ. ퟐퟔ 6 17.10 + 31.22 + 21.74 + 17.56 + 19.84 + 12.55 푅 = = ퟐퟎ. ퟎퟎ 6 SCM 302 - Quality & SPC
Ratcliffe 42 Control Chart Factors
TABLE S6.1 Factors for Computing Control Chart Limits (3 sigma) SAMPLE SIZE, MEAN FACTOR, UPPER RANGE, LOWER RANGE,
n A2 D4 D3 2 1.880 3.268 0 6 samples of 5 in each 3 1.023 2.574 sample.0 n=5 4 .729 2.282 0 5 .577 2.115 0 6 .483 2.004 0 7 .419 1.924 0.076 8 .373 1.864 0.136 9 .337 1.816 0.184 10 .308 1.777 0.223 12 .266 1.716 0.284 SCM 302 - Quality & SPC
Ratcliffe 43 Step 2: Compute UCL and LCL, 푥 -chart 50.94 + 47.44 + 55.63 + 53.10 + 41.51 + 43.45 푥 = = 48.26 6 17.10 + 31.22 + 21.74 + 17.56 + 19.84 + 12.55 푅 = = 20.00 From Control Chart 6 Factors Table UCL X A R UCL 2 48.68 0.57720.00 60.22
Center Line X 48.68
LCL X A R LCL 2 48.68 0.57720.00 37.14
1. These limits are derived when the process is known to be in-control. 2. Any future samples which falls out of the control limits indicates a shift in sample mean and the process in not in-control. SCM 302 - Quality & SPC
Ratcliffe 44 Step 2: Compute UCL and LCL, 푅-chart From Control Chart Factors Table
UCL UCL D4 R 2.11520.00 42.21
17.10 31.22 21.74 17.56 19.84 12.55 Center R 20.00 Line 6
LCL LCL D3 R 020.00 0.00 SCM 302 - Quality & SPC
Ratcliffe 45 Step 3. Graph Sample Means and Ranges on Control Charts. Is the Process In-Control? Sample Measurement Mean Range 1 2 3 4 5 101 36.62 50.01 44.39 35.84 50.41 43.45 14.58 102 42.91 34.72 54.82 51.67 56.01 48.03 21.28 103 57.50 49.69 69.49 43.18 51.50 54.27 26.31 104 58.36 53.28 55.59 59.06 41.70 53.60 17.36 105 30.22 16.00 51.87 44.67 94.27 47.40 78.28 106 2.92 28.45 76.67 66.05 29.04 40.63 73.75 SCM 302 - Quality & SPC
Ratcliffe 46 Need to Look at Both X-bar Chart and R X-bar Chart Looks like Process Is in R Chart Shows the Process Has Gone Chart Control Out of Control
UCL: upper control limit=60.28
Mean =48.68 UCL: upper control limit=42.21
LCL: lower control limit=37.08 Mean range =20.00
LCL: lower control limit=0.00
Sometimes the X-bar chart captures an out-of-control situation and the R chart does not. How might this happen?
Is it bad if a sample range falls below the LCL ? SCM 302 - Quality & SPC
Ratcliffe 47 SPC Exercise #1 – Part A
• As a quality inspector for Phillips Medical Imaging department, you monitor the average rotation time of a line of CT scanners. The following sample data (in msec) was collected when the production process was known to be in control. Each sample consisted of 6 observations: • Calculate the 3σ upper and lower control limits and the center lines for both the mean ( X ) and range (R) charts. Use the “factors” from the class slides or textbook assuming a normal distribution.
Rotation Time (msec) Sample 1 2 3 4 5 6 Number 1 469.92 468.67 479.76 454.38 469.58 454.46 2 457.34 454.37 475.28 453.46 480.03 480.4 3 473.96 459.26 460.42 462.04 450.6 451.52 4 480.06 469.86 456.42 460.63 465.66 466.99 5 467.46 476.56 474.01 465.34 475.27 462.97 6 473.06 475.86 472.97 454.93 470.73 466.24 7 456.27 476.37 479.5 459.86 470.73 452.35 SCM 302 - Quality & SPC
Ratcliffe 48 SPC Exercise #1 - Part B • To save on costs, Phillips recently changed their supplier of a key component to one that is less expensive. To evaluate if this change has an impact on rotation time, the following 10 samples were collected after this change. 1. Plot the sample mean and sample range for each of the 10 samples on the appropriate control chart using the upper and lower control limits and center lines you computed. 2. Is the production process still in control? Why or why not?
Rotation Time (msec) Sample 1 2 3 4 5 6 Number 1 472.8 468.03 465.41 469.37 471.47 455.12 2 490.78 478.32 488.63 482.03 457.71 488.56 3 461.89 469.81 456.02 483.89 475.24 463 4 472.68 472.87 460.93 488.32 474.2 475.75 5 450.95 486.69 469.77 467.12 469.5 467.77 6 476.77 453.16 472.63 456.29 480.5 464.82 7 468.4 464.35 454.87 452.14 455.77 464.96 8 489.75 464.01 490.75 484.49 474.63 487.18 9 475.39 472.08 489.52 474.26 450.36 480.9 10 474.28 476.5 478.16 479.69 470.66 470.75 SCM 302 - Quality & SPC
Ratcliffe 49 Steps to Creating a P-chart
1. For each sample, count the number of defective outputs, 푿풊
• i.e. count the number outputs that failed the attribute test
푿 2. Calculate the proportion of defective outputs, 풑 = 풊 풊 풏 • i.e. the number of defective outputs divided by the sample size
3. Estimate for the average proportion of defects based on the results from N samples, 풑 풑 = 풊 풏 • p-bar equals the average proportion of defects
풑 ퟏ−풑 4. Estimate the standard deviation of the average proportion of defects, 흈 = 풑 풏
5. Set control limits as 푼푪푳 = 풑 + ퟑ흈풑 and L푪푳 = 풑 − ퟑ흈풑 SCM 302 - Quality & SPC
Ratcliffe 50 Calculate the P-Chart Control Limits Sample Size = n =100
Sample # defective Proportion 푝 1 − 푝 0.0756 1 − 0.0756 1 3 = 3 100 = ퟎ. ퟎퟑ 흈 = = 풑 푛 100 = 10 100 = ퟎ. ퟏퟎ 2 10 흈풑 = ퟎ. ퟎퟐퟔퟒ 3 4 = 4 100 = ퟎ. ퟎퟒ 푈퐶퐿 = 푝 + 3휎푝 4 8 = 8 100 = ퟎ. ퟎퟖ = 0.0756 + 3 0.0264 5 12 = 12 100 = ퟎ. ퟏퟐ 푼푪푳 = ퟎ. ퟏퟓퟒퟖ 6 7 = 7 100 = ퟎ. ퟎퟕ L퐶퐿 = 푝 − 3휎푝 = 0.0756 − 3 0.0264 7 1 = 1 100 = ퟎ. ퟎퟏ 푈퐶퐿 = −0.0036 Round up if below zero = 9 100 = ퟎ. ퟎퟗ 8 9 푼푪푳 = ퟎ 9 14 = 14 100 = ퟎ. ퟏퟒ
0.03 + 0.1 + 0.04 + 0.08 + 0.12 + 0.07 + 0.01 + 0.09 + 0.14 풑 = = ퟎ. ퟎퟕퟓퟔ 9 SCM 302 - Quality & SPC
Ratcliffe 51 SPC Exercise #2 • Toyota tracks the number of defective gas pedals which stick in each lot of 1000 finished Camry sedans every week. Following data were collected when gas pedal quality was known to be in control. • Calculate the 3σ upper and lower control limits and center lines for proportion of defective gas pedals.
Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 # of defects per lot 17 14 9 3 20 6 6 4 17 2 10 2 5 18 1
• After the control chart in part (a) was constructed, Toyota continued to monitor the proportion of defective gas pedals in lots of 1000 for the next 10 weeks. Plot the proportion of defectives for each of the 10 samples given below on the appropriate control chart using computations from part (a). Is the process in control according to the chart?
Week 16 17 18 19 20 21 22 23 24 25 # of defects per lot 7 3 20 17 6 1 20 5 22 6 SCM 302 - Quality & SPC
Ratcliffe 52 Steps to Creating a C-chart
1. For each sample, count the number of defective outputs, 푿풊 • i.e. count the number outputs that failed the attribute test 2. Estimate for the average number of defects based on the results 푿 from N samples, 풄 = 풊 풏 • c-bar equals the average number of defects
4. Estimate the standard deviation of the average proportion of defects, 흈풄 = 풄
5. Set control limits as 푼푪푳 = 풄 + ퟑ흈풄 and L푪푳 = 풄 − ퟑ흈풄 SCM 302 - Quality & SPC
53 Control Limits vs. Tolerances Control Limits Engineering Specs • Derived tolerance • Designed tolerance • Statistical results based • Not statistically on sampling determined • Internally determined • Externally imposed
Then the question becomes whether your process is capable of meeting the specs?
Ratcliffe SCM 302 - Quality & SPC
Ratcliffe 54 Process capability
(a) In statistical control and capable of producing within Frequency control limits Lower control limit Upper control limit (b) In statistical control but not capable of producing within control limits
(c) Out of control
Size (weight, length, speed, etc.) Figure S6.2 SCM 302 - Quality & SPC
Ratcliffe 55 XYZ Co. Machines Metal Disks Disk Thickness is Critical to Customers
XYZ’s produces disks of thickness 2mm but with some variation Say XYZ specifies that disks will have a thickness of 2+/-0.01mm Prob. Density 0.09 • Do you think XYZ’s process is capable of achieving this? 0.08 0.07 0.06 0.05 0.04 Say XYZ specifies that disks will have a thickness of 2+/-0.005mm 0.03 0.02 • Do you think XYZ’s process is capable of achieving this? 0.01
0.00
1.988 1.990 1.993 1.995 1.998 2.000 2.003 2.005 2.008 2.010 2.013
Disc Thickness SCM 302 - Quality & SPC
Ratcliffe 56 Process Capability Depends on Specifications and Variability Process Appears Capable of Process Does Not Appear Capable Delivering 2+/-0.01mm of Delivering 2+/-0.005mm
Prob. Density Prob. Density 0.09 0.09 0.08 0.08 0.07 0.07 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.02 0.02 0.01 0.01
0 0
2.008 1.988 1.990 1.993 1.995 1.998 2.000 2.003 2.005 2.008 2.010 2.013 1.988 1.990 1.993 1.995 1.998 2.000 2.003 2.005 2.010 2.013
Disk Thickness Disk Thickness SCM 302 - Quality & SPC
Ratcliffe 57 A Common Measure of Process Capability
Equation Cp=1 i.e. USL-LSL=6σ
lower upper Prob. Density LSL USL specification limit specification 0.09 limit 0.08 0.07 USL LSL 0.06 Cp 0.05 6 0.04 3 3 0.03 process standard 0.02 deviation 0.01
0
1.990 1.993 1.995 1.998 2.000 2.003 2.005 2.008 2.010 2.013 Cp > 1 : Process capable 1.988 Cp < 1 : Process not capable Probability Disk Thickness Probability Cp = 1 : Process borderline capable below above LSL=0.135% USL=0.135% Probability of Defect = 0.27% SCM 302 - Quality & SPC
Ratcliffe 58
UCL
Design Mean or Center Line Specifications
LCL
• Recall that UCL and LCL are 3 σ away from the mean
• Natural variation greater than tolerances ( C p<1) • Parts produced when process “in control” may need to be scrapped or reworked • Process needs to be redesigned SCM 302 - Quality & SPC
Ratcliffe 59
UCL Design Specifications
LCL
•Process is barely capable of meeting the specifications. Cp= 1 • 3 sigma limits translate to about 2.7 defects per thousand – That’s 99.73% SCM 302 - Quality & SPC
Ratcliffe 60
UCL Design Specifications
LCL
• Process capability exceeds specification
• Cp > 1 • Defective (non-spec) measured in parts per billion SCM 302 - Quality & SPC
Ratcliffe 61 Are the Following Processes Capable?
Process Sigma USL LSL Cp
A1 0.05 100.03 99.97
A2 0.01 100.03 99.97
B1 0.001 5.05 4.95
B2 0.0005 5.05 4.95
B3 0.02 5.05 4.95 SCM 302 - Quality & SPC
Ratcliffe 62 Are the Following Processes Capable?
Process Sigma USL LSL Cp
A1 0.05 100.03 99.97 0.2
A2 0.01 100.03 99.97 1.0
B1 0.001 5.05 4.95 16.67
B2 0.0005 5.05 4.95 33.33
B3 0.02 5.05 4.95 0.83 SCM 302 - Quality & SPC
Ratcliffe 63
You Need to Be Careful With Cp
Cp=1 and Process Centered Cp=1 but Process Mean High by 1.5σ
Prob. Density LSL USL Prob. Density LSL USL 45 45 40 40 35 35 30 30 25 25 20 20 15 15 4.5 1.5 10 10 3 5 5
0 0
99.950 99.960 99.970 99.980 99.990 100.000 100.010 100.020 100.030 100.040 100.050
100.030 99.950 99.960 99.970 99.980 99.990 100.000 100.010 100.020 100.040 100.050
Output Output Probability below LSL Probability below LSL Probability above USL =1- Probability above USL =1- =normsdist(-4.5)=0.00034% =normsdist(-3)=0.135% normsdist(3)=0.135% normsdist(1.5)=6.68% Probability of Defect = 0.27% Probability of Defect = 6.68% ! SCM 302 - Quality & SPC
Ratcliffe 64
Another common measure is Cpk
Process mean Cpk > 1 : Process capable USL LSL Cpk < 1 : Process not capable Cpk min , 3 3 Cpk = 1 : Process borderline capable
Calculate the Cp and Cpk for A2 if the mean is 100
Calculate the Cp and Cpk for A2 if the mean is 100.015 SCM 302 - Quality & SPC
Ratcliffe 65
Another common measure is Cpk Process mean
USL LSL Cpk min , 3 3
Calculate the Cp and Cpk for A2 if the mean is 100
100.0399.97 Cp 1 6(0.01)
100.03100 100 99.97 Cpk min , min1,11 3(0.01) 3(0.01)
Calculate the Cp and Cpk for A2 if the mean is 100.015 100.0399.97 Cp 1 6(0.01)
100.03100.015 100.015 99.97 Cpk min , min0.5,1.5 0.5 3(0.01) 3(0.01) SCM 302 - Quality & SPC
Ratcliffe 66 Process Capability - Example
• A manufacturer of granola bars has a weight specification 2 ounces plus or minus 0.05 ounces. The mean weight of bar-making process is 2.01 ounces with a standard deviation of 0.015 ounces (when the process is in-control). • Is the process capable of meeting specifications according to Cp measure?
• Is the process capable of meeting specifications according to Cpk measure? SCM 302 - Quality & SPC
Ratcliffe 67 SPC Exercise #3
• Deep Sea Diggers estimate that the time until failure for the battery used on its blowout preventers should be at least 36 months and at most 96 months. The manufacturing process is such that the time until failure is (approximately) normally distributed with a mean of 57 months and standard deviation of 8 months. The company aims for 3σ performance for this process. a. Calculate Cp. Is the process capable of 3σ performance based on Cp? b. Calculate Cpk. Does your answer from part (a) regarding process capability change when you also use Cpk? SCM 302 - Quality & SPC
Ratcliffe 68
Comparing Cp and Cpk • Same… • Both measure if a process is capable of meeting its design specification
• The process is capable if cp or cpk ≧ 1
• Difference
• Cp: good measure only when the process mean does not skew from the center of design specification (USL and LSL)
• Cpk: Consider process mean and it is good whether the process mean is skewed or not SCM 302 - Quality & SPC
Ratcliffe 69
Is 3σ quality good enough?
• Large Volume or Costly Defects1 • At least 54,000 defective drug prescriptions a year • More than 5000 pieces of mail lost every hour • More than 10,000 newborn babies accidentally dropped by doctors or nurses each year
• Products with multiple components2 • A printer has about 200 parts. If each part is only at 3σ quality, then the printer defect rate3 would be greater than 40%. • An automobile has more than 10,000 parts, Good Luck!!!
1 What is six sigma? Motorola Inc., 1987. 2 Product Design and Development, Ulrich and Eppinger, 1995 3 Probability of at least one defective part in the printer SCM 302 - Quality & SPC
Ratcliffe 70
Six Sigma Process Capability
• Wants the probability of a defect to be no higher than 3.4 in a million
• Realizes that process mean might shift from the center of the specification limits • Assumes that process mean will not shift from center by more than 1.5σ
• Therefore, defines a process as capable if USL LSL Cpk min , 1 6 6 SCM 302 - Quality & SPC
Ratcliffe 71
Six Sigma Illustration
Process Centered Cp=1 but Process Mean High by 1.5σ
Prob. Density LSL USL Prob. Density LSL USL 90 45 80 40 70 35 60 30 50 25 40 20 30 15 7.5 4.5 20 6 10 10 5
0
100.010 99.960 99.970 99.980 99.990 100.000 100.020 100.030 100.040 100.050
99.950 0
100.040 99.950 99.960 99.970 99.980 99.990 100.000 100.010 100.020 100.030 100.050
Output Output Probability below LSL Probability above USL Probability below LSL Probability above USL =1- =normsdist(-6)=0.000% =1-normsdist(6)=0.000% =normsdist(-7.5)=0.000% normsdist(4.5)=0.00034% Probability of Defect ~ 0.0% Probability of Defect = 0.00034% ! SCM 302 - Quality & SPC
Ratcliffe 72 Inspection Requires Some Key Decisions
• How often should I inspect? • Inspection often involves sampling from a “lot” of items
• What should my sampling plan be? • What sample size should I use? • How do I decide to accept or reject the lot being inspected? SCM 302 - Quality & SPC
Ratcliffe 73 Decisions Involve Trade-offs Cost Versus Quality
• The more you inspect the higher the cost but the lower the risk of defective items going undetected • If defective items could be extremely costly then you will be willing to spend more money on inspection • But it probably makes sense to invest effort in creating a capable process that requires much less (or no) inspection • Human inspection is never perfect which is another reason for creating capable processes SCM 302 - Quality & SPC
Ratcliffe 74 TQM In Services
• Service quality is more difficult to measure than the quality of goods • Service quality perceptions depend on 1. Intangible differences between products 2. Intangible expectations customers have of those products
• The Operations Manager must recognize: 1. The tangible component of services is important 2. The service process is important 3. The service is judged against the customer’s expectations 4. Exceptions will occur SCM 302 - Quality & SPC
Ratcliffe 75 Determinants of Service Quality
Table 6.5 Reliability involves consistency of performance and dependability Responsiveness concerns the willingness or readiness of employees to provide service Competence means possession of the required skills and knowledge to perform the service Access involves approachability and ease of contact Courtesy involves politeness, respect, consideration, and friendliness Communication means keeping customers informed and listening to them Credibility involves trustworthiness, believability, and honesty Security is the freedom from danger, risk, or doubt Understanding/knowing the customer involves making the effort to understand the customer’s needs Tangibles include the physical evidence of the service SCM 302 - Quality & SPC
Ratcliffe 76 Practice Problems
• See SPC Practice Problems Handout!!!
• 6S.6: Use only first 5 hours as “control period” (i.e. to set control limits). Then determine if process was out of control during hours 6-24.
• 6S.15
• 6S.27: Use Cp and Cpk