IE 135: Quality Control Lecture 1 PDF

Outline Definitions of Quality A Brief History of Quality Management Aspects of Quality Improvement Quality Terminologies Statistical Methods in Quality Control & Improvement Quality Gurus QUALITY Quality Even though quality is hard to define, you know what quality is Quality is o...

Outline Definitions of Quality A Brief History of Quality Management Aspects of Quality Improvement Quality Terminologies Statistical Methods in Quality Control & Improvement Quality Gurus QUALITY Quality Even though quality is hard to define, you know what quality is Quality is one of the most important decision factors for consumers in their selection between products and services This applies to any form of consumer, from individuals to industrial organizations to banks to military defense agencies Therefore, understanding and improving quality are key to organizational success, growth, and competitiveness The Definition of Quality Traditional Definition: Quality is fitness for use Quality of design Quality of conformance The Definition of Quality Quality of design Intentional design differences in the production of goods and services (e.g., material, component specifications, accessories) Quality of conformance How well the product conforms to specifications required by the design The Definition of Quality Quality of design Intentional design differences in the production of goods and services (e.g., material, component specifications, accessories) Quality of conformance How well the product conforms to specifications required by the design Problem: Quality became more associated with the conformance aspect than the design aspect The Definition of Quality Traditional Definition: Quality is fitness for use Quality of design Quality of conformance Modern Definition: ??? The Definition of Quality Traditional Definition: Quality is fitness for use Quality of design Quality of conformance Modern Definition: Quality is inversely proportional to variability (in a product’s important characteristics) 1 𝑄𝑢𝑎𝑙𝑖𝑡𝑦 ∝ 𝑉𝑎𝑟𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦 The Definition of Quality Consider a comparative study on the manufacturing of transmissions for a US plant vs. a Japanese supplier The Definition of Quality Analysis of warranty claims and repair costs revealed a distinct difference LSL – Lower Specification Limit; USL – Upper Specification Limit The Definition of Quality “The customer doesn’t see the mean of your process, he only sees the variability around that target that you have not removed.” - Jack Welch, Retired CEO of General Electric The Definition of Quality Why did the Japanese supplier do this (reduce variability)? To reduce costs and improve customer perception of the product This reinforces that quality is truly inversely proportional to variability! A Brief History of Quality A Brief History of Quality Lean six sigma Total quality TRIZ / axiomatic management BPM Statistical engineering Zero defects Control charts Robust engineering Design of Poka yoke Standardization of experiments Lean production parts Acceptance ISO / MBNQ Division of labor sampling Specialization of labor www Scientific Post-WW management Assembly line Economy of motions World wars Industrial revolution Pre- Industrial A Brief History of Quality Quality has always been an integral part of products and services. But our awareness of its importance and the introduction of formal methods for quality control and improvement have been an evolutionary development. 1900 Frederick Taylor introduced principles of scientific management as mass production industries began to develop 1924 Walter Shewhart of Bell Laboratories developed the statistical control chart, which is often considered as the formal beginning of statistical quality control Late 1920s Harold Dodge and Harry Romig developed statistically based acceptance sampling as an alternative to 100% inspection Mid 1930s Statistical quality control methods were widely used in Western Electric (manufacturing arm of Bell Laboratories) WW II Greatly expanded use and acceptance of statistical quality-control concepts in manufacturing industries 1950-1960s - Emergence of reliability engineering and the introduction of several important textbooks in statistical quality control - First introduction of designed experiments in the US Late 1970s Western companies discovered that their Japanese competitors had been systematically using DOE since the 1960s Quality Engineering Philosophies through the Ages “Design in Quality” “Plan in Quality” “Build in Quality” www “Inspect in Post-WW Quality” World wars Industrial revolution Pre- Industrial Management Aspects of Quality Effective management of quality requires the execution of three activities: 1) Quality Planning 2) Quality Assurance 3) Quality Control and Improvement 1) Quality Planning Involves the identification of the customers and their needs (often called the voice of the customer) By first determining the needs of its customers, businesses can be better situated to meet or exceed expectations Without a good strategic quality plan, an organization may face faulty designs, manufacturing defects, and customer complaints The dimensions of quality are an important part of this process 1) Quality Planning Dimensions of Quality Garvin’s 8 Dimensions of Quality: 1) Performance will the product do the intended job? 2) Reliability how often does it fail? 3) Durability how long does it last? 4) Serviceability how easy is it to fix? 5) Aesthetics what does it look like? 6) Features what else can it do? 7) Reputation what is the perception of the product/service? 8) Conformance is it made as the designer intended? 1) Quality Planning Dimensions of Quality (Service) 1) Responsiveness how long did it take the service provider to reply to your request for service? 2) Professionalism the knowledge and skills of the service provider, relates to competency 3) Attentiveness caring and personalized attention from service provider 1) Quality Planning Listen to Define quality Set goals and voice of the and how to targets to customer measure meet 2) Quality Assurance The use of documentation to ensure quality levels are properly maintained and quality issues are properly resolved Documentation of a quality system involves four DOCUMENTATION components: 1) Policy – explains what is to be done and why Policy Procedures 2) Procedures – methods and personnel that implement the policy 3) Work instructions and specifications – specific instructions to carry out a task Work instructions & Records 4) Records – tracking of specific units or specifications batches of products/services (for customer complaints handling or corrective actions) 3) Quality Control and Improvement What is Quality Improvement? Quality improvement is the reduction of variability in processes and products Excessive variability in process performance often results in waste Therefore, an alternative definition for quality improvement is the reduction of waste caused by variability 3) Quality Control and Improvement Recall: US vs. Japanese Car Manufacturer Why did the Japanese supplier do this (reduce variability)? To reduce costs and improve customer perception of the product This reinforces that quality is truly inversely proportional to variability! How did the Japanese supplier do this? Through the systematic and effective application of statistical quality control methods 3) Quality Control and Improvement Quality control and improvement is the set of activities to ensure products and services are maintained and improved upon on a continuous basis Statistical techniques such as statistical process control and design of experiments are the major tools for quality control and improvement Quality improvement is often done on a project-by-project basis, with priority for ones with significant business impact and linked to overall business goals Statistical Methods in Quality Control & Improvement Statistical Design of Acceptance Process Experiments Sampling Control (SPC) (DOE) Quality Terminologies Quality engineering refers to the set of operational, managerial, and engineering activities that a company uses to ensure that the quality characteristics of a product are at required levels and that the variability around these desired levels is minimum Quality Terminologies Critical-to-Quality (CTQ) characteristics are the parameters/elements perceived to indicate quality for a particular product/service Types: Physical: length, weight, voltage, viscosity Sensory: taste, appearance, color Time Oriented: reliability, durability, serviceability We need to be able to measure something so we have a baseline and determine whether we are improving or not Quality Terminologies Attributes data refers to discrete data, often taking the form of counts Variables data refers to continuous measurements, such as length, voltage, and viscosity Quality Terminologies Specifications are the desired measurements of CTQ characteristics of components, subassemblies of the product, and the desired CTQ characteristic value of the final product Target value (or nominal value) is the desired value of the CTQ characteristic Upper specification limit (USL) is the max allowable value Lower specification limit (LSL) is the min allowable value E.g., Specification: The amount of sugar in a milk tea order should not be too much to oversweeten the drink and not too little to be unnoticeable Target value = 10g, USL = 12g, LSL = 8g Quality Terminologies Nonconforming products are products that fail to meet one or more of its specifications (i.e., one of the measurements of the CTQ characteristics is above its USL or below its LSL) A specific type of failure is called a nonconformity Note: a nonconforming product or a product with nonconformities is not necessarily unfit for use E.g., a cleanser may contain less active ingredients than the LSL, but can still perform well if a greater amount of the product is used Quality Terminologies Defective products are products with one or more defects A defect is a nonconformity serious enough to affect the safe and effective use of a product E.g., a paper cup produced too thin to be able to hold a reasonable amount of water Statistical Methods in Quality Control & Improvement Production Process Inputs and Outputs Statistical Methods in Quality Control & Improvement Control Chart One of the primary techniques of statistical process control (SPC) Control charts can detect the presence of unusual sources of variability, signaling that corrective action must be taken Useful in monitoring processes, reducing variability through elimination of assignable causes An on-line technique Statistical Methods in Quality Control & Improvement Design of Experiments (DOEs) Discovering key factors that influence performance (e.g. factorial designs, one- way ANOVA) Useful for process optimization Often conducted during development or early stages of a process An off-line technique Statistical Methods in Quality Control & Improvement Acceptance Sampling Closely connected with product inspection and testing An on-line technique for the inspection and classification of units randomly sampled from a larger population to evaluate the acceptability of the greater population With acceptance sampling, it can be determined whether to accept or reject the population (either for scrap or rework) Statistical Methods in Quality Control & Improvement Typical evolution of statistical methods in an organization Statistical Quality Control in a Nutshell Powerful collection of problem solving tools useful in: Achieving process stability Improving capability Through the reduction of variability Quality Gurus ______ __________ _____ Quality Gurus W. Edwards Deming Worked for Walter Shewhart at Western Electric Long career in US government Worked with defense contractors in WW2 for deploying statistical methods Consulted at various Japanese industries, leading many to adopt his quality philosophies Japanese Union of Scientists and Engineers created the Deming Prize for quality improvement Was an active consultant and speaker until the end of his career W. Edwards Deming 1900 –1994 Firmly believed the responsibility for quality rests with management Quality Gurus Deming’s 14 points 1) Create constancy of purpose towards improvement 2) Adopt a new philosophy that recognizes being in a new economic era 3) Cease reliance on mass inspection to “control” quality 4) End the practice of awarding business based on price alone and consider quality 5) Focus on continuous improvement 6) Institute training 7) Let leadership use modern supervision methods 8) Drive out fear (and foster openness) 9) Break down barriers between departments 10) Eliminate targets, slogans, and numerical goals for the workforce 11) Eliminate numerical quotas and work standards 12) Remove barriers that discourage employees from doing their jobs 13) Institute an ongoing program of education for all employees 14) Top management must advocate the previous 13 points Quality Gurus P-D-C-A Deming also promoted the Shewhart Cycle as a model to guide improvement Quality Gurus Joseph M. Juran One of the founding fathers of the field of quality-control and improvement Worked for Walter Shewhart at AT&T Bell Laboratories Played an important role in simplifying administrative and paperwork processes in a US government agency during WW2 Invited to speak to Japanese industry leaders as they began their transformation in 1950s Co-author of the Quality Control Handbook (a standard reference for quality methods and improvement since Joseph M. Juran 1904 –2008 1957) Emphasizes a more strategic and planning-oriented approach to quality than Deming Quality Gurus The Juran Trilogy 1) Planning – identifying customers and determining their needs; planning on a regular basis 2) Control – activities that ensure the product/service meets requirements 3) Improvement – aim to achieve a level of performance greater than the current level; done project-by-project and is either continuous/incremental improvement or a breakthrough improvement Quality Gurus Armand V. Feigenbaum Introduced the concept of company-wide quality control in his historic book, Total Quality Control Influenced early philosophy of quality management in Japan in the early 1950s Three-step approach to improving quality 1) Quality leadership 2) Quality technology 3) Organizational commitment Organizational structure and systems approach to improving quality Armand V. Feigenbaum The technical capability for quality control should be 1922 – 2014 concentrated in a specialized department Quality Gurus ✓ Quality is an essential, competitive weapon ✓ Management plays an important role in quality improvement ✓ Statistical methods are critical for “quality transformation” Outline Quality Management Strategies & Initiatives Total Quality Management Six Sigma, DFSS, Lean Systems Other Quality Management Initiatives Quality & Productivity Costs of Quality Total Quality Management (TQM) Implement and manage quality improvement activities organization-wide Quality is a shared responsibility that affects all aspects of the business Core principles: Customer focus Employee involvement Process-approach System integration Systematic approach Continuous improvement Facts-based decisions Communication ISO 9000 A set of international standards for quality systems developed by the International Standards Organization (ISO) Demonstrates a supplier’s ability to control its processes Heavy focus on documentation of the quality system Six Sigma Focus on reducing variability in key product quality characteristics to the level at which failure or defects are extremely unlikely Six Sigma Six Sigma A burger with 10 parts Is 99% of the time “good” for each part good enough?? Order one burger Family of four eating once a month For one whole year... Is 99% of the time “good” for each part good enough?? Order one burger P(good meal) = 0.9910 = 0.9044 Family of four eating once a month For one whole year... Is 99% of the time “good” for each part good enough?? Order one burger P(good meal) = 0.9910 = 0.9044 Family of four eating once a month P(good meal) = 0.90444 = 0.6690 For one whole year... Is 99% of the time “good” for each part good enough?? Order one burger P(good meal) = 0.9910 = 0.9044 Family of four eating once a month P(good meal) = 0.90444 = 0.6690 For one whole year P(good meal) = 0.669012... = 0.0080  99% Good (3.8σ) 99.99966% Good (6σ) Unsafe drinking water for Unsafe drinking water for one almost 15 minutes each day minute every seven months No electricity for almost seven One hour of no electricity hours each month every 34 years 200,000 wrong drug 68 wrong drug prescriptions each year prescriptions per year Two short or long landings at One short or long landing most major airports each day every five years 5,000 incorrect surgical 1.7 incorrect surgical operations per week operations per week Six Sigma (Evolved) Utilize specially trained individuals called “belts” to handle these projects Six sigma projects are typically 4 to 6 months in length and have high potential business impact Five-step problem-solving approach: DMAIC (Define, Measure, Analyze, Improve, Control) Six Sigma (Evolved) Generation I: defect elimination & basic variability reduction Generation II: Gen I + cost reduction Generation III: Gen II + value creation  Champions Business leaders with a conceptual understanding of six sigma Supports the team by removing obstacles to project completion Master Black Belts (MBBs) Six sigma experts with a thorough understanding of the methodology Mentors and coaches Black Belts Generally plays a strategic role in an organization, advising senior management on high impact improvement opportunities Structure of a six sigma project group  Black Belts (BBs) Leads cross-divisional improvement efforts Facilitates Green Belt and Yellow Belt trainings Advises MBBs and Champions on local- level improvements to support strategic initiatives Coaches Green Belts in completing local- level (departmental) improvements Structure of a six sigma project group  Green Belts Trained in fundamental six sigma concepts Can lead improvement teams in using some six sigma tools Aware of the full potential of six sigma methodology, so are able to engage BBs and MBBs in advanced tools to support efforts they are leading Leads local improvements in their area of expertise Generally do not have full-time six sigma responsibilities Structure of a six sigma project group  Yellow Belts Have a general understanding of six sigma principles Have no full-time six sigma responsibilities Ideal team members for improvement initiatives because of their understanding of six sigma Structure of a six sigma project group Six Sigma Design For Six Sigma (DFSS) and Lean Systems are two concepts often identified with six sigma Design for Six Sigma (DFSS) A structured and disciplined methodology for efficient commercialization of technology that results in new products, services, or processes Lean Systems Systems designed to eliminate waste or non-value-adding activities A process is value-adding if it: Brings a product/service closer to the final form Changes the form/fit/function Is an activity the customer is willing to pay for Otherwise, it is non-value-adding D efects O verproduction W waiting N on-utilized talent T ransportation I nventory M otion E xtra processing Other Quality Management Initiatives Just-In-Time (JIT) In-process inventory reduction, rapid set-up, and a pull-type production system Have just enough stock to produce what is needed when it is needed Poka-Yoke Mistake-proofing Quality and Productivity Quality and Productivity Ok! Quality and Productivity Fallout Ok! Quality and Productivity Fallout Rework Ok!  Quality and Productivity 100pcs 25% 40% Fallout Scrap Direct production cost = 20/unit Rework cost = 4/unit 60% 75% Rework Ok! Yield?  Quality and Productivity 100pcs 25% 40% Fallout Scrap Direct production cost = 20/unit Rework cost = 4/unit 60% 75% Rework Ok! Yield (incl. reworked units) = (100)(75%) + (100)(25%)(60%) = 90 good units Cost/good unit?  Quality and Productivity 100pcs 25% 40% Fallout Scrap Direct production cost = 20/unit Rework cost = 4/unit 60% 75% Rework Ok! Yield (incl. reworked units) = (100)(75%) + (100)(25%)(60%) = 90 good units Cost/good unit = [(20)(100) + (4)(100)(25%)(60%)] / 90 = 22.89 / good unit  Quality and Productivity 100pcs 5% 40% Fallout Scrap Direct production cost = 20/unit Rework cost = 4/unit 60% 95% Rework Ok! New Yield? New Cost/good unit?  Quality and Productivity 100pcs 5% 40% Fallout Scrap Direct production cost = 20/unit Rework cost = 4/unit 60% 95% Rework Ok! New Yield (incl. reworked units) = (100)(95%) + (100)(5%)(60%) = 98 good units New Cost/good unit = [(20)(100) + (4)(100)(5%)(60%)] / 98 = 20.53 / good unit  Quality and Productivity 100pcs 5% 40% Fallout Scrap Direct production cost = 20/unit Rework cost = 4/unit 60% 95% Rework Ok! New Yield (incl. reworked units) = (100)(95%) + (100)(5%)(60%) = 98 good units New Cost/good unit = [(20)(100) + (4)(100)(5%)(60%)] / 98 = 20.53 / good unit Yield: 90 → 98 (approx. 9% increase in yield) Cost/good unit: 22.89 → 20.53 (approx. 10% decrease in cost) Quality Costs Quality costs are categories of costs associated with producing, identifying, avoiding, and repairing products that do not meet requirements It is important to consider the cost of quality because: Products and services are growing increasingly complex Higher complexity → more quality costs Businesses are now more aware of life-cycle costs, including maintenance, spare parts, and field failures (i.e., failures resulting in products being returned to the seller) Quality engineers and managers need to effectively communicate quality issues to management Quality Costs Four types: 1) Prevention costs 2) Appraisal costs 3) Internal failure costs 4) External failure costs Quality Costs 1) Prevention Costs Costs associated with efforts in design and manufacturing directed towards the prevention of nonconformance “Make it right the first time” Examples o Quality planning and engineering – overall quality plan o New products review – bid proposals and other preproduction activities o Product/process design – costs related to design choices o Process control – techniques to monitor and bring a process into control (e.g., control charts) o Burn-in – testing of products under extreme operating conditions to detect early life field failures o Training (workers) – cost to train those directly involved in making the product o Quality data acquisition and analysis – set-up of a system to acquire data on process performance Quality Costs 2) Appraisal Costs Costs associated with measuring, evaluating, or auditing products, components, or purchased materials to ensure conformance Examples o Inspection and testing of incoming material – costs associated with inspecting and testing input materials (e.g., test equipment, salary of the workers specifically for inspection) o Product inspection and testing – costs associated with checking conformance throughout stages of production o Consumed materials/services – costs of materials and products consumed in destructive tests o Maintenance of test equipment – maintenance costs to ensure effectiveness of equipment used for testing Quality Costs 3) Internal Failure Costs Costs when products, components, materials, and services fail to meet quality requirements and discovered prior to delivery to the customer Examples o Scrap – loss of labor/material/overhead due to defective products that can’t be repaired/used o Rework – correcting units to meet specifications o Retest – reinspection and retesting of reworked products o Failure analysis – cost to determine product failures o Downtime – cost of idle production facilities due to nonconforming inputs o Yield losses – wastage due to variable/out-of-control processes o Downgrading/off-specing – price differential of good vs nonconforming units Quality Costs 4) External Failure Costs Costs when products, components, materials, and services fail to meet quality requirements and discovered after delivery to the customer Examples o Complaint adjustment – investigation and adjustment for complaints o Returned product/material – receipt/ handling of nonconforming products o Warranty charges – servicing customers under warranty o Failure analysis – cost to determine product failures o Liability costs – product liability litigation o Indirect costs – loss of business reputation, future business, and market share How much should quality costs be?! How much should quality costs be?! It depends… Analyzing Quality Costs Quality costs depend a lot on the type of organization/business and the success of their quality improvement effort For some, these are at about 4-5% of sales For others, these go as high as 35-40% of sales But in many cases, quality costs are higher than they should be… Analyzing Quality Costs Prevention Costs Cost of Attaining Quality Appraisal Costs Internal Failure Costs Cost of Poor Quality External Failure Costs The Cost of Poor Quality (COPQ) refer to the costs that would disappear if systems and processes were perfect Analyzing quality costs is useful because of the leverage effect Investment in prevention and appraisal is offset by reduction in COPQ Cost of Poor Quality Analyzing Quality Costs Let’s analyze COPQ in relation to sigma capability Suppose we have a ± 3 sigma process within specification (about 2,700 defects per million units) Assume a cost of Php 1,000 per defect COPQ = 2,700 x 1,000 = Php 2,700,000 for this 3 sigma process Analyzing Quality Costs Now what happens if the company improves its process from a 3 sigma level? refers to incremental savings vs previous sigma level Analyzing Quality Costs Now what happens if the company improves its process from a 3 sigma level? refers to incremental savings vs previous sigma level We can see that in this example, we have diminishing returns Sometimes the additional cost from trying to improve the process may not be justified by the benefits gained Economic Balance of Quality Costs At any point in time, Total (quality) costs = costs due to conformance + costs due to nonconformance (Cost of Attaining Quality) (Cost of Poor Quality) Economic Balance of Quality Costs At any point in time, Total (quality) costs = costs due to conformance + costs due to nonconformance (Cost of Attaining Quality) (Cost of Poor Quality) You want to be here! Economic Balance of Quality Costs Economic Balance of Quality Costs You want to be here! Product Life-Cycle and Quality Costs It also matters when in the life-cycle the quality costs are incurred Overall, we want to ensure that benefit (impact) outweighs the cost Product Life-Cycle and Quality Costs Cost increases as we go further into the process because more work is needed to affect the product as compared to doing this during design stages Generally, the turning point is around the delivery to the customer Beyond this point, costs sharply increase because of the “hidden” quality costs Product Life-Cycle and Quality Costs Before delivery to the customer, impact is still relatively high because we can still do something about the product before it reaches the customer Once delivered, the business can only do “damage control” with the dissatisfied customers We usually want to avoid significant COPQ because of generally higher costs Summary (Lec 1 & 2) Quality is a multi-faceted entity, incorporating several dimensions Recognizing and selecting which dimensions to compete on is a critical part of strategic management of quality Management must recognize that quality improvement must be a total company-wide activity wherein every organizational unit must participate It is the responsibility of management to obtain every unit’s participation in the quality improvement effort Strategic management of quality must involve the three components of Quality Planning, Quality Assurance, and Quality Control and Improvement The statistical understanding, tools, and methods are essential to quality control and improvement is critical to successful implementation Outline DMAIC Overview 5 Phases of DMAIC Define Measure Analyze Improve Control Examples Project Initiation and Selection Recall: Six Sigma Six Sigma focuses on reducing process variation and enhancing process control Utilizes a five-step problem-solving approach: DMAIC (Define, Measure, Analyze, Improve, Control) Lean + Six Sigma = Lean Six Sigma Lean six sigma is the combination of two powerful quality methodologies: lean and six sigma A fact-based, data-driven philosophy of improvement that values defect prevention over defect detection. It drives customer satisfaction and bottom-line results by reducing variation, waste, and cycle time, while promoting the use of work standardization and flow, thereby creating competitive advantage. (ASQ) LEAN SIX SIGMA Uses visual techniques Uses statistical Systematic approach to techniques reduce/eliminate Data-driven methodology activities that do not add to continuous improve value to the process process to be Emphasis on waste 99.999996% defect-free (muda) reduction Emphasis on variability reduction DMAIC Overview DMAIC is a methodology for improving quality via a five-step/phase approach that concentrates on the process that created the output (instead of focusing on the output) It can be used to: Complete projects by implementing solutions that solve root causes of quality and process problems Establish best practices to ensure solutions are permanent and replicable Improve PFQT – Productivity (how many), Financial (how much money), Quality (how well), and Time (how fast)  DMAIC Overview Define and scope the problem DEFINE Control performance / Measure current sustain improvement performance CONTROL MEASURE Improve performance by Analyze to isolate root causes a solution IMPROVE ANALYZE DMAIC Overview When do we use DMAIC? It should be used when a product/service is not meeting customer specifications or not performing adequately It is best used when the problem is complex or the risk is high. The discipline and structure prevents teams from skipping necessary steps to solve the problem, increasing the chances of success of the project DMAIC Overview Sample problem 1: In 2020, it took on average 8 hours for hospital beds to be available after a discharge order was written DMAIC project: Reduce the time between when a discharge order is written for a patient and when that hospital bed becomes available again Sample problem 2: The ISP experienced a 20% churn/attrition rate in 2020 DMAIC project: Prevent customer churn/attrition Note: Recall IE 33 on how to define a problem (a problem well-defined is a problem half- solved!) 5 Phases of DMAIC 5 Phases of DMAIC Before proceeding to the next phase, teams must pass through a “tollgate” DEFINE At a tollgate: Project team presents their work to managers and CONTROL MEASURE process owners Review to ensure project is on-track Opportunity to give guidance on use of specific tools IMPROVE ANALYZE or other info about the problem Organizational problems, other barriers to success, and strategies to deal with these are identified  5 Phases of DMAIC - Tools DEFINE MEASURE ANALYZE IMPROVE CONTROL Project Charter Operational Pareto Charts Brainstorming Control Charts Stakeholder Definitions Fishbone Solution Standard Analysis Data Collection Diagrams Selection Matrix Operating Communication Plan Brainstorming “To-Be” Process Procedures Plan Graphical (5 Why’s) Maps (SOPs) SIPOC Map Analysis (Pareto Non-Value- Piloting and Communication Voice of Chart, Added Analysis Simulation Plan Customer Histogram, Box Implementation Plot, Run Chart) Plan Detailed “As-Is” Training Plan Process Maps Process Control Plans Example: Improving service quality in a bank In Define and Measure, several CTQ characteristics were identified as needing to be improved: 1) Speed of service 2) Consistent service 3) An easy-to-use process 4) A pleasant environment 5) Knowledgeable staff The project team focused on two areas of improvement: 1) Improved teller and customer work stations 2) Training for the staff Example: Improving service quality in a bank In Analyze and Improve, the team decided to use a designed experiment to investigate how the chosen factors affect the CTQs Four branches were used to conduct actual experiments with different combinations of work stations and training programs over 30 days. Response data was collected through customer satisfaction surveys. Example: Improving service quality in a bank Experiment results showed a positive difference in favor of new work stations and a new training program Implementation of the new work stations and training program was expected to significantly improve customer satisfaction across all bank branches 1) Define Phase Objective: identify the project opportunity and validate that it presents a legitimate impact or potential for major improvements Questions answered: 1) What is the problem? 2) What is the goal/objective? 3) Who are the customers? 4) What are the critical stages of the process? 1) Define Phase Define the customers Who is the target audience? What are their needs? Their expectations? Define the project team members Who is involved in the improvement efforts? Define the project boundaries What processes are involved (the start and the end)? Define the project goal Example: reduce customer churn Define the process to be improved Suppliers, inputs, process, outputs, customers Define the problem 1) Define Phase Of the many tools that can be used in this step, we focus on these two: a) Project Charter b) SIPOC Diagram 1) Define Phase a) Project Charter The project charter is a good tool to define details of the project. Contents include: Project and scope Timeline (start and end date for each phase) Primary and secondary metrics to measure success Potential benefit to the customer Potential financial benefits to the organization Milestones to be accomplished Team members and their roles Resources needed for the project CTQs impacted by the project 1) Define Phase a) Project Charter – Basic Elements 1) Business case – why is the project important? 2) Problem/Opportunity statement – define the issue being resolved 3) CTQs – specify the problem from a customer perspective (may not be known until the Measure Phase) 4) Goal statement – describe the objective of the project 5) Project scope – what is and isn’t included? may also include constraints 6) Project plan – summarize milestone steps and provisional dates to the goal 7) Team structure – identify who is involved and their responsibilities Sample Project Charter CTQs: customer resolution cycle time, customer satisfaction 1) Define Phase b) SIPOC Diagram Graphic aids are useful tools in this phase The SIPOC diagram gives a simple overview of a process This is useful for understanding and visualizing basic process elements It also tells us where a process starts and ends 1) Define Phase b) SIPOC Diagram Suppliers – provides information, material, or other items worked on in the process Input – the information/material provided Process – the sequence of steps performed to do the work Output – the product, service, or information sent to the customer Customer – either the external customer or the next step in the business (internal customer) Sample SIPOC Diagram Sample SIPOC Diagram 1) Define Phase Tollgate questions Does the problem statement focus on symptoms, and not on possible causes or solutions? Are all the key stakeholders identified? What evidence is there to confirm the value opportunity represented by this project? Has the scope of the project been verified to ensure that it is neither too small nor too large? Has a SIPOC diagram or other high-level process map been completed? Have any obvious barriers or obstacles to successful completion of the project been ignored? Is the team’s action plan for the measure step of DMAIC reasonable? 2) Measure Phase Objective: evaluate and understand the current state of the process or quantify the current performance of the process (baseline) Questions answered: What is the current performance (baseline)? What is the defect rate? 2) Measure Phase Know the data What is available, where to source it, and develop a plan to gather it Summarize the data Use graphical tools Describe the problem with the data Tell the story using data Example: Problem is higher customer churn With data: Last month, 20% of the company’s customers unsubscribed 2) Measure Phase Many tools are useful for describing data. We only discuss a few here but your task is to identify the most appropriate tool to use. a) Baseline performance vs. Goal performance b) Benchmarking  2) Measure Phase c) Value Stream Map (VSM) Waste: waiting time Ideal Current performance 2) Measure Phase Tollgate questions Is there a comprehensive process flow chart or VSM? And are all major process steps and activities identified, along with suppliers and customers? And If appropriate, are areas where queues and work-in-process accumulate identified and queue lengths, waiting times, and work-in-progress levels reported? Is there a list of key process input variables (KPIVs) and key process output variables (KPOVs), along with identification of how the KPOVs relate to customer satisfaction or the customers CTQs? Is the measurement systems capability documented? Any assumptions that were made during data collection must be noted. Can the team answer questions such as, “Where did that data came from?”, “How did you decide what data to collect?”, “How valid is your measurement system?”, and “Did you collect enough data to provide a reasonable picture of process performance?” 3) Analyze Phase Objective: use data from Measure phase to determine cause-and-effect relationships in the process and understand the sources of variability Questions answered: 1) What are the sources of variation? 2) What are the root causes of defects? 3) Analyze Phase Determine the root cause of variation and poor performance Verify the root cause of variation Prioritize opportunities to improve (e.g., determine which of the problems causing variation should be addressed) 3) Analyze Phase Y = f(X) *List down the potential X’s which may be the cause(s) of the Y’s 3) Analyze Phase Many tools can be used to determine root causes. The task is to identify the appropriate tools out of all that are available. a) Stream Diagnostic Chart b) 5 Whys Helps visually map which causes may be A simple but effective tool for exploring cause- attributed to which effects and-effect relationships Helpful for prioritization 3) Analyze Phase Other Tools: Hypothesis testing Fishbone diagram (Ishikawa diagram) Confidence intervals Regression analysis Control charts (to be discussed in IE 135) Note: some tools are also applicable in other phases of DMAIC, depending on the purpose of their use 3) Analyze Phase Tollgate questions What opportunities are going to be targeted for investigation in the Improve phase? What data and analysis supports that investigating the targeted opportunities and improving/eliminating them will have the desired outcome in the KPOVs and customer CTQs that were the original focus of the project? Are there other opportunities that are not going to be further evaluated? If so, why not? Is the project still on track with respect to time and anticipated outcomes? Are any additional resources required at this time? 4) Improve Phase Objective: develop and evaluate the solution/s to address the problem Questions answered: How do we change the process? How do we verify that the changes will improve the process? 4) Improve Phase Directly address the cause Brainstorm potential solutions Prioritize solutions based on the VOC Test if solutions can solve the problem (e.g., pilot study) 4) Improve Phase There is also a selection of tools available from which we must pick what is most appropriate for our needs. a) Best Practices Look into what has been tried and tested 4) Improve Phase b) Brainstorming Other Tools: Failure Mode and Effects Analysis (FMEA) Pilot Testing Jointly come up with many ideas 4) Improve Phase Tollgate questions Is there adequate documentation of how the solution was obtained? Is there documentation on the alternative solutions considered? Are there complete results of the pilot test, including data displays, analysis, experiments, and simulation analyses? Are there plans to implement the pilot test results on a full-scale basis? These should include dealing with any regulatory requirements, personnel concerns, or impact on other business standard practices. Has there been an analysis of any risks of implementing the solution, and appropriate risk- management plans? 5) Control Phase Objective: complete all remaining work on the project and hand off the improved process to the process owner, along with a process control plan and other necessary procedures to ensure project gains are institutionalized Questions answered: Are the improvements consistent over time? How do we maintain the improvements into the future? 5) Control Phase Standardize and sustain the solutions over time Institutionalize the improvements through modification of systems and structures (staffing, training, incentives, documentation) Define roles of every relevant member in maintaining the “new” process 5) Control Phase Put in place a: Transition plan – to ensure a smooth transition to the improved process Process control plan – to monitor the “new” process, documenting elements of quality control to ensure set quality standards are met Response plan – how to respond when nonconformities are detected 5) Control Phase a) Response Plan b) Control Charts What to do in case event Z happens For studying the behavior of a process over time 5) Control Phase Other Tools: Transition plan Training plan Failure Mode and Effects Analysis (FMEA) Process capability analysis (to be discussed in IE 135) 5) Control Phase Tollgate questions Is there data illustrating that before and after results are in line with the project charter available? Were the original objectives accomplished? Is the process control plan complete? Are procedures to monitor the process, such as control charts, in place? Is all essential documentation for the process owner complete? Is a summary of lessons learned from the project available? Has a list of opportunities that were not pursued in the project been prepared? (useful for future projects; it is important to maintain an inventory of good potential projects to keep the improvement process going) Has a list of opportunities to use the results of the project in other parts of the business been prepared? Which project(s) should we pursue?  Which project(s) should we pursue? “What are the top ten things we would like to fix in this organization?”  Which project(s) should we pursue? “What are the top ten things we would like to fix in this organization?” Where to look?  Which project(s) should we pursue? “What are the top ten things we would like to fix in this organization?” Where to look? Signs indicating the potential for improvement High correction rates and rework levels Long processing times Too many steps where things go back and forth Excessive delays between steps Excessive checking High levels of working/buffer inventory Processes where no standard way of doing things exists High volume of customer complaints Late deliveries to customers Example: Improving On-Time Delivery for a Machine Tool Manufacturer A key client of the company contacted them regarding their recent poor performance in terms of delivery times. In the current process, only 85% of deliveries were on-time instead of the ideal 100%. The customer was now requesting a penalty clause in their contract with the manufacturer to reduce the paid price for the tools purchased. This meant a significant loss to the business since this customer represented a large volume of their current business. A team was formed and the project was started. Example: Improving On-Time Delivery for a Machine Tool Manufacturer Define? Measure? Analyze? Improve? Control? Example: Improving On-Time Delivery for a Machine Tool Manufacturer Define: Objective is to achieve 100% on-time delivery Customers concerned with capability for on-time delivery (can jeopardize customer production), so a penalty clause included at cost to the manufacturer Potential savings to meet on-time delivery requirement approx. 300K per qtr Customer satisfaction is critical Example: Improving On-Time Delivery for a Machine Tool Manufacturer Measure: CTQ is to meet contractual lead for delivery (~ 8 weeks) Process map constructed for the existing process (from PO to shipment) Collect both historical data and additional data over a 2-month period Example: Improving On-Time Delivery for a Machine Tool Manufacturer Analyze: From data collected, problem areas identified were: 1) Supplier quality issues (causes delay in testing due to premature failure) 2) PO process delay (POs not promptly processed) 3) Delay in customer confirmation (complicates production scheduling) Example: Improving On-Time Delivery for a Machine Tool Manufacturer Improve: Corrective actions taken: 1) Supplier quality control and improvement (create internal checklist for their supplier on required testing prior to shipment) 2) Improve internal PO process (common email address established to receive all PO notifications helped to improve transparency of the queue; designate 3 people to manage this account instead of just 1 to process more quickly) Example: Improving On-Time Delivery for a Machine Tool Manufacturer Control: Revised the production tracking spreadsheet with firm milestone dates and provided a more visual format Instituted a bi-weekly updating procedure by the factory to reflect up-to-date information (so project engineer can better monitor process and take action accordingly should unplanned deviations occur) Result: Cost savings amounted to more than $300,000 per qtr Customer was satisfied and continued to remain confident in manufacturer’s capability and capacity Outline Describing Variation Causes of Variation Concepts of Statistical Control Introduction to Control Charts Recall: Quality Definitions 1 𝑄𝑢𝑎𝑙𝑖𝑡𝑦 ∝ 𝑉𝑎𝑟𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦 Quality Improvement Quality improvement is the reduction of variability in processes and products Excessive variability in process performance often results in waste Therefore, an alternative definition for quality improvement is the reduction of waste caused by variability Describing Variation Descriptive statistics is a simple yet effective tool to describe the variation in a process Objectives are to: Quantitatively express variation Model the probability distribution of a CTQ characteristic Descriptive Statistics Tools Stem-and-leaf plot Histogram Numerical summary of data Box plot Probability distributions Stem-and-leaf Plot A graphical method for summarizing and presenting data Suppose each data point is a number having at least 2 digits. One way is to use one or more leading digits as the stem and the remaining digits as the leaf Stem-and-leaf plots are useful when we are interested in the values of observations Stem-and-Leaf Plot Stem-and-leaf Plot The stem-and-leaf plot quickly provides useful information on: the shape of the data the spread (variability) of the data The central tendency (i.e., middle) of the data Histogram A more compact summary of data than the stem-and-leaf plot Ranges are divided into class intervals (also called cells or bins) with a defined upper and lower boundary where the data will be sorted and a count is made for each bin Some may prefer the use of histograms with the vertical scale normalized as relative frequency (i.e., y = bin frequency / total observations) Histogram Like the stem-and-leaf, the histogram quickly provides useful information on: the shape of the data the spread (variability) of the data The central tendency (i.e., middle) of the data Numerical Summary of Data Formula Description Sample Average of a data sample Mean A measure of central tendency Average of the squared deviations Sample from the mean Variance A measure of variation (for interval- ratio variables) The square root of sample variance Sample A measure of variation (for interval- Standard ratio variables Deviation Advantage vs. variance: expressed in terms of the data’s original units interval data – has an order (scale) and magnitude, but no absolute zero ratio data – same as interval data but accommodates an absolute zero Box Plot A graphical display that simultaneously displays several important features of data such as: central tendency spread departure from symmetry outliers Box plot of sales across different regions Comparative box plots of a quality index for products produced at 3 plants Probability Distribution A mathematical model relating the value of a variable with the probability of its occurrence in the population The two general types of probability distributions are discrete and continuous Probability Distribution A probability distribution is associated with a mean and variance Mean – center of mass of the distribution; a measure of central tendency Variance – variability of the distribution; as variability increases, variance increases Probability Distribution Some common distributions: Discrete Hypergeometric (x out of N items w/o replacement) Binomial (x out of n items w/ replacement) Poisson (x occurrences over a fixed interval) Pascal/Negative binomial (rth success in the xth trial) Continuous Normal Lognormal (natural log of x is normally distributed) Exponential (time until occurrence of some event) Gamma (sum of r IID exponential distributions; time until r occurrences) Weibull (generalization of exponential distribution; has shape & scale) Probability Distribution Example: A manufacturing process produces thousands of semiconductor chips per day. On average, 1% of these chips do not conform to specifications. Every hour, an inspector selects a random sample of 25 chips and classifies each chip in the sample as conforming or nonconforming. What is the random variable? What is its probability distribution? Probability Distribution Example: A manufacturing process produces thousands of semiconductor chips per day. On average, 1% of these chips do not conform to specifications. Every hour, an inspector selects a random sample of 25 chips and classifies each chip in the sample as conforming or nonconforming. What is the random variable? Number of non-conforming chips What is its probability distribution? Probability Distribution Example: A manufacturing process produces thousands of semiconductor chips per day. On average, 1% of these chips do not conform to specifications. Every hour, an inspector selects a random sample of 25 chips and classifies each chip in the sample as conforming or nonconforming. What is the random variable? Number of non-conforming chips What is its probability distribution? Binomial Distribution Probability Distribution Importance of Normal Curve in Sampling Theory Central Limit Theorem: Irrespective of the shape of the distribution of a population, the distribution of average values, x-bar, of subgroups of size n, drawn from that population will tend toward a normal distribution as the subgroup size n grows without bounds. Recall: Statistical Methods in Q C & I Statistical Design of Acceptance Process Control Experiments Sampling (SPC) (DOE) Recall: Statistical Methods in Q C & I Statistical Design of Acceptance Process Control Experiments Sampling (SPC) (DOE) Statistical Process Control Objectives: To quickly detect the occurrence of assignable causes of process shifts Elimination of variability in the process Basic SPC Tools: The Magnificent Seven 1) Histogram/stem-and-leaf plot 2) Check sheet 3) Pareto chart 4) Cause-and-effect diagram 5) Defect concentration diagram 6) Scatter plot 7) Control chart Widely used in both the Analyze and Control steps of DMAIC Causes of Variation Chance (common) causes are the causes attributable to inherent or natural variability Probabilistically predictable variation Cumulative effect of many small and essentially unavoidable causes Action needed: none! A process is in statistical control or in-control when only chance causes are present Causes of Variation Assignable (special) causes are the causes attributable to new, unanticipated, emergent or previously neglected phenomena within the system Typical causes: operator error, defective raw material, improperly adjusted or controlled machines Large effect compared to chance causes, usually representing an unacceptable level of performance Non-random variation, which can be reduced or eliminated by finding and addressing the cause Action needed: investigation and corrective action to find and eliminate assignable causes A process is said to be out-of-control if assignable causes are also present (in addition to chance causes) Statistical Control When only chance causes are present, a process is said to be in statistical control When assignable causes are also present (in addition to chance causes), a process is said to be out-of-control Note # 1: No process is truly stable forever Assignable causes eventually occur, so SPC is needed to quickly detect and act upon assignable causes and reduce variability Note # 2: “Control” ≠ “Conformance” Statistical control only means that a process is consistent and stable “Control” ≠ “Conformance” Control Limits Specification Limits Derived from natural process Determined externally by customers or variability or the natural tolerance internally by designers limits of a process “Voice of the process” “Voice of the customer” Appear on control charts Appear on histograms, box plots, probability charts Guide for process actions Separate good items from bad items What the process is doing What we want the process to do Control Charts An on-line process-monitoring technique A graphical display of a quality characteristic that has been measured or computed from a sample versus the sample number or time Parts of a control chart Center line (CL) Control limits Upper control limit (UCL) Lower control limit (LCL) Measurement of the quality characteristic (sample points are often connected by straight-line segments for easier visualization) Control Charts Control limits are computed in such a way that nearly all of the sample points will fall between them (only freak occurrences will not) When points fall out of the control limits, then we can say that something has occurred, or the process has shifted to make it out-of- control But this is not the only instance when we can conclude a process is out-of-control; a process may be within control limits but still be out of control if it is behaving in a particularly unlikely manner (e.g., 18 of the last 20 points plot above the centerline) Fundamental Uses of Control Charts Reduction of process variability Monitoring and surveillance of a process Estimation of product or process parameters Benefits of Using Control Charts: Effective in preventing nonconformities Provide diagnostic information Prevent unnecessary process adjustments Provide information about process capability Improve productivity Control Charts and Hypothesis Testing Control charts have a close connection to hypothesis testing HO: the process is in-control HA: the process is out-of-control The concept of Type I and Type II error applies in analyzing a control chart Type I error: conclude a process is out-of-control when it is really in-control Type II error: conclude a process is in-control when it is actually out-of-control General Model of Control Charts Let w = a sample statistic that measures some quality of interest L = “distance” of control limits from the CL expressed in stdev units UCL = w + L w CL =  w LCL = w − L w *usually, we use L = 3 (3-sigma) Steps to Applying Control Charts 1) Selection of response variable 2) Establishing parameters 3) Collection of data 4) Construction of control charts 5) Capability analysis (initial) 6) Monitoring and correction 7) Revision Example I want to determine the “quality” of IE 135 students. Example 1) Selection of response variable Exam performance to gauge “quality” 2) Establishing parameters First exam scores would be the initial gauge to check students’ foundation of IE 135 3) Collection of Data Administering the first exam Example 4) Construction of Control Charts Example 5) Capability analysis (initial) Example 6) Monitoring and correction 2 possible points: Exam, Students 7) Revision Examine exam results and questions Give another test to see if consistent Using Control Charts to Improve Processes Most processes are not operating in a state of statistical control Routine and attentive use of control charts helps identify the presence of any assignable causes (once eliminated, variability is reduced and the process is improved) Using Control Charts to Improve Processes An important part of the corrective action process of using control charts is use of the out-of-control- action plan (OCAP) Flowchart of activities following detection of an out-of-control signal Consists of: Checkpoints – potential assignable causes Terminators – actions taken to resolve the out-of-control condition by eliminating the assignable cause The OCAP should be as complete as possible in its checkpoints and terminators and are arranged in an order that facilitates process diagnostic activities Types of Control Charts 1) Variables control charts For continuous quality characteristics Usually involves measurements E.g., dimension, volume, weight 2) Attributes control charts For discrete quality characteristics Usually involves counted data or proportions E.g., # of defects, # of mistakes, % of non-conforming units Types of Control Charts Xbar-R chart Variables Xbar-s chart I-MR chart Control Charts p-chart Defectives np-chart Attributes c-chart Defects u-chart *Note: There are other types of variables and attributes control charts but we will generally focus on these ones. Designing Control Charts Control chart design includes the choice of: Control limits Sample size Sampling frequency For example, in this control chart, we specified a sample size of five measurements (each point is an average of five measurements), three sigma control limits, and the sampling frequency to be every hour. Choice of Control Limits Specifying the control limits is one of the critical decisions that must be made in designing a control chart Wider control limits → lower Type I error, but higher Type II error *if narrower control limits, the effect is reversed We use 3 sigma limits (i.e., L = 3) because it yields good results in practice and it is difficult to determine the true distribution of a process Choice of Sample Size and Sampling Frequency Sample size is generally chosen with consideration to the size of the shift we are trying to detect In general, larger samples will make it easier to detect small shifts in the process Ideally, we would like to take large samples at short intervals, however this is not economically feasible Usually, we either take small samples at short intervals or larger samples at longer intervals Industry practice tends to favor smaller, more frequent samples, particularly in high- volume manufacturing processes, or industries where many types of assignable causes can occur Choice of Sample Size and Sampling Frequency Average Run Length (ARL) is the average number of points that must be plotted before a point indicates an out-of-control condition It can be used to evaluate the decisions regarding sample size and sampling frequency ARL = 1/p where p = probability a point exceeds control limits For 3 sigma limits, p = 0.0027. Therefore, ARL = 1/0.0027 = 370. Therefore, even when in-control, an out-of-control signal is generated every 370 samples on average Choice of Sample Size and Sampling Frequency Average Time to Signal (ATS) is the average time it takes to detect a shift in the process ATS is occasionally used to express the performance of the control chart ATS = ARL x h where h corresponds to the fixed interval of time between two points Rational Subgrouping The concept of rational subgroups means that subgroups or samples should be selected such that if assignable causes are present, the chance for differences between subgroups is maximized while the chance for difference within subgroups is minimized Control charts provide a statistical test to determine if variation between subgroups is consistent with variations within subgroups Rational Subgrouping Time order is frequently a good basis for forming subgroups because it allows us to detect assignable causes occurring over time Order of production is one logical basis for subgrouping but other factors also influence the choice of subgroups Rational Subgrouping Two schemes proposed by Grant (1999): 1) Each subgroup is as homogenized as possible by taking samples of consecutive units Essentially gives a snapshot of the process at the point in time a sample is collected Gives the best estimate of σ if assignable causes can be eliminated Gives more sensitive measurement of shifts in process average 2) Each subgroup is representative of all units produced (in terms of quality level/process performance) since the last sample by taking a random sample of all outputs over the sampling interval Reflects changes when process shifts happen between subgroups Preferred when one purpose of control charting is to influence decisions on product rejection/acceptance on all units since the last sample Rational Subgrouping Considerable care must be taken in interpreting control charts in the 2nd scheme If process mean drifts over the sampling interval between samples, this may cause variability within samples to be large, resulting in wider control limits Rational Subgrouping Other bases for forming rational subgroups exist Proper selection of samples requires careful consideration of the process, with the objective of obtaining as much useful information as possible from the control chart analysis Example: We want to use a control chart for a process that utilizes several machines and pools their output into a common stream of output Rational Subgrouping Other bases for forming rational subgroups exist Proper selection of samples requires careful consideration of the process, with the objective of obtaining as much useful information as possible from the control chart analysis Example: We want to use a control chart for a process that utilizes several machines and pools their output into a common stream of output It’s difficult to monitor if any particular machine is out-of-control if we monitor the common stream, so a logical approach to rational subgrouping is to apply control charting to each individual machine It depends on the context of the problem being analyzed what is a good basis for establishing subgroupings Rational Subgrouping “The ultimate object is not only to detect trouble but also to find it, and such discovery naturally involves classification. The engineer who is successful in dividing his data initially into rational subgroups based upon rational hypotheses is therefore inherently better off in the long run than the one who is not thus successful.” Walter A. Shewhart Rational Subgrouping Objective Select subgroups in a way that minimizes the opportunity for variation within a subgroup while maximizing it across subgroups It is desirable for subgroups to be as small as possible Ideal subgroup size According to Shewhart, n = 4 In industry, common subgroup size = 5 Factors to consider Statistics (subgroup size of 4 is better than 2 or 3) Computation Cost of measurement Sensitivity to small variations (larger subgroup size → narrower control limits) Resources required Rational Subgrouping Sources of variability in rational subgroups 1) Cyclical/stream-to-stream variation Variation between consecutive units from a process in the same general time frame Variation among groups of units (e.g., batch to batch, lot to lot, machine to machine, operator to operator, line to line, plant to plant) 2) Temporal/time-to-time variation E.g., hour to hour, shift to shift, day to day, week to week 3) Positional/piece positional variation Variations within a single unit (e.g., left side vs. right side, top vs. bottom, center vs. edge, taper, out of round) Variations across a single unit containing many parts (e.g., wafer with many chips) Variations by location or position in a batch loading process (e.g., cavity to cavity position in a mold press) 4) Piece-to-piece variation 5) Error of measurement