Six Sigma Green Belt Exam Study NotesCpk- see Natural Tolerance •decreases with spec width Cp- see Natural Tolerance •decreases with spec width •Cp = 1 for centered process - natural tolerance =spec width Cause and Effect Diagram - Fishbone Diagrams - Ishikawa Diagrams •used to identify and organize potential root causes • problem solving analysis done by brainstorming •common categories - Measurement, Materials, People, Process, Equipment, Environment •ask “Why?” 3 times to get to root cause •have detailed problem statement at head of fish - “effect” •need corresponding process map •should fit on one 8-½ x 11 page •should have all 6 fishbones and at least 3 levels deep C-bar •C-bar is the average of all the subgroup C-values in C-Chart C – Chart - see Attribute Data Control Charts •Count chart •a specialized version of U chart •used to monitor the number of errors found - occurrences per unit -error count •number of units or subgroup size MUST remain constant Census •count or measurement of the entire population Continuous Data •measured – weigh, timed, •can be measured and broken down into smaller parts and still have meaning. Money, temperature andtime are continous.Volume (like volume of water or air) and size are continuous data. Control Charts •indicate stability over time Chart Rules – Control Charts •P-chart or NP-chart - count number of items in error or defectives •U-chart or C-chart - count number of errors or defectsin items Common causes - see variation control limits •Provide boundaries for a process running in control • based upon process data CTQ - Critical to Quality •key measurable characteristics of a product or process whose performance standards or specificationlimits must be met in order to satisfy the customer •CTQ’s represent the product or service characteristics that are defined by the customer (internal or external). They may include the upper and lower specification limits or any other factors related to the product or service. •the product or service characteristics that are defined by the customer as critical to their needs •what the customer expects of a product DATA Attribute Data Control Charts •Attribute data - qualitative data that can be counted for recording and analysis good/bad, yes/no •the average and dispersion are closely related; therefore, only one chart needed •P-Chart – proportions percent defective with variable or constant sample size • NP-chart– number of defectives with constant sample size •C-Chart – count of defects with constant sample size •U-Chart – defects per unit with variable or constant sample size Variable Data Control Charts •Variable data – measured - two types (Discrete) count data and (Continuous) data •X and MR – for financial, mtce costs, efficiency ratings, productivity – (usually 2 charts) •X-bar and Range •X-bar and S (standard deviation) – X-bar for sample average and “S” to monitor process dispersion Defect •non-conformities – a single characteristic not meeting defined requirements Defective •non-conformance – contains one or more defects DET - see FMEA Discrete Data •counted (usually in whole numbers) DMAIC •Define – project charter, problem statement, scope, goals, resources, financial, process maps •Measure – collect data, process maps, fishbone, Pareto, QFD, need accuracy & precision •Analyze - root cause is verified, hypothesis testing (verifying assumptions and predictions regarding therelationship between process inputs and the CTQ values) •Improve – brainstorming for ideas & solutions to problems identified in Analyze phase •Control – helps to reduce variation in the process and eliminate defects •Control - project responsibilities transition from process improvement team to operations team •Six Sigma Methodology used for process improvement DPMO (defects per million opportunities) •defect level for a process •number of defects divided by number of opportunities multiplied by one million DOE - Design of Experiments •math & statistics used in the design & analysis phase of an experiment to find best settings •optimize a process, reduce common cause variation, and maximize ROI •organized method for determining the relationship between factors (Xs) affecting a process and theoutput of that process (Y) •experimental methods used to quantify indeterminate measurements of factors and interactions betweenfactors statistically through observance of forced changes made methodically as directed bymathematically systematic tables Fish Bone - see Cause and Effect Diagram FMEA - Failure Mode and Effects Analysis •tool to identify where in the process if the source of failure •RPN - Risk Priority Number relative risk of a particular failure mode = SEV x OCC x DET •OCC or Likelihood of Occurrence rating - likelihood of the failure occurring •DET – detection rating measures likelihood current control system will detect cause or failure •SEV – severity rating how significant the impact of the effect is to the customer •vital x’s (root causes from low-level fishbones) go into potential cause column and can occur in morethan one process step Gauge R&R •Repeatability & Reproducibility Gauge Repeatability •how consistently same operator or measurement system measures same even over time Gauge Reproducibility •how consistently several operators or measurement systems measure same even over time Histogram •tool used in the Measure phase to illustrate shape, central tendency, and dispersion of data Leverage •applying proven methods to other projects via lessons learned - share ideas & best practices •reduces costs, increase efficiency, improve customer service •identifying “spin-off” projects that can benefit Master Attribute •standard or correct answer in an Attribute Gauge R & R study MR = Moving RangeMean •arithmetic average •the statistic most often used as the measure of central tendency or center of data •represented by Greek symbol “μ” (pronounced mu) •center line (process average) in a control chart between UCL and LCL Measurement systems •see Gauge Reproducibility and Gauge Reproducibility •Accuracy – how close the average are equal to the target •Precision – variation in repeated measurement of the same event •Linearity – performance over a range of events •Stability – performance over time Measurement system analysis •used to validate the measurement system natural tolerance • Natural tolerance is also called “6 sigma” because it is defined as 6 times the population standarddeviation of the individual observations. •3 sigma on each side of the process mean Cp = Process capability potential = spec width/natural tolerance = (U - L) / 6 sigma CpU = Upper capability index = (U - Mean) / 3 sigma CpL = Lower capability index = (Mean - L) / 3 sigma Cpk = Process capability index = Minimum of CpU and CpL Cp k = P r o c e s s c a p a b i l i t y i n d e x = Mi n i mu m o f Cp U a n d Cp L If the process capability potential, Cp, is greater than 1.0, the specification limits are wider than the naturaltolerance, and the process has the potential for meeting specifications if held in control at a mean of (U - L)/2. net profit •selling price minus costs NP-Bar •centerline or process average of all subgroups in NP-Chart NP - Chart - see Attribute Data Control Charts •a specialized version of the P-chart used when your sample size is constant •used to monitor the number rather than the proportion of items with a defined characteristic •subgroups MUST be equal size •used to track the actual number of defective items or the actual number of good items •average and dispersion are closely related; therefore, only one chart is required Pareto Chart •simple bar chart where the height of each bar represents the frequency of a given category •can be used to rank problems by their dollar costs rather than frequency • prioritize problems from those that happen most often to those that happen least often •cumulative percentage curve added to show ∑% of occurrences up to and including a given category •stratification - systematic subdivision of a problem into its subcomponents •identifies which opportunity or problem the team should focus on •categories are listed in order of frequency – higher on left •height of each bar represents the frequency of a given category •80-20 rule - 80% of occurrences of problems are accounted for by 20% of the categories of problems •developed by Italian economist named Vilfredo Pareto P-Chart - see Attribute Data Control Charts •monitor proportion or percentage •values plotted will always be a proportion and result in a number from zero to one •P-chart is required to monitor the process average and dispersion. With attribute data, the average anddispersion are closely related. Therefore, only one chart is needed. •sub-group sample sizes may vary. The control limits will vary but the centerline stays constant. •larger sub-group size has narrower limits because larger sample size reduces sampling error •With unequal subgroup sizes, p-bar is a weighted average of the individual sub-group proportions. Aweighted average just means the individual p’s don’t all carry the same weight in the calculation of p- bar. Problem statement •data-driven statement that does not include opinions on root causes or possible solutions Process capability •the extent to which a stable process is able to meet specifications •assessed using either continuous data or discrete data •when using attribute data should be expressed as percent, PPM, PPB defective, DPMO, etc. •assessed with a histogram with specification limits •capable process has a high Cp value and Cpk=Cp Process Capability Index: distance of mean to near spec Cpk = ―――――――――――― half the natural tolerance) Process Capability Index (if centered): voice of customer (spec width) Cp= ―――――――――――――― voice of process (natural tolerance or 6 sigma) Process out-of-control - see process shift process shift •a cluster of eight consecutive data points either all above or below the median •a point outside of control limits is indication that process may be shifting • process shift makes it inappropriate to calculate the overall average (or standard deviation) of the data Process maps •shows the inter-relationships of the steps in a process •used to discipline teams to produce solutions that are definable, repeatable, predictable and measurable •walk the process •clearly define the boundaries of the process •should include data, sigma level, COPQ, defect rate, flow rate •“as is" •include rework loops •oval – starting or stopping point •rectangle – process step or action •diamond - decision projects selecting potential projects consider - resource availability, reward, complexity, risk Project Charter •set expectations and obtain buy-in on scope, goal, and resources •accelerate the acquisition of resources •avoid scope creep •documentation •easy and effective means to document a Six Sigma project Project selection •considerations = Complexity, Risk, Reward, Resource availability Quality Function Deployment - QFD •tool used to analyze customer requirements R = RangeRoot Causes •often found in low-level fishbones during analyze phase •easier to find the root cause of a problem that is detected as it is happening •see Cause and Effect Diagram ROI = Return On Investment •for Six Sigma project is calculated by dividing the project savings by the project cost •used to measure the impact of a Six Sigma project on business results •Reduced operating costs •Increase in operating efficiencies •Improved morale •Communicating project savings •Sharing ideas and best practices •Identifying “spin-off” projects RPN – see FMEA S = Standard Deviation - see standard deviation S-Chart - see Variable Data Control Charts •to monitor process dispersion Sample •subset of the population •every element in a sample is also an element of the population •Stratified sampling – grouping members into similar subgroups before sampling Sample Mean •used to estimate the population mean •sample = subset of the population Savings •soft = non-tangible – time, customer satisfaction, morale •hard = money, cost, can be counted, direct impact upon the company's bottom line Scatter Diagram •shows the type of correlation between two variables •strength of the relationship between two variables is determined visually by the tightness of the cluster of points on the scatter diagram around the line of best fit drawn through the points •extrapolation is used to predict a value outside the range of the data plotted Scope Creep •Tendency for project to expand scope •limited by clearly defining boundaries SEV - see FMEA Sigma - see standard deviation SIRPORC Suppliers, Inputs, Requirements, Process, Outputs, Requirements and Customers •the system view of a process Six Sigma - ∂ •a commitment to your customers. •a method that uses best management ideas and practices for flexible system for process improvement •a means to stretch your thinking with respect to quality and customer satisfaction •customer focused •fact-based strategy focused on process improvement, variation reduction and defect elimination •uses two types of data - continuous and discrete Solution design matrix •used to organize alternative solutions Spec width = USL – LSLSpecial causes - see variation Specification Limits •used to determine if a product meets customer requirements Standard Deviation = sigma •measures dispersion from the mean – shows on average how far the values are from the mean •“s” represents standard deviation of a sample •sigma or Standard Deviation is used in combination with X Bar to describe the "Normal Distribution •To find six sigma, calculate sigma, multiply by 6, and add or subtract the result to the calculated mean. •68.27% of normal population lies within +/- one sigma from its average (mean) μ •95.45% of normal population lies within +/- two sigma’s from its average (mean) μ •99.73% of normal population lies within +/- three sigma’s from its average (mean) μ Sigma, (Standard Deviation), Formula Statistics •Uses Qualitative and Quantitative data types •Systematic Sampling - uses a rule or pattern to select elements from the population to form the sample •Qualitative = discrete data – counted , Not measured •Quantitative data - continuous data - different depending on types of questions X-bar Chart - see Variable Data Control Charts •used to monitor central tendency X-bar and S Chart - see Variable Data Control Charts __ X-bar = X •mean or average of sample •typically charted on a line control chart with the center line being X Double Bar, (an average of theaverages), and upper control limits and lower control limits •We use averages because they are more susceptible to change than single values. XmR Charts - see Variable Data Control Charts •control chart which uses a moving range. Typically two but can have a larger range •usually used when one measurement is available for each subgroup Upper Control Limit - UCL •control limit for points above the central line in a control chart U - Chart - see Attribute Data Control Charts •a graph of the number of errors per unit - - error rate •unit may be time, area, machines, or length •value of U could be a number greater than 1 •equal sample or subgroup size is NOT a requirement •used to track the number of occurrences of some event per unit •average and dispersion are closely related. Therefore, only ONE chart is needed •larger subgroup size = narrower limits (larger sample size reduces sampling error) Variable •a characteristic or property of an individual element in a population or sample Variation •Common Cause - causes of variation that are inherent in a process over time. They affect every outcome •Common cause – variation inside control limits - do NOT adjust process •Special Cause - relatively large, unusual variation usually comes from outside the process Z value •Z value is a data point's position between the mean and another location (usually mean) as measured bythe number of standard deviations. •Z is a measure of process capability and corresponds to the process sigma value that is reported by the businesses. For example, a 3 sigma process means that three standard deviations lie between the meanand the nearest specification limit. Three is the Z value. COST Appraisal costs •inspection costs incurred to identify defective products before the products are shipped to customers •Test and inspection of incoming materials •Test and inspection of in-process goods •Final product testing and inspection •Supplies used in testing and inspection •Supervision of testing and inspection activities •Depreciation & maintenance of test equipment •field testing and appraisal at customer site COPQ (Cost Of Poor Quality) •rework loop cost = (Defect rate) x (Volume) x (Cost of rework per unit) • penalty from not performing work correctly the first time or not meeting customer’s expectation •cost categories = appraisal, internal failure, prevention, external •most often calculated in the design stage of the Six Sigma Methodology Entitlement cost •cost of doing the right thing right the first time Internal failure Costs •Internal failure costs result from identification of defects before shipping to customers •Costs include scrap, rejected products,reworkingof defective units, and downtime External Failure Costs •defective product is delivered to customer •costs include warranty, repairs and replacements, product recalls, liability arising from legal actionsagainst a company, and lost sales arising from a reputation for poor quality Prevention Costs •Prevention costs support activities whose purpose is to reduce the number of defects. •Examples - statistical process control, quality engineering, training, and tools Sigma to DPMO to Yield to Cpk Table Sigma DPMO Yield Cpk 1.50 500,000 50% 0.50 3.00 66,800 93.32% 1.00 3.50 22,700 97.73% 1.17 4.00 6,210 99.38% 1.33 4.50 1,350 99.87% 1.50 5.00 230 99.98% 1.67 6.00 3.4 100.00% 2.00 Assumptions No analysis would be complete without properly noting the assumptions made. In the above table, we haveassumed that the standard sigma shift of 1.5is appropriate, the data is normally distributed, and the process isstable