Report

What is Six Sigma? It is a business process that allows companies to drastically improve their bottom line by designing and monitoring everyday business activities in ways that minimize waste and resources while increasing customer satisfaction. Mikel Harry, Richard Schroeder What Six Sigma Can Do For Your Company? Sigma level 4.8 6 4.7 5 MAIC D 5 5.1 2 3 F 4 S 3 S 3 Average company 2 0 1 years of implementation What Six Sigma Can Do For Your Company? THE COST OF QUALITY SIGMA LEVEL DEFECTS PER MILLION OPPORTUNITIES COST OF QUALITY 2 308,537 ( Noncompetitive companies ) 3 66,807 25-40% of sales 4 6,210 ( Industry average ) 15-25% of sales 5 233 5-15 of sales 6 3.4 ( World class ) < 1% of sales Each sigma shift provides a 10 percent net income improvement Not applicable The Cost of Quality (COQ) Traditional Cost of Poor Quality (COQ) 5-8% Inspection Warranty Rejects Rework ยอดขายลดลง งานเอกสารส่ งผิดที่ เวลาผลิตยาวนาน ค่าของเงินตามกาลเวลา ใช้ เวลา Set up นาน ค่าเร่ งการผลิต Lost Opportunity ความไม่ พอใจ ข้ อมูลที่ไม่ ถูกต้ อง แนวทางที่แตกต่ าง ในการทาธุรกิจ Note: % of sales ค่าบริการขนส่ ง 15-20% ค่าบัตรโทรศัพท์ การขนส่ งล่าช้ า ความปลอดภัย การติดตั้ง รายการสั่งซื้อมากเกินไป การสั่งวัตถุดบิ มาก เกินความจาเป็ น Less Obvious Cost of Quality (COQ) DMAIC : The Yellow Brick Road C O R E P H A S E Breakthrough & People DEFINE MEASURE ANALYZE >>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>> Champion Champion DEFINE - Definition of Opportunity 1.>>>>>>>>>>> Project Definition 2. Determine Champion Impact & Priority 3. Collect Baseliine Metric Data Definition of 4. Savings/Cost Opportunity Assessment 1. Project Definition 5. Establish 2. Determine Planned Impact & Priority Timeline 3. Collect Baseliine 6. Search Library Metric Data 7. Identify Project 4. Savings/Cost Authority Assessment 1. Problem 5. Establish Statement Planned 2. Goals/Objectives Timeline 3. Projected 6. Search Library Business 7. Identify Project Benefits Authority 4. Financial Value 1. Problem 5. Key Metrics Statement 6. Team 2. Goals/Objectives Assignment 3. Projected Business P1 (not validated) Benefits IMPROVE >>>>>>>>>>>> CONTROL- >>>>>>>>>>>>>> >>>>>>>>>>>>> Black Belt Assess the Current Process Blackbelts IMPROVE - Confirm f(x) for Y MEASURE ANALYZE 1.>>>>>>>>>>>>>>> Map the Process 1.>>>>>>>>>>>>> Determine the Vital 2. Determine the Baseline 3. Prioritize the Inputs to Assess 4. Assess the Assess the Current Process Measurement System 5. Capability Assessment 1. Map the Process 6. Short Term 2. Determine the Baseline 7. Long Term 3. Prioritize the Inputs to 8. Determine Entitlement Assess 9. Process Improvement 4. Assess the 10. Financial Savings Measurement System 5. Capability Assessment 1. Macro / Micro Process 6. Short Term Charts 7. Long Term 2. Rolling Throughput 8. Determine Entitlement Yield 9. Process Improvement 3. Fishbone, Cause Effect 10. Financial Savings Matrix 4. GR&R Study 1. Macro / Micro Process 5. Establish Sigma Score Charts 6. Apply ‘Shift & Drift’ 2. Rolling Throughput 7. Baseline vs Entitlement Yield 8. Translate to $$$ 3. Fishbone, Cause Effect P1 (validated) Matrix P5 Reviewed Variables Affecting Black the Response f(x) = Y Optimize f(x) for Y 1.>>>>>>>>>>>> Determine the Best BeltCombination of ‘Xs’ for Producing the Best ‘Y’ REALIZATION Financial Rep & Process Owner Finance Rep.& Process Owner 1.>>>>>>>>>>>>>> Establish Controls for 1.>>>>>>>>>>>>> Financial Maintain Improvements CONTROL- Sustain the BenefitREALIZATION 2. KPIVs and their Assessment and & Financial Rep ‘settings’ Input Actual Process Owner 3. Establish Reaction Savings Plans 2. Functional Confirm f(x) for Y Optimize f(x) for Y Maintain Improvements Sustain the Benefit 2. Confirm Manager/Process Relationships and Owner – Monitor 1. Determine the Vital 1. Determine the Best 1. Establish Controls for 1. Financial Establish the KPIV 3. Control/Implementa Variables Affecting Combination of ‘Xs’ 2. KPIVs and their Assessment and tion the Response for Producing the ‘settings’ Input Actual f(x) = Y Best ‘Y’ 3. Establish Reaction Savings Plans 2. Functional 2. Confirm Manager/Process Relationships and Owner – Monitor 1. Multi-Vari Studies Design of Experiments 1. Process Control Plan 1. Monthly Benefit Establish the KPIV 3. Control/Implementa 2. Correlation Analysis 1. Full Factorial 2. SPC Charting Update tion 3. Regression Analysis 2. Fractional Factorial x-Bar & R Single / Multiple 3. Blocking Pre-Control Experiments 4. Hypothesis Testing Etc 4. Custom Methods Mean Testing (t, Z) 3. Gauge Control Plans 5. RSM Variation (Std Multi-Vari Studies 1. Design of Experiments 1. Process Control Plan 1. Monthly Benefit Dev)(F,etc) Analysis 1. Full Factorial 2. Correlation 2. SPC Charting Update 3. ANOVA Regression Analysis 2. Fractional Factorial x-Bar & R Single / Multiple 3. Blocking Pre-Control Experiments 4. Hypothesis Testing Etc P5 Reviewed P5 P5 Reviewed 4.Reviewed Custom Methods Mean Testing (t, Z) 3. Gauge Control Plans P8 (Sign Off) Define What is my biggest problem? Customer complaints Low performance metrics Too much time consumed What needs to improve? Big budget items Poor performance Where are there opportunities to improve? How do I affect corporate and business group objectives? What’s in my budget? Define : The Project Projects DIRECTLY tie to department and/or business unit objectives Projects are suitable in scope BBs are “fit” to the project Champions own and support project selection Define : The Defect High Defect Rates Rework Low Yields Customer Complaints Excessive Cycle Time Excessive Test and Inspection Excessive Machine Down Time Constrained Capacity with High High Maintenance Costs High Consumables Usage anticipated Capital Expenditures Bottlenecks Define : The Chronic Problem Special Cause ( ปัญหานาน ๆ ครั้ง ) Reject Rate ปัญหาฝังแน่ น (Chronic) Optimum Level Time Define : The Persistent Problem 25 14 12 20 10 15 8 6 10 4 5 2 0 0 WW01 WW02 WW03 WW04 WW05 WW06 WW07 WW08 WW09 WW10 WW11 WW01 WW12 WW02 WW03 WW04 WW05 WW06 WW07 WW08 WW09 WW10 WW11 WW12 WW07 WW08 WW09 WW10 WW11 WW12 Is process in control? 40 14 35 12 30 10 25 8 20 6 15 4 10 2 5 0 0 WW01 WW02 WW03 WW04 WW05 WW06 WW07 WW08 WW09 WW10 WW11 WW12 WW01 WW02 WW03 WW04 WW05 WW06 Define : Refine The Defect Assembly Yield Loss % Yield Loss Refined Defect = a1 a1 PSA a2 RSA a3 Gram Load a4 Bent Gimbal KPOV a5 Solder Defect a6 Contam a7 Damper Defect MAIC --> Identify Leveraged KPIV’s Outputs Tools Process Map 30 - 50 C&E Matrix and FMEA Inputs Variables Potential Key Process Gage R&R, Capability Measure Multi-Vari Studies, Correlations T-Test, ANOM, ANOVA Analyze 10 - 15 8 - 10 Input Variables (KPIVs) KPIVs Screening DOE’s DOE’s, RSM Improve 4-8 Optimized KPIVs 3-6 Key Leverage KPIVs Quality Systems SPC, Control Plans Control Measure The Measure phase serves to validate the problem, translate the practical to statistical problem and to begin the search for root causes Measure : Tools To validate the problem Measurement System Analysis To translate practical to statistical problem Process Capability Analysis To search for the root cause Process Map Cause and Effect Analysis Failure Mode and Effect Analysis Work shop #1: • Our products are the distance resulting from the Catapult. • Product spec are +/- 4 Cm. for both X and Y axis • Shoot the ball for at least 30 trials , then collect yield • Prepare to report your result. Measure : Measurement System Analysis Objectives: Validate the Measurement / Inspection System Quantify the effect of the Measurement System variability on the process variability Measure : Measurement System Analysis Attribute GR&R : Purpose To determine if inspectors across all shifts, machines, lines, etc… use the same criteria to discriminate “good” from “bad” To quantify the ability of inspectors or gages to accurately repeat their inspection decisions To identify how well inspectors/gages conform to a known master (possibly defined by the customer) which includes: How often operators decide to over reject How often operators decide to over accept Measure : Measurement System Analysis Measure : Measurement System Analysis % Appraiser Score •% REPEATIBILITY OF OPERATOR # 1 = 16/20 = 80% •% REPEATIBILITY OF OPERATOR # 2 = 13/20 = 65% •% REPEATIBILITY OF OPERATOR # 3 = 20/20 = 100% Measure : Measurement System Analysis % Attribute Score •% UNBIAS OF OPERATOR # 1 = 12/20 = 60% •% UNBIAS OF OPERATOR # 2 = 12/20 = 60% •% UNBIAS OF OPERATOR # 3 = 17/20 = 85% % Screen Effective Score •% REPEATABILITY OF INSPECTION = 11/20 = 55 % % Attribute Screen Effective Score •% UNBIAS OF INSPECTION 50 % = 10/20 = 50% Measure : Measurement System Analysis Variable GR&R : Purpose Study of your measurement system will reveal the relative amount of variation in your data that results from measurement system error. It is also a great tool for comparing two or more measurement devices or two or more operators. MSA should be used as part of the criteria for accepting a new piece of measurement equipment to manufacturing. It should be the basis for evaluating a measurement system which is suspect of being deficient. Measure : Measurement System Analysis Observed Variation Actual Variation Long-Term Process Varaition Short-Term Process Variation Measurement Variation Variation Within Sample Precision Repeatability Variation due to Gage Stability Reproducibility Linearity Accuracy Measure : Measurement System Analysis Resolution? “Precision” (R&R) Bias? Calibration? Linearity? Stability? Measurement System Metrics Measurement System Variance: 2 s meas = 2 s repeat + 2 s reprod To determine whether the measurement system is “good” or “bad” for a certain application, you need to compare the measurement variation to the product spec or the process variation • Comparing s2meas with Tolerance: – Precision-to-Tolerance Ratio (P/T) • Comparing s2meas with Total Observed Process Variation (P/TV): – % Repeatability and Reproducibility (%R&R) – Discrimination Index Uses of P/T and P/TV (%R&R) • The P/T ratio is the most common estimate of measurement system precision – Evaluates how well the measurement system can perform with respect to the specifications – The appropriate P/T ratio is strongly dependent on the process capability. If Cpk is not adequate, the P/T ratio may give a false sense of security. • The P/TV (%R&R) is the best measure for Analysis – Estimates how well the measurement system performs with respect to the overall process variation – %R&R is the best estimate when performing process improvement studies. Care must be taken to use samples representing full process range. Number of Distinct Categories •Automobile Industry Action Group (AIAG) recommendations: •Categories Remarks < 2 System cannot discern one part from another = 2 System can only divide data in two groups e.g. high and low = 3 System can only divide data in three groups e.g. low, middle and high 4 System is acceptable Measure : Measurement System Analysis Variable GR&R : Decision Criterion BEST ACCEPTABLE REJECT % Bias % Linearity DR %P/T %Contribution <5 <5 > 10 < 10 <2 5 - 10 5 - 10 5 - 10 10-30 2-7.7 > 10 > 10 <5 > 30 > 7.7 Note : Stability is analyzed by control chart Example: Minitab • Enter the data and tolerance information into Minitab. – Stat > Quality Tools > Gage R&R Study (Crossed ) Enter Gage Info and Options. (see next page) ANOVA method is preferred. FN: Gageaiag.mtw Enter the data and tolerance information into Minitab. – Stat > Quality Tools > Gage R&R Study – Gage Info (see below) & Options Gage R&R Output Gage name: Date of study: Reported by: Tolerance: Misc: Gage R&R (ANOVA) for Response Components of Variation By Part Percent 100 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 %Cont ribut ion %St udy Var %Tolerance 50 0 Gage R&R Repeat Reprod Part Part -t o-Part 1 2 3 R Chart by Operator Sample Range 0.15 1 2 0.05 R= 0.03833 0.00 LCL= 0 0 Operator 3 UCL= 0.8796 Mean= 0.8075 LCL= 0.7354 0 Average Sample Mean Xbar Chart by Operator 2 6 7 8 9 10 By Operator UCL= 0.1252 1 5 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 3 0.10 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 4 1 2 Operator* Part I nteraction 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 Part 3 Operator 1 2 3 1 2 3 4 5 6 7 8 9 10 Gage R&R Output Gage R&R, Variation Components Variance due to the measurement system (broken down into repeatability and reproducibility) Source VarComp Total Gage R&R Repeatability Reproducibility Operator Operator*PartID Part-To-Part Total Variation 0.004437 0.001292 0.003146 0.000912 0.002234 0.037164 0.041602 Variance due to the parts %Contribution (of VarComp) 10.67 3.10 7.56 2.19 5.37 89.33 100.00 Source StdDev (SD) Total Gage R&R Repeatability Reproducibility Operator Operator*PartID Part-To-Part Total Variation 0.066615 0.035940 0.056088 0.030200 0.047263 0.192781 0.203965 0.34306 0.18509 0.28885 0.15553 0.24340 0.99282 1.05042 Total variance Standard deviation for each variance component Study Var %Study Var %Tolerance (5.15*SD) (%SV) (SV/Toler) 32.66 17.62 27.50 14.81 23.17 94.52 100.00 22.87 12.34 19.26 10.37 16.23 66.19 70.03 Gage R&R, Results Source VarComp Total Gage R&R Repeatability Reproducibility Operator Operator*PartID Part-To-Part Total Variation 0.004437 10.67 0.001292 3.10 0.003146 7.56 0.000912 2.19 0.002234 5.37 0.037164 89.33 0.041602 100.00 Source StdDev (SD) Total Gage R&R Repeatability Reproducibility Operator Operator*PartID Part-To-Part Total Variation 0.066615 0.035940 0.056088 0.030200 0.047263 0.192781 0.203965 0.34306 0.18509 0.28885 0.15553 0.24340 0.99282 1.05042 %Contribution (of VarComp) 2 s MS Contribution 2 s total P / TV 0.004437 0.1067 0.041602 smeas StudyVar s total 0.3430 0.3266 1.0504 Study Var %Study Var %Tolerance (5.15*SD) (%SV) (SV/Toler) 32.66 17.62 27.50 14.81 23.17 94.52 100.00 22.87 12.34 19.26 10.37 16.23 66.19 70.03 5.15 * s MS Tol USL LSL 0.3430 0.2287 1.5 P /T Question: What is our conclusion about the measurement system? Measure : Process Capability Analysis •Process capability is a measure of how well the process is currently behaving with respect to the output specification. •Process capability is determined by the total variation that comes from common causes -the minimum variation that can be achieved after all special causes have been eliminated. •Thus, capability represents the performance of the process itself,as demonstrated when the process is being operated in a state of statistical control Measure : Process Capability Analysis Translate practical problem to statistical problem Characterization Large Off-Target LSL Variation LSL USL Outliers LSL USL USL Measure : Process Capability Analysis Two measures of process capability Process Potential Cp Process Performance Cpu Cpl Cpk Cpm Measure : Process Capability Analysis Process Potential Cp Engineerin g Tolerance Natural Tolerance USL LSL 6s Measure : Process Capability Analysis The Cp index compares the allowable spread (USL-LSL) against the process spread (6s). It fails to take into account if the process is centered between the specification limits. Process is centered Process is not centered Measure : Process Capability Analysis Process Performance The Cpk index relates the scaled distance between the process mean and the nearest specification limit. C pu USL 3s C pl LSL 3s C pk Minimum C pu , C pl NSL 3s Measure : Process Capability Analysis There are 2 kind of variation : Short term Variation and Long term Variation lity Capabi Studies Entitlement Performance (Short Term) (Long Term) Type of Variability Only common cause # of Data Points 25-50 subgroups Production Example (Lumen Output): Commercial Example (Response Time): -1 lot of raw mat’l -1 shift; 1 set of people -Single “set-up” -“Best” Cust. Serv. Rep. -1 Customer (i.e., Grainger) -1 month in the summer All causes 200 points -3 to 4 lots of raw mat’l -All shifts; All people -Over Several “set-ups” -All Cust. Serv. Reps -All Customers -Several months including Dec/Jan Rule of Thumb: Poor Man’s -“Best 2 weeks” Historical data Process: Running like it was designed or intended! Running like it actually does! Rev. 1 12/98 Measure : Process Capability Analysis Short Term VS LongTerm ( Cp Vs Pp or Cpk vs Ppk ) Measure : Process Capability Analysis Process Potential VS. Process Performance ( Cp Vs Cpk ) 1.If Cp > 1.5 , it means the standard deviation is suitable 2.Cp is not equal to Cpk, it means that the process mean is off-centered Workshop#3 1. Design the appropriate check sheet 2. Define the subgroup 3. Shoot the ball for at least 30 trials per subgroup 4. Perform process capability analysis, translate Cp, Cpk , Pp and Ppk into statistical problem 5. Report your results. Measure : Process Map Process Map is a graphical representation of the flow of a “as-is” process. It contains all the major steps and decision points in a process. It helps us understand the process better, identify the critical or problems area, and identify where improvement can be made. Measure : Process Map OPERATION All steps in the process where the object undergoes a change in form or condition. TRANSPORTATION All steps in a process where the object moves from one location to another, outside of the Operation STORAGE All steps in the process where the object remains at rest, in a semi-permanent or storage condition DELAY All incidences where the object stops or waits on a an operation, transportation, or inspection INSPECTION All steps in the process where the objects are checked for completeness, quality, outside of the Operation. DECISION Measure : Process Map Scrap Bad Bad Good Good • • • • How many Operational Steps are there? How many Decision Points? How many Measurement/Inspection Points? How many Re-work Loops? • How many Control Points? Warehouse Measure : Process Map High Level Process Map KPIVs Major Step KPOVs KPIVs Major Step Major Step KPOVs KPOVs These KPIVs and KPOVs can then be used as inputs to Cause and Effect Matrix KPIVs Workshop #2 : Do the process map and report the process steps and KPIVs that may be the cause Measure : Cause and Effect Analysis A visual tool used to identify, explore and graphically display, in increasing detail, all the possible causes related to a problem or condition to discover root causes To discover the most probable causes for further analysis To visualize possible relationships between causes for any problem current or future To pinpoint conditions causing customer complaints, process errors or nonconforming products To provide focus for discussion To aid in development of technical or other standards or process improvements Measure : Cause and Effect Matrix There are two types of Cause and Effect Matrix 1. Fishbone Diagram - traditional approach to brainstorming and diagramming cause-effect relationships. Good tool when there is one primary effect being analyzed. 2. Cause-Effect Matrix - a diagram in table form showing the direct relationships between outputs (Y’s) and inputs (X’s). Measure : Cause and Effect Matrix C/N/X Methods Materials C C N N N N N Problem/ Desired Improvement C C C Machinery C = Control Factor N = Noise Factor X = Factor for DOE (chosen later) Manpower Fishbone Diagram Measure : Cause and Effect Matrix Cause and Effect Matrix 7 8 9 Requirement Requirement Requirement Requirement Requirement Requirement Requirement Requirement 10 11 12 13 14 15 Requirement 6 Requirement 5 Requirement 4 Requirement 3 Requirement 2 Requirement 1 Requirement Rating of Importance to Customer Total Process Step Process Input Lower Spec Target Upper Spec 0 0 0 0 0 0 0 0 0 0 0 0 0 Total 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Workshop #4: Team brainstorming to create the fishbone diagram Measure : Failure Mode and Effect Analysis FMEA is a systematic approach used to examine potential failures and prevent their occurrence. It enhances an engineer’s ability to predict problems and provides a system of ranking, or prioritization, so the most likely failure modes can be addressed. Measure : Failure Mode and Effect Analysis Measure : Failure Mode and Effect Analysis RPN = S x O x D Severity (ความรุนแรง ) X Occurrence (โอกาสการเกิดขึน้ ) X Detection (การตรวจจับ) Measure : Failure Mode and Effect Analysis สิ่งสำคัญมีน้อย (Vital Few) สิ่งจิ๊บจ๊ อยมีมำก (Trivial Many) Workshop # 5 : Team Brainstorming to create FMEA Measure : Measure Phase’s Output Check and fix the measurement system Determine “where” you are Rolled throughput yield, DPPM Process Capability Entitlement Identify potential KPIV’s Process Mapping / Cause & Effect / FMEA Determine their likely impact Analyze The Analyze phase serves to validate the KPIVs, and to study the statistical relationship between KPIVs and KPOVs Analyze : Tools To validate the KPIVs Hypothesis Test 2 samples t test Analysis Of Variances etc. To reveal the relationship between KPIVs and KPOVs Regression analysis Correlation Analyze : Hypothesis Testing The Null Hypothesis Statement generally assumed to be true unless sufficient evidence is found to the contrary Often assumed to be the status quo, or the preferred outcome. However, it sometimes represents a state you strongly want to disprove. Designated as H0 Analyze : Hypothesis Testing The Alternative Hypothesis Statement generally held to be true if the null hypothesis is rejected Can be based on a specific engineering difference in a characteristic value that one desires to detect Designated as HA Analyze : Hypothesis Testing NULL HYPOTHESIS: Nothing has changed: For Tests Of Process Mean: H0: = 0 For Tests Of Process Variance: H0: s2 = s20 ALTERNATE HYPOTHESIS: Change has occurred: MEAN VARIANCE INEQUALITY Ha: 0 H a: s 2 s 20 NEW OLD Ha: 0 H a: s 2 s 20 NEW OLD Ha: 0 H a : s 2 s 20 Analyze : Hypothesis Testing State the practical problem Common Language Statistical Language Ho A is the same as B A=B Ha A is not same as B A>B (or) A = B (or) A<B Collect and Analyze Data (in Minitab) Result P-Value 0.05 Do not reject Ho P-Value < 0.05 Reject Ho Conclusion about the claim: If A is the same B Then If A is NOT better than B Then Actions to be taken: Analyze : Hypothesis Testing See Hypothesis Testing Roadmap Example: Single Mean Compared to Target • The example will include 10 measurements of a random sample: – 55 56 57 55 58 54 54 54 53 53 The question is: Is the mean of the sample representative of a target value of 54? • The Hypotheses: Ho: = 54 Ha: 54 Ho can be rejected if p < .05 Single Mean to a Target - Using Minitab Stat > Basic Statistics > 1-Sample t One-Sample T: C1 Test of mu = 54 vs mu not = 54 Variable N Mean C1 10 54.900 Variable 95.0% CI C1 ( 53.710, 56.090) StDev SE Mean 1.663 T 0.526 P 1.71 0.121 Our Conclusion Statement Because the p value was greater than our critical confidence level (.05 in this case), or similarly, because the confidence interval on the mean contained our target value, we can make the following statement: “We have insufficient evidence to reject the null hypothesis.” Does this say that the null hypothesis is true (that the true population mean = 54)? No! However, we usually then choose to operate under the assumption that Ho is true. Single Std Dev Compared to Standard •A study was performed in order to evaluate the effectiveness of two devices for improving the efficiency of gas home-heating systems. Energy consumption in houses was measured after 2 device (damper=1& damper =2) were installed. The energy consumption data (BTU.In) are stacked in one column with a grouping column (Damper) containing identifiers or subscripts to denote the population. You are interested in comparing the variances of the two populations to the current (s=2.4). •ฉ All Rights Reserved. 2000 Minitab, Inc. Example: Single Std Dev Compared to Standard (Data: Furnace.mtw, Use “BTU_in”) Note: Minitab does not provide an individual c2 test for standard deviations. Instead, it is necessary to look at the confidence interval on the standard deviation and determine if the CI contains the claimed value. Example: Single Standard Deviation Stat > Basic Statistics > Display Descriptive Statistics Running the Statistics…. Descriptive Statistics Variable: BTU.In Damper: 1 Anderson-Darling Normality Test A-Squared: P-Value: 4 7 10 13 Mean StDev Variance Skewness Kurtosis N 16 Minimum 1st Quartile Median 3rd Quartile Maximum 95% Confidence I nterval for Mu 0.475 0.228 9.90775 3.01987 9.11960 0.707524 0.783953 40 4.0000 7.8850 9.5900 11.5550 18.2600 95% Confidence I nterval for Mu 8.9419 9 10 11 95% Confidence I nterval for Sigma 2.4738 95% Confidence I nterval for Median 10.8736 3.8776 95% Confidence I nterval for Median 8.6170 10.3212 Running the Statistics…. Descriptive Statistics Variable: BTU.In Damper: 2 Anderson-Darling Normality Test A-Squared: P-Value: 4 7 10 13 16 95% Confidence I nterval for Mu 0.190 0.895 Mean StDev Variance Skewness Kurtosis N 10.1430 2.7670 7.65640 -9.9E-02 -2.7E-01 50 Minimum 1st Quartile Median 3rd Quartile Maximum 2.9700 8.1275 10.2900 12.2125 16.0600 95% Confidence I nterval for Mu 9.3566 9 10 11 95% Confidence I nterval for Sigma 2.3114 95% Confidence I nterval for Median 10.9294 3.4481 95% Confidence I nterval for Median 8.7706 11.2363 Two Parameter Testing Step 1: State the Practical Problem Means: 2 Sample t-test Sigmas: Homog. Of Variance Medians: Nonparametrics Failure Rates: 2 Proportions Step 2: Are the data normally distributed? Step 3: State the Null Hypothesis: For s: For : Ho: spop1= spop2 Ho: pop1 = pop2 (normal data) Ho: M1 = M2 (non-normal data) State the Alternative Hypothesis: For s: For : Ha: spop1 spop2 Ha: pop1 pop2 Ha: M1 M2 (non-normal data) Two Parameter Testing (Cont.) Step 4: Determine the appropriate test statistic F (calc) to test Ho: spop1 = spop2 T (calc) to test Ho: pop1 = pop2 (normal data) Step 5: Find the critical value from the appropriate distribution and alpha Step 6: If calculated statistic > critical statistic, then REJECT Ho. Or If P-Value < 0.05 (P-Value < Alpha), then REJECT Ho. Step 7: Translate the statistical conclusion into process terms. Comparing Two Independent Sample Means • The example will make a comparison between two group means • Data in Furnace.mtw ( BTU_in) • Are the mean the two groups the same? • The Hypothesis is: – Ho: 1 2 – Ha : 1 2 • Reject Ho if t > t a/2 or t < -t n2 - 2 degrees of freedom a/2 for n1 + t-test Using Stacked Data Stat >Basic Statistics > 2-Sample t t-test Using Stacked Data Descriptive Statistics Graph: BTU.In by Damper Two-Sample T-Test and CI: BTU.In, Damper Two-sample T for BTU.In Damper N Mean StDev SE Mean 1 40 9.91 3.02 0.48 2 50 10.14 2.77 0.39 Difference = mu (1) - mu (2) Estimate for difference: -0.235 95% CI for difference: (-1.464, 0.993) T-Test of difference = 0 (vs not =): T-Value = -0.38 P-Value = 0.704 DF = 80 2 variances test Stat >Basic Statistics > 2 variances 2 variances test Test for Equal Variances for BTU.In 95% Confidence I ntervals for Sigmas Factor Levels 1 2 2 3 4 F-Test Test Statistic: 1.191 P-Value : 0.558 Levene's Test Test Statistic: 0.000 P-Value : 0.996 Boxplots of Raw Data 1 2 4 9 14 BTU.I n 19 Characteristics About Multiple Parameter Testing • One type of analysis is called Analysis of Variance (ANOVA). – Allows comparison of two or more process means. • We can test statistically whether these samples represent a single population, or if the means are different. • The OUTPUT variable (KPOV) is generally measured on a continuous scale (Yield, Temperature, Volts, % Impurities, etc...) • The INPUT variables (KPIV’s) are known as FACTORS. In ANOVA, the levels of the FACTORS are treated as categorical in nature even though they may not be. • When there is only one factor, the type of analysis used is called “One-Way ANOVA.” For 2 factors, the analysis is called “Two-Way ANOVA. And “n” factors entail “n-Way ANOVA.” General Method Step 1: State the Practical Problem Step 2: Do the assumptions for the model hold? • Response means are independent and normally distributed • Population variances are equal across all levels of the factor –Run a homogeneity of variance analysis--by factor level—first Step 3: State the hypothesis Step 4: Construct the ANOVA Table Step 5: Do the assumptions for the errors hold (residual analysis)? • Errors of the model are independent and normally distributed Step 6: Interpret the P-Value (or the F-statistic) for the factor effect • P-Value < 0.05, then REJECT Ho • Otherwise, operate as if the null hypothesis is true Step 7: Translate the statistical conclusion into process terms Step 2: Do the Assumptions for the Model Hold? • Are the means independent and normally distributed – Randomize runs during the experiment – Ensure adequate sample sizes – Run a normality test on the data by level • Minitab: Stat > Basic Stats > Normality Test • Population variances are equal for each factor level (run a homogeneity of variance analysis first) • For s Ho: spop1 = spop2 = spop3 = spop4 = .. Ha: at least two are different Step 3: State the Hypotheses Mathematical Hypotheses: Ho: ’s = 0 Ha: k 0 Conventional Hypotheses: Ho: 1 = 2 = 3 = 4 Ha: At least one k is different Step 4: Construct the ANOVA Table One-Way Analysis of Variance Analysis of Variance for Time Source DF SS Operator 3 149.5 Error 20 229.2 Total 23 378.6 MS 49.8 11.5 F 4.35 SOURCE SS df MS Between SStreatment g-1 MStreatment = SStreatment / (g-1) Within SSerror N-g MSerror = SSerror / (N-g) Total SStotal N-1 Where: g = number of subgroups n = number of readings per subgroup P 0.016 Test Statistic F = MStreatment / MSerror What’s important the probability that the Operator variation in means could have happened by chance. Steps 5 - 7 Step 5:Do the assumptions for the errors hold (residual analysis) ? • Errors of the model are independent and normally distributed – Randomize runs during the experiment – Ensure adequate sample size – Plot histogram of error terms – Run a normality check on error terms Residual Analysis – Plot error against run order (I-Chart) – Plot error against model fit Step 6:Interpret the P-Value (or the F-statistic) for the factor effect • P-Value < 0.05, then REJECT Ho. • Otherwise, operate as if the null hypothesis is true. Step 7:Translate the statistical conclusion into process terms Example, Experimental Setup • Twenty-four animals receive one of four diets. • The type of diet is the KPIV (factor of interest). • Blood coagulation time is the KPOV • During the experiment, diets were assigned randomly to animals. Blood samples taken and tested in random order. Why ? DIET A 62 60 63 59 DIET B 63 67 71 64 65 66 DIET C 68 66 71 67 68 68 DIET D 56 62 60 61 63 64 63 59 Example, Step 2 • Do the assumptions for the model hold? • Population by level are normally distributed – Won’t show significance for small # of samples • Variances are equal across all levels of the factor – Stat > ANOVA > Test for Equal Variances Ho: _____________ Ha :_____________ Test for Equal Variances for Coag_Time 95% Confidence Intervals for Sigmas Factor Levels 1 Bartlett's Test Test Statistic: 1.668 2 3 P-Value : 0.644 Levene's Test Test Statistic: 0.649 P-Value 4 0 5 10 : 0.593 Example, Step 3 • State the Null and Alternate Hypotheses Ho: µ diet1= µ diet2= µ diet3= µ diet4 (or) Ho: ’s = 0 Ha: at least two diets differ from each other(or) Ha:’s0 • Interpretation of the null hypothesis: the average blood coagulation time of each diet is the same (or) what you eat will NOT affect your blood coagulation time. • Interpretation of the alternate hypothesis: at least one diet will affect the average blood coagulation time differently than another (or) what type of diet you keep does affect blood coagulation time. Example, Step 4 • Construct the ANOVA Table (using Minitab): Stat > ANOVA > One-way ... Hint: Store Residuals & Fits for later use Example, Step 4 One-way Analysis of Variance Analysis of Variance for Coag_Tim Source DF SS MS Diet_Num 3 228.00 76.00 Error 20 112.00 5.60 Total 23 340.00 Level 1 2 3 4 N 4 6 6 8 Mean 61.00 66.00 68.00 61.00 StDev 1.826 2.828 1.673 2.619 Pooled StDev = 2.366 F 13.57 P 0.000 Individual 95% CIs For Mean Based on Pooled StDev ---+---------+---------+---------+--(------*------) (-----*----) (----*-----) (----*----) ---+---------+---------+---------+--59.5 63.0 66.5 70.0 Example, Step 5 Do the assumptions for the errors hold? Best way to check is through a “residual analysis” Stat > Regression > Residual Plots ... • Determine if residuals are normally distributed • Ascertain that the histogram of the residuals looks normal • Make sure there are no trends in the residuals (it’s often best to graph these as a function of the time order in which the data was taken) • The residuals should be evenly distributed about their expected (fitted) values Example, Step 5 Individual residuals trends? Or outliers? How normal are the residuals ? Histogram - bell curve ? Ignore for small data sets (<30) This graph investigates how the Residuals behave across the experiment. This is probably the most important graph, since it will signal that something outside the experiment may be operating. Nonrandom patterns are warnings. Random about zero without trends? This graph investigates whether the mathematical model fits equally for low to high values of the Fits Example, Step 6 • Interpret the P-Value (or the F-statistic) for the factor effect – Assuming the residual assumptions are satisfied: – If P-Value < 0.05, then REJECT Ho If P is less than 5% then – Otherwise, operate as if null hypothesis at least one group mean is different. In this case, is true Analysis of Variance for Coag_Tim Source Diet_Num Error Total DF SS 3 228.00 76.00 13.57 0.000 20 112.00 5.60 23 340.00 s1 s2 s3 s4 2 s 2 Pooled 2 2 4 When group sizes are equal 2 MS F P F-test is close to 1.00 when group means are similar. In this case, The F-test is much greater. we reject the hypothesis that all the group means are equal. At least one Diet mean is different. An F-test this large could happen by chance, but in less than one time out of 2000 chances. This would be like getting 11 heads in a row from a fair coin. Work shop#6: Run Hypothesis to validate your KPIVs from Measure phase Analyze : Analyze Phase’s output Refine: KPOV = F(KPIV’s) Which KPIV’s cause mean shifts? Which KPIV’s affect the standard deviation? Which KPIV’s affect yield or proportion? How did KPIV’s relate to KPOV’s? Improve The Improve phase serves to optimize the KPIV’s and study the possible actions or ideas to achieve the goal Improve : Tools To optimize KPIV’s in order to achieve the goal Design of Experiment Evolutionary Operation Response Surface Methodology Improve : Design Of Experiment Factorial Experiments The GOAL is to obtain a mathematical relationship which characterizes: Y = F (X1, X2, X3, ...). Mathematical relationships allow us to identify the most important or critical factors in any experiment by calculating the effect of each. Factorial Experiments allow investigation of multiple factors at multiple levels. Factorial Experiments provide insight into potential “interactions” between factors. This is referred to as factorial efficiency. Improve : Design Of Experiment Factors: A factor (or input) is one of the controlled or uncontrolled variables whose influence on a response (output) is being studied in the experiment. A factor may be quantitative, e.g., temperature in degrees, time in seconds. A factor may also be qualitative, e.g., different machines, different operator, clean or not clean. Improve : Design Of Experiment • Level: The “levels” of a factor are the values of the factor being studied in the experiment. For quantitative factors, each chosen value becomes a level, e.g., if the experiment is to be conducted at two different temperatures, then the factor of temperature has two “levels”. Qualitative factors can have levels as well, e.g for cleanliness , clean vs not clean; for a group of machines, machine identity. • “Coded” levels are often used,e.g. +1 to indicate the “high level” and -1 to indicate the “low level” . Coding can be useful in both preparation & analysis of the experiment Improve : Design Of Experiment k1 x k2 x k3 …. Factorial : Description of the basic design. The number of “ k’s ” is the number of factors. The value of each “ k ” is the number of levels of interest for that factor. Example : A2 x 3 x 3 design indicates three input variables. One input has two levels and the other two, each have three levels. Test Run (Experimental Run ) : A single combination of factor levels that yields one or more observations of the output variable. Center Point • Method to check linearity of model called Center Point. • Center Point is treatment that set all factor as center for quantitative. • Result will be interpreted through “curvature” in ANOVA table. • If center point’s P-value show greater than a level, we can do analysis by exclude center point from model. ( linear model ) • If center point’s P-value show less than a level, that’s mean we can not use equation from software result to be model. ( non - linear ) • There are no rule to specify how many Center point per replicate will be take, decision based on how difficult to setting and control. Sample Size by Minitab • Refer to Minitab, sample size will be in menu of Stat->Power and Sample Size. Sample Size By Minitab Specify number of factor in experiment design. Process sigma Specify number of run per replicated. Enter power value, 1-b, which can enter more than one. And effect is critical difference that would like to detect (d). Center Point case Exercise : DOECPT.mtw “0” indicated that these treatments are center point treatment. Center Point Case Estimated Effects and Coefficients for Weight (coded units) Term Effect Constant Coef StDev Coef T P 2506.25 12.77 196.29 0.000 A 123.75 61.87 12.77 4.85 0.017 B -11.25 -5.62 12.77 -0.44 0.689 C 201.25 100.62 12.77 7.88 0.004 D 6.25 3.12 12.77 0.24 0.822 A*B 120.00 60.00 12.77 4.70 0.018 A*C 20.00 10.00 12.77 0.78 0.491 A*D -17.50 -8.75 12.77 -0.69 0.542 B*C -22.50 -11.25 12.77 -0.88 0.443 B*D 7.50 3.75 12.77 0.29 0.788 C*D 12.50 6.25 12.77 0.49 0.658 A*B*C 16.25 8.13 12.77 0.64 0.570 A*B*D -11.25 -5.63 12.77 -0.44 0.689 A*C*D -18.75 -9.38 12.77 -0.73 0.516 B*C*D 3.75 1.88 12.77 0.15 0.893 -22.50 -11.25 12.77 -0.88 0.443 -33.75 28.55 -1.18 0.322 A*B*C*D Ct Pt H0 : Model is linear Ha : Model is non linear P-Value of Ct Pt (center point) show greater than a level, we can exclude Center Point from model. Reduced Model • Refer to effect table, we can excluded factor that show no statistic significance by remove term from analysis. • For last page, we can exclude 3-Way interaction and 4-Way interaction due to no any term that have P-Value greater than a level. • We can exclude 2 way interaction except term A*B due to P-value of this term less than a level. • For main effect, we can not remove B whether PValue of B is greater than a level, due to we need to keep term A*B in analysis. Center Point Case Fractional Factorial Fit: Weight versus A, B, C Estimated Effects and Coefficients for Weight (coded units) Term Effect Constant Coef 2499.50 SE Coef 8.636 T P 289.41 0.000 A 123.75 61.87 9.656 6.41 0.000 B -11.25 -5.62 9.656 -0.58 0.569 C 201.25 100.62 9.656 10.42 0.000 A*B 120.00 60.00 9.656 6.21 0.000 Final equation that we get for model is Weight = 2499.5 + 61.87A – 5.62B + 100.62C + 60AB DOE for Standard Deviations • The basic approach involves taking “n” replicates at each trial setting • The response of interest is the standard deviation (or the variance) of those n values, rather than the mean of those values • There are then three analysis approaches: – Normal Probability Plot of log(s2) or log(s)* – Balanced ANOVA of log(s2) or log(s)* – F tests of the s2 (not shown in this package) * log transformation permits normal distribution analysis approach Standard Deviation Experiment The following represents the results from 2 different 23 experiments, where 24 replicates were run at each trial combination A B -1 1 -1 1 -1 1 -1 1 C -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 1 1 Expt1 s^2 Expt2 s^2 0.823 0.596 1.187 1.55 3.186 2.025 2.34 2.242 0.651 3.212 1.477 2.882 2.048 3.847 1.516 6.265 File: Sigma DOE.mtw * Std Dev Experiment Analysis Set Up After putting this into the proper format as a designed experiment: Stat > DOE > Factorial > Analyze Factorial Design Under the Graph option / Effects Plots Normal A B -1 1 -1 1 -1 1 -1 1 A -1 -1 1 1 -1 -1 1 1 C B -1 1 -1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 1 1 Expt1 C s^2 Expt2 Expt1s^2 s^2 Expt1 Expt2 ln(s^2) s^2 Expt2 Expt1ln(s^2) ln(s^2) Expt2 ln(s^ -1 0.823-1 0.596 0.823 -0.1942 0.596 -0.51693 -0.1942 -0.51 -1 1.187-1 1.187 1.55 0.17162 1.55 0.43811 0.17162 0.43 1 3.186-1 2.025 3.186 1.15888 2.025 0.70565 1.15888 0.70 1 2.34-1 2.242 2.34 0.84997 2.242 0.80715 0.84997 0.80 -1 0.6511 3.212 0.651 -0.42921 3.212 -0.42921 1.16704 1.16 -1 1.4771 2.882 1.477 0.38995 2.882 1.05863 0.38995 1.05 1 2.0481 3.847 2.048 0.71679 3.847 1.34727 0.71679 1.34 1 1.5161 6.265 1.516 0.41602 6.265 1.83501 0.41602 1.83 ln(s2) Normal Probability Plots • Plot all the effects of a 23 on a normal probability plot – Three main effects: A, B and C – Three 2-factor interactions: AB, AC and BC – One 3-factor interaction: ABC • If no effects are important, all the points should lie approximately on a straight line • Significant effects will lie off the line – Single significant effects should be easily detectable – Multiple significant effects may make it hard to discern the line. Probability Plot: Experiment 1 Results from Experiment 1 Using Normal Probability Plot of the Effects ln(s2) (response is Expt 1, Alpha = .10) 1.5 B Normal Score 1.0 A: A B: B C: C 0.5 Minitab does not identify these points unless they are very significant. You need to look at Minitab’s Session Window to identify. 0.0 -0.5 -1.0 -1.5 -0.5 0.0 0.5 Effect The plot shows one of the points--corresponding to the B main effect--outside of the rest of the effects ANOVA Table: Experiment 1 Results from Experiment 1 Using ln(s2) Analysis of Variance for Expt 1 Source A B C Error Total DF 1 1 1 4 7 SS 0.0414 1.2828 0.0996 0.5463 1.9701 MS 0.0414 1.2828 0.0996 0.1366 F 0.30 9.39 0.73 P 0.611 0.037 0.441 Sample Size Considerations • The sample size computed for experiments involving standard deviations should be based on a and b, as well as the critical ratio that you want to detect--just as it is for hypothesis testing • The Excel program “Sample Sizes.xls” can be used for this purpose • If “m” is the sample size for each level (computed by the program), and the experiment has k treatment combinations, then the number of replicates, n, per treatment combination = 1 + 2(m-1) k * Workshop # 7 : Run DOE to optimize the validate KPIV to get the desired KPOV Improve : Improve Phase’s output Which KPIV’s cause mean shifts? Which KPIV’s affect the standard deviation? Levels of the KPIV’s that optimize process performance Control The Control phase serves to establish the action to ensure that the process is monitored continuously for consistency in quality of the product or service. Control: Tools To monitor and control the KPIV’s Error Proofing (Poka-Yoke) SPC Control Plan Control: Poka-Yoke Why Poka-Yoke? Strives for zero defects Leads to Quality Inspection Elimination Respects the intelligence of workers Takes over repetitive tasks/actions that depend on one’s memory Frees an operator’s time and mind to pursue more creative and value added activities Control: Poka-Yoke Benefit of Poka-Yoke? Enforces operational procedures or sequences Signals or stops a process if an error occurs or a defect is created Eliminates choices leading to incorrect actions Prevents product damage Prevents machine damage Prevents personal injury Eliminates inadvertent mistakes Control: SPC SPC is the basic tool for observing variation and using statistical signals to monitor and/or improve performance. This tool can be applied to nearly any area. Performance characteristics of equipment Error rates of bookkeeping tasks Dollar figures of gross sales Scrap rates from waste analysis Transit times in material management systems SPC stands for Statistical Process Control. Unfortunately, most companies apply it to finished goods (Y’s) rather than process characteristics (X’s). Until the process inputs become the focus of our effort, the full power of SPC methods to improve quality, increase productivity, and reduce cost cannot be realized. Types of Control Charts The quality of a product or process may be assessed by means of • Variables :actual values measured on a continuous scale e.g. length, weight, strength, resistance, etc • Attributes :discrete data that come from classifying units (accept/reject) or from counting the number of defects on a unit If the quality characteristic is measurable • monitor its mean value and variability (range or standard deviation) If the quality characteristic is not measurable • monitor the fraction (or number) of defectives • monitor the number of defects Defectives vs Defects • Defective or Nonconforming Unit • a unit of product that does not satisfy one or more of the specifications for the product – e.g. a scratched media, a cracked casing, a failed PCBA • Defect or Nonconformity • a specific point at which a specification is not satisfied – e.g. a scratch, a crack, a defective IC Shewhart Control Charts - Overview Walter A Shewhart Shewhart Control Charts for Variables Control: SPC Choosing The Correct Control Chart Type Attributes Defects Area of opportunity constant from sample to sample? Variables Type of data Defectives Counting defects or defectives? Yes Data tends to be normally distributed because of central limit theorem Individuals Individual measurements or sub-groups? Measurement Sub-groups c Normally Distributed data? No Yes X, mR No Interested primarily in sudden shifts in No mean? Yes u Constant sub-group size? MA, EWMA, Yes p, np or CUSUM X-bar, R X-bar, s No p More effective in detecting gradual long-term changes Use of modified control chart rules okay on x-bar chart Control: Control Phase’s output Y is monitored with suitable tools X is controlled by suitable tools Manage the INPUTS and good OUTPUTS will follow Breakthrough Summary DEFINE MEASURE ANALYZE >>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>> Champion Champion DEFINE - Definition of Opportunity 1.>>>>>>>>>>> Project Definition 2. Determine Champion Impact & Priority 3. Collect Baseliine Metric Data Definition of 4. Savings/Cost Opportunity Assessment 1. Project 5. EstablishDefinition 2. Planned Determine Impact & Priority Timeline 3. CollectLibrary Baseliine 6. Search Metric Data 7. Identify Project 4. Authority Savings/Cost Assessment 1. Problem 5. Statement Establish Planned 2. Goals/Objectives Timeline 3. Projected 6. Business Search Library 7. Benefits Identify Project AuthorityValue 4. Financial 1. Problem 5. Key Metrics Statement 6. Team 2. Assignment Goals/Objectives 3. Projected Business P1 (not validated) Benefits IMPROVE >>>>>>>>>>>> CONTROL- >>>>>>>>>>>>>> >>>>>>>>>>>>> Black Belt Assess the Current Process Blackbelts ANALYZE IMPROVE Confirm f(x) for Y MEASURE 1.>>>>>>>>>>>>>>> Map the Process 1.>>>>>>>>>>>>> Determine the Vital 2. Determine the Baseline 3. Prioritize the Inputs to Assess 4. Assess the Assess the Current Process Measurement System 5. Capability Assessment Map Term the Process 6.1. Short 2. Determine 7. Long Term the Baseline Prioritize the Inputs to 8.3. Determine Entitlement Assess 9. Process Improvement 4. Financial Assess the 10. Savings Measurement System Capability Assessment 1.5. Macro / Micro Process 6. Charts Short Term Long Term 2.7. Rolling Throughput 8. Yield Determine Entitlement Process Improvement 3.9. Fishbone, Cause Effect 10.Matrix Financial Savings Variables Affecting Black the Response f(x) = Y Optimize f(x) for Y 1.>>>>>>>>>>>> Determine the Best BeltCombination of ‘Xs’ for Producing the Best ‘Y’ REALIZATION Financial Rep & Process Owner Finance Rep.& Sustain the Benefit CONTROLProcess Owner 1.>>>>>>>>>>>>>> Establish Controls for 1.>>>>>>>>>>>>> Financial Maintain Improvements REALIZATION - 2. KPIVs and their AssessmentRep and & Financial ‘settings’ Input Actual Process Owner 3. Establish Reaction Savings Plans 2. Functional Confirm f(x) for Y Optimize f(x) for Y Maintain Improvements Sustain the Benefit 2. Confirm Manager/Process Relationships and Owner – Monitor 1. Establish Determine Vital 1. Determine the Best 1. Establish Controls for 3.1. Control/Implementa Financial thethe KPIV Variables Affecting Combination of ‘Xs’ 2. KPIVs and their Assessment and tion the Response for Producing the ‘settings’ Input Actual Best ‘Y’ 3. Establish Reaction Savings f(x) = Y Plans 2. Functional 2. Confirm Manager/Process Relationships and Owner Benefit – Monitor 1. Multi-Vari Studies Design of Experiments 1. Process Control Plan 1. Monthly Establish the KPIV 3. Control/Implementa 2. Correlation Analysis 1. Full Factorial 2. SPC Charting Update tion 3. Regression Analysis 2. Fractional Factorial x-Bar & R Single / Multiple 3. Blocking Pre-Control Experiments 4. Hypothesis Testing Etc 4. Custom Methods Mean Testing (t, Z) 3. Gauge Control Plans 4. GR&R Study 5. RSM Variation (Std Multi-Vari Studies Macro / Micro 1. Design of Experiments 1. Process Control Plan 1. Monthly Benefit 5.1. Establish SigmaProcess Score Dev)(F,etc) Charts 2. Correlation Analysis 1. Full Factorial 2. SPC Charting Update 6. Apply ‘Shift & Drift’ 3. ANOVA 2. Rolling Throughput Regression Analysis 2. Fractional Factorial x-Bar & R 7. Baseline vs Entitlement Yield to $$$ Single / Multiple 3. Blocking Pre-Control 8. Translate 3. Fishbone, Cause Effect 4. Hypothesis Testing Experiments Etc P1 (validated) P5 Reviewed P5 P5 Reviewed Matrix 4.Reviewed Custom Methods Mean Testing (t, Z) 3. Gauge P5 Reviewed P8 (Sign Off)Control Plans Hard Savings Savings which flow to Net Profit Before Income Tax (NPBIT) Can be tracked and reported by the Finance organization Is usually a reduction in labor, material usage, material cost, or overhead Can also be cost of money for reduction in inventory or assets Finance Guidelines - Savings Definitions • Hard Savings • Direct Improvement to Company Earnings • Baseline is Current Spending Experience • Directly Traceable to Project • Can be Audited Hard Savings Example • Process is Improved, resulting in lower scrap • Scrap reduction can be linked directly to the successful completion of the project Potential Savings Savings opportunities which have been documented and validated, but require action before actual savings could be realized an example is capital equipment which has been exceeded due to increased efficiencies in the process. Savings can not be realized because we are still paying for the equipment. It has the potential for generating savings if we could sell or put back into use because of increases in schedules. Some form of a management decision or action is generally required to realize the savings Finance Guidelines - Savings Definitions Potential Savings • Improve Capability of company Resource Potential Savings Example • Process is Improved, resulting in reduced manpower requirement • Headcount is not reduced or reduction cannot be traced to the project Potential Savings might turn into hard savings if the resource is productively utilized in the future Identifying Soft Savings Dollars or other benefits exist but they are not directly traceable Projected benefits have a reasonable probability (TBD) that they will occur Some or all of the benefits may occur outside of the normal 12 month tracking window Assessment of the benefit could/should be viewed in terms of strategic value to the company and the amount of baseline shift accomplished Finance Guidelines - Savings Definitions Soft Savings • Benefit Expected from Process Improvement • Benefit cannot be directly traced to Successful Completion of Project • Benefit cannot be quantified Soft Savings Example • Process is Improved; decreasing cycle time • Benefit cannot be quantified