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IX C USTOMER & C OMPETITIVE I NTELLIGENCE FOR S YSTEMS I NNOVATION & D ESIGN S IGMA S D EPARTMENT OF S TATISTICS D R. R ICK E DGEMAN, P ROFESSOR & C HAIR – S IX S IGMA B LACK B ELT REDGEMAN@UIDAHO.EDU OFFICE: +1-208-885-4410
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IX S IGMA S D EPARTMENT OF S TATISTICS DMAIC: T he A nalyze P hase
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IX S IGMA S D EPARTMENT OF S TATISTICS a highly structured strategy for acquiring, assessing, and applying customer, competitor, and enterprise intelligence for the purposes of product, system or enterprise innovation and design.
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Alternative Six Sigma Definitions <ul><li>“ Six Sigma is a business improvement approach that seeks to find and eliminate causes of mistakes or defects in business processes by focusing on process outputs that are of critical importance to customers.” (Snee, 2004). </li></ul><ul><li>“ Six Sigma is a useful management philosophy and problem-solving methodology but it is not a comprehensive management system. “ (McAdam & Evans, 2004) </li></ul>
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Alternative Six Sigma Definitions <ul><li>“ A Six Sigma initiative is designed to change the culture in an organisation by the way of breakthrough improvement in all aspects of the business.” (Breyfogle III et al., 2001) </li></ul><ul><li>“ Six Sigma is a programme that combines the most effective statistical and non-statistical methods to make overall business.” (Pearson, 2001) </li></ul>
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Alternative Six Sigma Definitions <ul><li>“ Six Sigma is a highly disciplined process that helps us focus on developing and delivering near-perfect products and services. The central idea behind Six Sigma is that you can measure how many defects you have in a process, you can systematically figure out how to eliminates them and get as close to ‘zero defects’ as possible. Six Sigma has changed the DNA of GE – it is the way we work - in everything we do in every product we design” (General Electric at www.ge.com ) </li></ul>
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D efine C ontrol I mprove A nalyze M easure S ix S igma I nnovation & the DM A IC Algorithm D efine the problem and customer requirements. M easure defect rates and document the process in its current incarnation. A nalyze process data and determine the capability of the process. I mprove the process and remove defect causes. C ontrol process performance and ensure that defects do not recur.
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Analyze: Where are we now? Where are we going? What can prevent us from reaching our goals? At this stage we determine the process sigma level and regard variation as an enemy. We must determine process capability, that is, the ability of the process to meet customer requirements. We require several “z-scores” to make this evaluation. Z BENCH Z st Z LT Z LSL Z USL Where “BENCH” = benchmark, “st” = short term, “LT” = long term “ LSL” = lower specification limit, and “USL” = upper specification limit.
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Analyze : Where are we now? Where are we going? What can prevent us from reaching our goals? Z ST = best performance that can be expected from a process Z LT = allows for drift through time (1 to 2 sigma drift is typical) Z LSL = (X – LSL) / S then determine P LSL (d) Z USL = (USL – X) / S then determine P USL (d) P(d) = P LSL (d) + P USL (d) then apply inverse use of the Z-table to find Z BENCH (long-term) P(d) * 1,000,000 = DPMO or PPM Z BENCH P(d) Zx.y 0.0X
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Analyze : Where are we now? Where are we going? What can prevent us from reaching our goals? Z SHIFT = Z ST – Z LT drift over time (DPMO tables assume 1.5) Z ST = (Specification Limit – Target) / ST * process sigma is determined here * indicates potential process performance if only common cause variation is present. Z LT = (Specification Limit - ) / LT * reveals long-term process capability * used to estimate DPMO or PPM (“parts per million” same as DPMO) * includes special cause variation ^ ^
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Analyze: An Alternative Means of Approximating the Sigma Capability for Your Process <ul><li>Step Action Equations Your Calculations </li></ul><ul><li>What process do you want to consider? N/A Billing & Charging </li></ul><ul><li>How many units were put through the N/A 2,000 </li></ul><ul><li>process? </li></ul><ul><li>Of the units that went into the process, N/A 1,800 </li></ul><ul><li>how many were OK? </li></ul><ul><li>4 Compute process yield (step 3)/(step 2) 0.9000 </li></ul><ul><li>5 Compute defect rate 1.0 – (step 4) 0.1000 </li></ul><ul><li>Determine the number of potential N = number of 16 </li></ul><ul><li>things that could create a defect critical-to-quality </li></ul><ul><li> characteristics </li></ul><ul><li>Compute the defect rate per CTQ (step 5)/(step 6) 0.00625 </li></ul><ul><li>characteristic </li></ul><ul><li>8 Compute DPMO (step 7)*(1 million) 6,250 </li></ul><ul><li>9 Convert DPMO to value conversion chart About 4.0 </li></ul><ul><li>10 Draw conclusions JUST ABOUT INDUSTRY AVERAGE </li></ul>
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Process Capability : The Control Chart Method for Variables Data <ul><li>Construct the control chart and remove all special causes. </li></ul><ul><li>NOTE : special causes are “special” only in that they come and </li></ul><ul><li>go, not because their impact is either “good” or “bad”. </li></ul><ul><li>Estimate the standard deviation. Used approach depends on whether an R or S chart is used to monitor process variability. </li></ul><ul><li>^ _ ^ _ </li></ul><ul><li> = R / d 2 = S / c 4 </li></ul><ul><li>Several capability indices are provided on the following slide. </li></ul>NOTE : Control Charts are presented in later slide sets.
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Process Capability Indices : Variables Data ^ ^ C P = (engineering tolerance)/6 = (USL – LSL) / 6 This index is generally used to evaluate machine capability. It compares tolerance to the engineering requirements. Assuming that the process is (approximately) normally distributed and that the process average is centered between the specifications, an index value of “1” is considered to represent a “minimally capable” process. HOWEVER … allowing for a drift, a minimum value of 1.33 is ordinarily sought … bigger is better. A true “Six Sigma” process that allows for a 1.5 shift will have C p = 2.
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Process Capability Indices : Variables Data ^ ^ C R = 100*6 / (Engineering Tolerance) = 100* 6 / (USL – LSL) This is called the capability ratio . Effectively this is the reciprocal of Cp so that a value of less than 75% is generally needed and a Six Sigma process (with a 1.5 shift) will lead to a C R of 50%.
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Process Capability Indices : Variables Data ^ ^ C M = (engineering tolerance)/8 = (USL – LSL) / 8 This index is generally used to evaluate machine capability . Note … this is only MACHINE capability and NOT the capability of the full process. Given that there will be additional sources of variation (tooling, fixtures, materials, etc.) C M uses an 8 spread, rather than 6 . For a machine to be used on a Six Sigma process, a 10 spread would be used.
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Process Capability Indices : Variables Data = ^ = ^ Z U = (USL – X) / Z L = (X – LSL) / Z min = Minimum (Z L , Z U ) C pk = Z min / 3 This index DOES take into account how well or how poorly centered a process is A value of at least +1 is required with a value of at least +1.33 being preferred. C p and C pk are closely related. In some sense C pk represents the current capability of the process whereas C p represents the potential gain to be had from perfectly centering the process between specifications.
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Process Capability : Example <ul><li>Assume that we have conducted a capability analysis using X-bar and R charts </li></ul><ul><li>with subgroups on size n = 5. Also assume the process is in statistical control </li></ul><ul><li>with an average of 0.99832 and an average range of 0.02205. A table of d 2 </li></ul><ul><li>values gives d 2 = 2.326 (for n = 5). Suppose LSL = 0.9800 and USL = 1.0200 </li></ul><ul><li>^ _ </li></ul><ul><li> = R / d2 = 0.02205/2.326 = 0.00948 </li></ul><ul><ul><li>C p = (1.0200 – 0.9800) / 6(.00948) = 0.703 </li></ul></ul><ul><ul><li>C R = 100*(6*0.00948) / (1.0200 – 0.9800) = 142.2% </li></ul></ul><ul><ul><li>C M = (1.0200 – 0.9800) / (8*(0.00948)) = 0.527 </li></ul></ul><ul><ul><li>Z L = (.99832 - .98000)/(.00948) = 1.9 </li></ul></ul><ul><ul><li>Z U = (1.02000 – .99832)/(.00948) = 2.3 so that Z min = 1.9 </li></ul></ul><ul><ul><li>C pk = Z min / 3 = 1.9 / 3 = 0.63 </li></ul></ul>
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Process Capability : Interpretation C p = 0.703 … since this is less than 1, the process is not regarded as being capable. C R = 142.2% implies that the “natural tolerance” consumes 142% of the specifications (not a good situation at all). C M = 0.527 = Being less than 1.33, this implies that – if we were dealing with a machine, that it would be incapable of meeting requirements. Z L = 1.9 … This should be at least +3 and this value indicates that approximately 2.9% of product will be undersized. Z U = 2.3 should be at least +3 and this value indicates that approximately 1.1% of product will be oversized. C pk = 0.63 … since this is only slightly less that the value of Cp the indication is that there is little to be gained by centering and that the need is to reduce process variation.
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Analyze : Where are we now? Where are we going? What can prevent us from reaching our goals? Yield Rates A yield rate is a pass rate and can be characterized in various ways: Classical Yield Rate = Y C = (total defect free parts) / (total parts) First Time Yield Rate = Y FT = (parts defect free on the first pass)/(total parts) Throughput Yield = Y T = e –DPU where “DPU” = “defects per unit” and is calculated as DPU = (number of defects at any stage) / (total inspected). Note that due to rework some items may be inspected multiple times with each inspection adding to the “total”.
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Where are we now? Where are we going? What can prevent us from reaching our goals? Yield Rates Classical Yield Rate = (total defect free parts) / (total parts) = ¾ = 75% First Time Yield Rate = (parts defect free on the first pass) / (total parts) = ¼ = 25% Throughput Yield = e –DPU where “DPU” = “defects per unit” and is = e –18/8 = .1054 The “rework” that it takes to raise “throughput yield” to the “classical yield” level is called Hidden Factory . X Analyze Scrapped X Meets Specifications Defect Meaning Symbol
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Analyze: Setting Performance Objectives Critical to the Setting of Performance Objectives are the Concepts of ‘ Baseline’, ‘Process Entitlement’, ‘Benchmark’ and ‘Benchmarking’ BASELINE : This is the process performance level at the start of the Six Sigma Project. PROCESS ENTITLEMENT : This is our best expectation for process performance (e.g., the ‘sigma level’) with the current technology – that is, without substantial reengineering or investment. This can be estimated from Z st . BENCHMARK : This is the current ‘best in class’ performance level. BENCHMARKING : The process of finding the benchmark performance level and then matching or exceeding that performance.
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<ul><li>Analyze : </li></ul><ul><li>Sources of Variation </li></ul><ul><li>This is the search for the Vital X’s – the factors that drive the customer CTQs. </li></ul><ul><li>Various statistical and quality methods are useful in this effort. Among these are: </li></ul><ul><li>HYPOTHESIS TESTING , which can </li></ul><ul><li>Reveal Significant Differences in Performance Between Processes </li></ul><ul><li>Validate Process Improvements </li></ul><ul><li>Identify Factors that Impact the Process Mean and Variation. </li></ul><ul><li>FISHBONE or CAUSE-AND-EFFECT DIAGRAMS </li></ul>
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<ul><li>Analyze: </li></ul><ul><li>Sources of Variation: </li></ul><ul><li>The Hypothesis Testing Algorithm </li></ul><ul><li>Formulate the Null and Alternative Hypotheses, H 0 and H A . </li></ul><ul><li>Specify the Sample Size and Significance Level of the Test, n and </li></ul><ul><li>Determine Which Type of Test Should be Employed. </li></ul><ul><li>State the Critical Value(s) & the Test Statistic & Specify the Decision Rule. </li></ul><ul><li>Collect and Validate Process Data. </li></ul><ul><li>Determine the Calculated Value of the Test Statistic ( Data Based ) </li></ul><ul><li>As Appropriate, Construct and Interpret Confidence Intervals. </li></ul><ul><li>Determine and Pursue a Course of Action. </li></ul><ul><li>Key Vocabulary: Type I and II Errors, and </li></ul>
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IX S IGMA S D EPARTMENT OF S TATISTICS E nd of S ession
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