The Six Sigma (6σ) PDF

0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat The Six Sigma (6σ) Introduction Six Sigma is based...

0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat The Six Sigma (6σ) Introduction Six Sigma is based on the concept of a natural curve introduced by Carl Friedrich Gauss (1777-1855), after that, in the 1920s Walter Shewhart used the concept as measurement standards to design the quality control charts. Later Six Sigma approach was first conceptualized at Motorola (Harry, 1998) as a response to the demand for its products, then developed in the late 1980s, by Bill Smith (1929 – 1993) along with Mikhel Harry , The aim of Six Sigma is reducing variation in major product quality characteristics to the level at which failure or nonconformities are extremely unlikely. In 1985 Bill Smith presented a paper about the correlation between the extent of repair a product underwent during production and its service life, Subsequently Mikhel Harry developed a structured Six-Sigma approach. Their development was dependent on the actions of others, such as Shewhart, Juran, Taguchi, Deming, and Ishikawa, and their contribution to quality control, total quality management, and zero defects, even though Motorola is the founder of six sigma. Credit for returning Japanese quality control methods to the United States goes to Smith, Harry, and Motorola chief executive officer (CEO) Bob Galvin. As a result of implementing the Six Sigma program, Motorola was the first to win the Malcolm Baldrige Award, then Six Sigma became widely known, accordingly, books, scientific research, and various studies have spread that dealt with Six Sigma from its multiple aspects, the most famous books [2, 3]. Then companies continued to apply this concept. Six Sigma has spread beyond Motorola and has come to encompass much more. Allied Signal was the next company to apply the concept in the early 1990s, then General Electric (GE) followed in 1995, then Ford, Nissan, and Honeywell in 2002, as shown in figure 1, the application of the concept then spread to several companies from that time until today, where the concept of Six Sigma is applied in many industrial environments, especially those companies that apply the principles of lean production management. Page 1 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Figure 1: Historical implementation of six sigma. There are three levels of Six Sigma applications. Level 1 Six Sigma aims to eliminate sources of defects and reduce variance, the case of Motorola in the 1980s is an example. Level 2 Six Sigma, the emphasis on eliminating sources of defects and variability reduction remained, focusing on tying these efforts to performance improvement activities through cost reduction, in 1995 General Electric was the leader of this generation of Six Sigma. Level 3 Six Sigma, where the Six Sigma focus extends creating value over production journey from cradle to grave, as applied by Bank of America in 2004, and Caterpillar in 2005. Six sigma has three different meanings. a) as a statistical tool, it focuses on maintaining 3.4 defects per million opportunities, b) as an improvement process, where the DMAIC (Define/ Measure/ Analyze/ Improve/ Control) approach considered the cornerstone for this process. c) and as a philosophy six sigma is focused on producing products and services in the most efficient and effective ways (lean six sigma). Statistical Background Process Sigma or process standard deviation, (σ), is a statistic that tells how output data (individual measurements, (xi)) spread out from the process mean, (μ) in terms of data units. As shown in figure 2, a larger standard deviation indicates a wider spreading of data around its mean. The population standard deviation (σ population) is a parameter, which is a fixed value calculated from every individual in the population, where as a sample standard deviation (σ sample) is a statistic, this means that it is calculated from only some of the individuals in a population as shown in figure 3. Page 2 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Figure 2: Wide and close standard deviation n n  (x i − μ )  (x − μ ) 2 2 i 2 2 σ Population = i =1 σ Sample = i =1 n n−1 n n  (x − μ )  (x − μ ) 2 2 i i Variance Population = i =1 Variance Sample = i =1 n n−1 Figure 3: Variation in population and sampling The process sigma level, or process, (z), is a measure with no unit for the distance from the mean, (μ), to an individual data value, (x), the higher the sigma level the fewer defects the process makes. x− μ z= = sigma level σ Accordingly, a given specification limit, (SL) is distant from the mean, (μ), by: SL −  z=  If the Upper Specification Limit (USL), and the Lower Specification Limit (LSL) at six standard deviations (6σ) on either side of the mean, then the process is a Six Sigma level process, in this situation the probability of producing a product within these specifications is 99.9999998, which corresponds to 0.002 part per million (ppm) defectives, as in figure 4. This web of page https://www.statology.org/area-between-two-z-scores-calculator/ is recommended to find the area between two Z-Scores calculator. Page 3 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Figure 4: Normal distribution centered at the target (T) with six sigma specification limits In this regard, I quote what Montgomery (2012) said : “When the Six Sigma concept was initially developed, an assumption was made that when the process reached the Six Sigma quality level, the process mean was still subject to disturbances that could cause it to shift by as much as 1.5 standard deviations off target”. This situation is shown in Figure 5 that explains the evaluation of Sigma quality level evaluation under all possible scenarios. Figure 5: Evaluation of sigma quality level under different scenarios Six Sigma and Quality Control Charts The Shewhart charts, or process behavior charts, are typically used to hear the voice of the process and to view the behavior of the process. Page 4 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Seven different types of control charts six sigma are commonly used. The Individual Moving Range (I-MR) chart, sample mean and range (x-bar R) chart, and sample mean and variance (x-bar s) chart, these three forms are used for continuous data type. Fraction nonconforming (p) control chart, number of nonconforming (np) chart, number of defects (c) chart, and number of defects per unit (u) chart, these four forms are used for discrete data type. All quality control charts have three main elements: one central line (mean), upper control limit (UCL) and lower control limit (LCL) at ±3 standard deviations of the mean. The area within the control limits covers 99.73% of all the points on the chart, and a nonconforming rate of at least 0.27% is expected. Mapping Critical Needs of Customer to the VOC Critical to Quality CTQ breakdowns customer needs into quantified needs. Inputs of any process create its output (Y) that must be linked to the Critical to Quality (CTQ) from the view of the customer. Customer’s CTQ include cost, quality, delivery, and others. The VOP is defined by the Process Output Variables (POV). The VOP is a function of all CTQ inputs (X), this analogy is depicted in figure 6. Figure 6: Mapping customer needs to the VOP A customer may require a length (Y) for a specific part equal to 100mm ± 5mm (VOC: LSL= 105 mm, USL= 95 mm). The length is affected by several inputs (x's), like the design, machine, processing technology, inspection, material, and labor etc. Part length (Y) = f (x 1, x2... xn). The strategy behind Six Sigma is to identify influencing and critical inputs and their root causes, so that the process produces the length closer to the VOC every-time with Page 5 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat minimal variation between units accurately and precisely, then control the reproduction process. The Six sigma approach to problem solving uses a transfer function, a transfer function is a mathematical expression of the relationship between the inputs and outputs of a system. Y = f(x) is the relational transfer function that is used by all six sigma practitioners. It is critical that you understand and embrace this concept. “Y” refers to the measure or the output of a process, its usually the primary process metric, “Y “is the measure of process performance that you are trying to improve, f(x) means “function of x.”, x’s are factors or inputs that affect the Y. In simple terms: process performance is dependent on certain x’s. The objective in a Six Sigma project is to identify the critical x’s that have the most influence on the output (Y) and adjust them so that the Y improves. With this approach, all potential x’s are evaluated throughout the DMAIC methodology. The x’s should be narrowed down to the vital few x’s that significantly influence the process performance. Figure 7 explains what variables affect auto accidents. Figure 7: Variable affected auto accidents (ref. ….. ) Defect Defective and Opportunities A defect is a flaw in a process or in a product where more than one flaw defect can be found. For example, a bill may have a defect in the (1) address line, (2) due amount, (3) quantity, (4) Page 6 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat client name, or (5) discount, any of these five errors is an opportunity to make a defect on the bill and can cause customer interruption and dissatisfaction. A defective product is a product that has one or more defects that make it nonconforming (unacceptable). A bill can have up to four different types of defects (conformities), which could then be defined as a defective one. A bill can be accepted (conforming) even though it has a slight spelling defect somewhere, while another bill is rejected (nonconforming) because it includes several defects in it, an incorrect due amount, client name, and wrong quantity. The two bills are not erroneous to the same degree although both have errors. This simple comparison illustrates the downside of using defective units as a measure of quality performance, thus quality scientists have adopted the number of defects as a measure. A unit is the final product shipped to a consumer. Opportunities are everything that turns into producing the final product – raw material, employees, shipping, etc. Each of these opportunities may have a defect. Number of defect opportunities refers to the number of issues or flaws that may occur. The most common process performance metrics used when considering six sigma are; Defects Per Unit (DPU), Defects per Million Opportunities (DPMO), Parts per Million Defective (PPM), and the Rolled Throughput Yield (RTY), before explaining how each is used, it’s important to know three terms, defect defective and opportunity, which are commonly used in connection with these metrics. Defects Per Unit and Defect Per Million Opportunity The average number of defects per unit is used to calculate what is called Defects Per Unit (DPU), if 50 units are made and a total of 150 defects have been found, the DPU equals 3. DPU is computed following equation (3). Total numberof defects foundin a sample DPU = (3) samplesize Defects Per Million Opportunities (DPMO) is the number of defects in one million opportunities. DPMO is computed following equation (4). Total numberof defects foundin a sample DPMO= (4) (samplesize)(numberof defectsopportunities per unitin thesample) Page 7 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Example: a bill may have a defect in the (1) address line, (2) due amount, (3) quantity, (4) client name, or (5) discount, any of these five areas is an opportunity to make a defect on the bill and can cause customer interruption and dissatisfaction, consider a sample of 100 bills, if total the total number of defects found in the sample is 150 defects, then DPU = 1.5, DPMO = 300,000, and the corresponding sigma level is 2.02, as shown below- figure 8. Total num berof defects foundin a sam ple 150 DPU = = = 1.5 sam plesize 100 Total num berof defects foundin a sam ple 150 DPMO = =  1,000,000= 300,000 (sam plesize)(num berof defectsopportunities per unitin the sam ple) (100)(5 ) Figure 8: DPMO and sigma level Figure 7 illustrates that a value of 300000 DPMO, returns 2.02 sigma level, the sigma level can be calculated in Microsoft office Excel using the code =(NORMSINV(1-(B3/1000000))) +1.5, where the value of DPMO in cell B3, see figure 9 which also shows that a value of 3.4 DPMO reflects a 6-sigma level. Figure 9: Converting DPMO value to a sigma level calculator Example (Copied on 2/12/2022 from: https://www.indeed.com/career-advice/career-development/what-is-dpmo-and-how-to-calculate-it.) Middleview Brake Pads Inc. produces millions of brake pads for a variety of vehicles each year. Recently, customers began reporting to their mechanics that their new brakes feel softer than usual, and mechanics informed Middleview that their inspection of the pads noted unusual dents. Middleview began a process improvement audit to discover the extent of the issue by using a sample of 1,000 brake pads. Page 8 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Their investigation found there were six opportunities for the dents to occur throughout the production process because of different machines being used. The audit turned up 450 pads with abnormal dents in the sample among the company's manufacturing plants. a. What is the number of defects opportunities for one dent? b. Compute the Defects Per Unit DPU c. Compute the Defect Per Million Opportunity DPMO d. Estimate the Sigma Level of the production process Total numberof defects foundin a sample 450 DPU = = = 0.45 samplesize 1000 Total numberof defects foundin a sample 450 DPMO = =  1,000,000= 75,000 (samplesize)(num berof defectsopportunities per unitin the sample) (1000)(6 ) Using Microsoft office Excel using, the code =(NORMSINV(1-(B4/1000000))) +1.5, where the value of DPMO =75000 in cell B4, yields 2.94 Sigma Level. Example (Copied on 2/12/2022 from: https://www.indeed.com/career-advice/career-development/what-is-dpmo-and-how-to-calculate-it.) Johnny's T's, a custom T-shirt company, has discovered some problems with a few of their recent orders. For every order, the company estimates there are three opportunities for defects to occur: a typo in the logo, incorrect coloration or general damage. They pull aside a sample of 200 T-shirts to inspect and find 26 total defects. The company typically ships a few thousand shirts a quarter, so they substitute in 1,000 for the 1,000,000 opportunities. and their calculation looks like this: a. What is the number of defects opportunities that may occur? b. Compute the Defects Per Unit DPU c. Compute the Defect Per Thousand Opportunity DPTO d. Estimate the Sigma Level of the production process Total numberof defects foundin a sample 26 DPU = = = 0.13 samplesize 200 Total numberof defects foundin a sample 26 DPTO = =  1,000= 43 (samplesize)(numberof defectsopportunities per unitin the sample) (200)(3 ) Page 9 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Using Microsoft office Excel using, the code =(NORMSINV(1-(B5/1000000))) +1.5, where the value of DPMO =43000 in cell B5, yields 3.22 Sigma Level. Parts Per Million Defective (PPM) PPM is the number of defective (nonconforming) units per 1 million units, the PPM would include the total number of defective products per every 1 million manufactured products, PPM is computed following equation (5). Total numberof defectiveunits foundin a sample PPM =  1000,000 (5) samplesize For example, a sample of 150 bills found that six are defective. The PPM defective is then: 6 PPM =  1,000,00 0 = 40,000 150 Rolled Throughput Yield (RTY) Rolled Throughput Yield (RTY) or the First Pass Yield, is the probability of producing a defect-free unit. This requires a map to know how many steps are involved in the production process. RTY is computed following equation (6). RTY = (Y1)(Y2)(Y3)(Y4)… (Yn) (6) Where yi is the probability (reliability) of producing a defect-free unit in process step i. Example It has been estimated that safe aircraft carrier landings operate at about the 5.2σ level, assuming the 1.5σ shift in the mean customary for Six Sigma applications. What DPMO does this imply? x − μ 5.2σ − 1.5σ z= = = 3.7 σ σ  (3.7) = 0.999892 DPMO = 1000,000(1− 0.999892)= 108(See figure 10) Figure 10: Example interpretation Page 10 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Example: A data point with a value of x = 35 mm is 12 mm away from a mean (μ) of 23 mm. If the standard deviation (σ) is 4 mm, the data point is (x-μ) /σ = 12/4) or 3 standard deviations away from the mean. Therefore, the process is at a 3-sigma level. To achieve the Six Sigma quality level, the process sigma (σ) must be reduced to 2. As shown by figure 11, this case is statistically investigated under two scenarios, scenario (A) of one side specification limit, and scenario (B) of two-sided specification limits, the sigma level and the Defects Per Million Opportunities, (DPMO) are computed for both cases. When the DPMO is calculated, it can be translated into the sigma level using the conversion scheme presented in table 1. Suggested Lean Six Sigma projects. Several examples of lean six sigma projects can be found in the literature, below is a list of some suggested projects’ areas. - Improving manufacturing cycle time - Improving help desk response time - Reducing a system downtime - Defects in the manufacturing - Number of failed welds - Medicare billing rejections for a healthcare organization - Failure to catch bid and tenders. - Improving forecasting accuracy and timing - Eliminating rework in preparing budgets and other financial documents Page 11 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Under Six Sigma Level Under the current Sigma Level Probability Z x (μ) (σ) Variation σ=2 σ=4 Probability Z x (μ) (σ) Cumulative mass DPMO = 0.000987 1350 Cumulative mass 0.00000 0.00000 -8.5 6 23 2 Sigma level = 6 3 0.00001 0.00001 -4.25 6 23 4 0.00000 0.00000 -8 7 23 2 0.00003 0.00003 -4 7 23 4 0.00000 0.00000 -7.5 8 23 2 0.00009 0.00009 -3.75 8 23 4 0.00000 0.00000 -7 9 23 2 0.00023 0.00022 -3.5 9 23 4 0.00000 0.00000 -6.5 10 23 2 0.20000 0.00058 0.00051 -3.25 10 23 4 LSL 0.00000 0.00000 -6 11 23 2 σ =2, μ = 23 0.00135 0.00111 -3 11 23 4 LSL 0.00000 0.00000 -5.5 12 23 2 6-σ Limit Level 0.00298 0.00227 -2.75 12 23 4 SL = 35 0.00000 0.00000 -5 13 23 2 0.15000 0.00621 0.00438 -2.5 13 23 4 0.00000 0.00001 -4.5 14 23 2 0.01222 0.00793 -2.25 14 23 4 0.00003 0.00007 -4 15 23 2 σ = 4, μ = 23, 0.02275 0.01350 -2 15 23 4 0.10000 3-σ Limit Level 0.00023 0.00044 -3.5 16 23 2 0.04006 0.02157 -1.75 16 23 4 0.00135 0.00222 -3 17 23 2 0.06681 0.03238 -1.5 17 23 4 0.00621 0.00876 -2.5 18 23 2 0.05000 0.10565 0.04566 -1.25 18 23 4 0.02275 0.02700 -2 19 23 2 0.15866 0.06049 -1 19 23 4 0.06681 0.06476 -1.5 20 23 2 0.22663 0.07528 -0.75 20 23 4 0.00000 0.15866 0.12099 -1 21 23 2 0.30854 0.08802 -0.5 21 23 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 0.30854 0.17603 -0.5 22 23 2 0.40129 0.09667 -0.25 22 23 4 0.50000 0.19947 0 23 23 2 0.50000 0.09974 0 23 23 4 0.69146 0.17603 0.5 24 23 2 0.59871 0.09667 0.25 24 23 4 0.84134 0.12099 1 25 23 2 0.20000 σ =2, μ = 23 0.69146 0.08802 0.5 25 23 4 0.93319 0.06476 1.5 26 23 2 6-σ Limit Level 0.77337 0.07528 0.75 26 23 4 0.97725 0.02700 2 27 23 2 LSL = 11 USL = 35 0.84134 0.06049 1 27 23 4 0.15000 0.99379 0.00876 2.5 28 23 2 0.89435 0.04566 1.25 28 23 4 0.99865 0.00222 3 29 23 2 σ = 4, μ = 23, 0.93319 0.03238 1.5 29 23 4 0.99977 0.00044 3.5 30 23 2 0.10000 3-σ Limit Level 0.95994 0.02157 1.75 30 23 4 0.99997 0.00007 4 31 23 2 0.97725 0.01350 2 31 23 4 1.00000 0.00001 4.5 32 23 2 0.98778 0.00793 2.25 32 23 4 0.05000 1.00000 0.00000 5 33 23 2 0.99379 0.00438 2.5 33 23 4 1.00000 0.00000 5.5 34 23 2 0.99702 0.00227 2.75 34 23 4 USL 1.00000 0.00000 6 35 23 2 0.00000 0.99865 0.00111 3 35 23 4 USL 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 1.00000 0.00000 6.5 36 23 2 0.99942 0.00051 3.25 36 23 4 1.00000 0.00000 7 37 23 2 0.99977 0.00022 3.5 37 23 4 1.00000 0.00000 7.5 38 23 2 Variation σ=2 σ=4 0.99991 0.00009 3.75 38 23 4 1.00000 0.00000 8 39 23 2 DPMO = 0.001973 2699.796 0.99997 0.00003 4 39 23 4 1.00000 0.00000 8.5 40 23 2 If the new σ is used to adjust the UNTL & LNTL 6- σ UNTL LNTL 0.99999 0.00001 4.25 40 23 4 1.00000 0.00000 9 41 23 2 DPMO = 2699.796 29 17 ??? 1.00000 0.00000 4.5 41 23 4 Figure 11: Statistical Example of the example Table 1: Converting DPMO into Sigma level Process Capability Analysis The off centeredness of the process output can be measured by the process capability index, Cpk, as follows, USL − x x − LSL  C pk = Min. ,   3 3  Page 12 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat A one Sigma level indicates a value of process capability equal to two (1/3), similarly, an n Sigma level indicates a value of process capability equal to two (n/3). Table 2, and table 3 present useful information about process capability indices. Process capability indices are commonly used in the measure phase and in the control phase, when processes are in statistical control, the following capability indices may be analyzed: PPM, DPPM, Z-short term and Z-long term scores, Cp, Cpk, Pp, and Cpm. Sigma measures the extent to which a process differs from perfection, based on the number of defects that may occur in a million units of output, at a Sigma level of two, a process, product, or service would create conformance 691463 times for every 1,000,000 opportunities, which creates a level of 308537 defects per million opportunities (DPMO). Table 2 below shows conformance level, and DPMO for variant values of process capability, Cpk, for every 1,000,000 opportunities, the tables, also shows that, six sigma performance creates a level of 3.4 defects per million opportunities (DPMO). Table 2: Conformance level, and DPMO for variant values Sigma level for every 1,000,000 opportunities. (σ) (μ) SL Sigma level Process Capability Conformance level DPMO Z= (SL-μ)/ σ Cpk (Yield/Million) 4 23 31 2 ⅔ 308537 691463 4 23 35 3 1.0 66807 933193 4 23 39 4 1⅓ 6210 993790 4 23 47 6 2.0 3.4 999996.6 Table 3: Useful information about process capability indices Index Abbreviation Formula Notes Process USL − x x − LSL  Cpk C pk = Min. ,  Capability  3 3  USL − LSL Long term Cp = 6 LT Along with z-  (X − X ) capability Process Pp 2 score and PPM Capability index  LT = n −1 Cp C pm = Taguchi 1+ (x − T ) 2 function of the Cpm w specification capability index  (X − X ) 2 limits, T. w = =s n −1 Page 13 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Voice of Customer vs. Voice of the Process The Voice of the Customer (VOC) provides; Lower Specification Limit (LSL), Upper Specification Limit (USL), and Target Value (or Nominal Value of specification). While the Voice of the Process (VOP) provides; Lower control limits (LCL), and Upper control limits (UCL). Reference to figure 10, The VOC is the space between the LSL and the USL, While VOP is the green curve line. The process in figure 12 is not meeting the VOC, a shift toward the USL reduces the non-conformances occurring above the USL. Figure 12: Presentation of VOC versus VOP In figure 11 process A is meeting customer specifications. The VOP is within the VOC, this distribution is more precise and more accurate, and too many resources are being committed to maintain this tight control of the process. Figure 13 also shows that process B is meeting customer specifications most of the time. However, there will be instances of non- conformance, distribution of process B is not precise and accurate, and in this case the process variation needs to be improved. Figure 13: Variant presentations of VOC versus VOP Continual improvement and DMAIC Six Sigma is a process of continuous quality improvement, where DMIAC and DFSS (Design for Six Sigma) drive this process, to improve an existing process DMAIC is followed, as shown by figure 14, DMAIC is an improvement cycle method that being used to drive Six Sigma missions, where many different tools can be used at each phase. The acronym DMAIC Page 14 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat comprises: Define, Measure, Analyze, Improve and Control. Actions that can be taken at each phase and the expected results of each phase are summarized in table 4. Design for Six Sigma (DFSS) Design for Six Sigma (DFSS) is an engineering design methodology that is followed when creating a new process, it is used to perfect products and processes prior to their production. DFSS is applied during the product design or process design phase. DFSS is tightly associated to operations research to address various dilemmas as in the example of trim loss, knapsack, workflow balancing, etc. DFSS is mainly a design effort requiring tools including, Quality Function Deployment (QFD), Design of Experiments (DOE), rapid prototyping, Taguchi methods, axiomatic design, theory of Inventive Problem Solving (TRIZ), Design for X, design thinking, system thinking, agile design, etc. Measure Project Y (output) Voice of Customer (VOC), Operational Definitions Analyze C&E Diagram, 5 Whys, C&E Matrix, Data Descriptive Statistics, Collection I-MR chart, Plan (DCP), Normality Plot (AD test), Sample Size Calculator, Process Capability Short/Long Term Data Performance Objectives Define Measurement System Hypothesis Testing CTQ Drilldown, Analysis (MSA) Problem Statement, Project Scope, Project Financial Savings, Pre-Assessment (Min/Max Analysis) Control Stakeholder Analysis (ARMI), Buy-In/ FMEA, Sponsorship (CAP model) Pilot/Implementation Plan, Scorecard, MSA Improve High-level Process Map, SIPOC Control Charts, SOPs, Control Plan, Project, Compiling Statistical Test Project Charter, Results, Project Storyboard Closure, Sponsorship Transfer Function Brainstorming Solutions, Impact Matrix (PICK chart), FMEA , Pilot Implementation Plan, Pilot Duration, Scorecard, MSA Figure 14: The DMAIC improvement cycle and tools that can be used at each phase. Page 15 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Table 4: Actions to be taken at each of the DMAIC phases and the expected output. Phase Description Questions Expected Phase output - Identify the process and the CTQ to be improved. - Problem Statement and its Understand the - How would you define the problem and output variables? Scope. problem, its scope - Define processes in all levels related to the problem. - Project Charter, Project Define and its surrounding - Define information needed and its corresponding Story Board environment communication methods? - SIPOC diagram and Map - Define a team that agrees with the problem focus. - Benefits expectations. - What information did you collect to assess or measure the problem, and how to verify its accuracy and precision? Gather reliable - Input variables xs - What metric reflects the output variables? information about - Output variables ys - How you can describe the information you collected, and Measure variables and - Voice of Customer (VOC) what if the information or your assumptions were wrong? measurement - A reliable and relatively - How would that have affected the situation? analysis comprehensive dataset - How to define defects and the causes (root cause) in the process and/or outputs? - Statistical analysis of root cause. - Identify and analyze the process capability and the voice of the process. Root cause - What is the targeted sigma level and objective - Process capability metrics, Analyze analysis and performance? - hypothesis testing results. validation - What information helped you confirm what the root cause - Statistical Results was? - Hypothesis testing and which input variables are significant. - What and how many improvements are needed to fix the - Improvement’s list Adjusting the input input variables xs? - List of outcomes Improve variables and - Eliminating the root causes? - Charts eliminating causes - Evaluating the improvement outcomes and their results - Evaluation out put - Make sure the improvements are implemented? - Check for successful and permanent resolving the considered problem. Implement the - Updated final project - Has the root cause recurred? If so, what measurements or resulting description. controls have put into place to prevent that root cause improvements, and - Control charts Control from recurring? maintain the - Control plans - Transferring control and the follow up responsibility of sustainability of - Standard Operating the improvements to the process owner. their application Procedure (SOP) - Ensure that the team, including the sponsor and the champion, has endorsed the improvements and their implementation. DFSS can be described as a business process management approach, like the DMIAC approach, DFSS is used in many industries including manufacturing, finance, marketing, engineering design, water treatment process, waste and bullion management, telecommunications, digital products, space industries, and more. DMADV is another acronym that is used sometimes in place of DFSS, DMADV comprises the following five steps: Define, Measure, Analyze, Design and Verify. Figure 15 presents those phases as well as the main activities that are handled by each phase. Page 16 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Launch pilot Verify/ validate Measure concepts Verify/ validate DFSS solutions Cycle Solutions implementation Evalution Figure 15: Design for Six Sigma (DFSS) approach Lean and Six Sigma Both Lean and Six Sigma are an improvement method to help improve performance of business processes. As a philosophy Six sigma focuses on what the systems produce from goods and services in the most efficient and effective ways, this is achieved by reducing defects and defective products and improving quality of accuracy level. In contrast to lean, focuses on increasing the efficiency of the production process itself through the elimination of probable sources of all types of waste. Efficiency means doing the right things, while effectiveness means doing things right. Therefore, lean targets efficiency and Six Sigma targets efficiency, while Lean Six Sigma targets efficiency and effectiveness, see figure 16. Figure 16: Six sigma as a philosophy for efficient and effective production. Page 17 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Six Sigma Organization and Certification The terms Six Sigma White Belt Certification, Six Sigma Yellow Belt Certification, Six Sigma Green Belt Certification, Six Sigma Black Belt Certification, Six Sigma Master Black Belt Certification, are terms given to individuals that practice the Six Sigma methodology. Criteria for such certification vary, there is no standard certification body, certification are offered by various quality associations, like the American Society for Quality. Table 5 shows the typical requirements for GBs, BBs, and MBs. Table 5: Typical requirement for Six Sigma Green Belt, Six Sigma Black Belt, and Six Sigma Master Belt Certification. Green Belts (GBs) Black Belts (BBs) Master Black Belts (MBBs) - Coursework of 40 hrs. – 160 hrs. - Coursework of 160 hrs. – 360 hrs. - 500-1,000 hours of coursework - Participation in at least one Six - Evidence of at least one project - Review of completed projects. Sigma project completion - Proof using project management - Mentoring of other Green Belts, - Proof using project management tools. White Belts, tools. - Proof showing application of or Yellow Belts - Proof showing application of statistics and hypothesis testing. - Proof using project management statistics and hypothesis testing. - Proof of understanding the Lean tools. - Proof of understanding the Lean principles. - Proof showing basic application of principles. - Mentoring of other Black Belts, statistics. - Mentoring of other Black Belts, Green Belts or Yellow Belts - Proof of understanding the Lean Green Belts, White Belts, or Yellow - Written examination principles. Belts - References - Written examination - Written examination - References http://www.six-sigma-material.com/Black-Belt-Training.html Leaders’ companies like Motorola developed Six Sigma organizational structure and certification programs at the relevant skill level. Following Motorola, many organizations started offering Six Sigma organization and certification to their employees. A typical Six Sigma organizational structure is shown in figure 17; this structure was adapted in 2005 by Snee and Hoerl. In the context of Six Sigma, the skills needed to fight quality problems are classified into several levels called “belts” mirrored from martial artists' colors. Each belt requires a corresponding skill level corresponds to the assigned roles when launching a lean Six Sigma project. Page 18 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat Figure 17: The structure of a Six Sigma organization. References: Harry, M.J. (1998) Six Sigma: A Breakthrough Strategy for Profitability. Quality progress, 31(5), pp.60-64. Shemelis N. W. & Ewnetim S. (2019). Six-Sigma for quality and productivity improvement of pharmaceuticals manufacturing industries. International Journal of Engineering Applied Sciences and Technology, Vol. 4, Issue 4, Pages 218-225. Niavand, H., & Tajeri, M. (2014). Statistical Control Process: A Historical Perspective. International Journal of Science and Modern Engineering (IJISME), Vol. 2, Issue 2, Pages 9-9. Harry, M. and Schroeder, R. (2000) Six Sigma: The Breakthrough Management Strategy Revolutionizing the World’s Top Corporations. Doubleday, New York. D.C. Montgomery (2012). Statistical Quality Control, A Modern Introduction, 7th edition, John Wiley & Sons, New York. Shewhart, W.A. (1931) Economic Control of Quality of Manufactured Product. D. Van Nostrand Company, Inc., New York. Breyfogle, F. W. III. (2003). Implementing Six Sigma: Smarter Solutions Using Statistical Methods (2nd ed.). Austin, TX: Smarter Solutions, Inc. Wiley. Page 19 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat De Feo, Joseph A.; Barnard, William (2005). JURAN Institute's Six Sigma Breakthrough and Beyond – Quality Performance Breakthrough Methods. Tata McGraw-Hill Publishing Company Limited. ISBN 0-07-059881-9. Snee, R., & Hoerl, R. (2005). Six Sigma: Beyond the factory floor. Financial Times Prentice-Hall Review Questions: Reference to figure 2, Explain the follwing Chart: ODD. Johnny's T's, a custom T-shirt company, has discovered some problems with a few of their recent orders. For every order, the company estimates there are three opportunities for defects to occur: a typo in the logo, incorrect coloration or general damage. They pull aside a sample of 200 T-shirts to inspect and find 26 total defects. The company typically ships a few thousand shirts a quarter, so they substitute in 1,000 for the 1,000,000 opportunities. and their calculation looks like this: a. What is the number of defect opportunities that may occur? b. Compute the Defects Per Unit DPU Page 20 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat c. Compute the Defect Per Thousand Opportunity DPTO num berof defectsopportunities = 3 Total num berof defects foundin a sam ple 26 DPU = = = 0.13 sam plesize 200 Total num berof defects foundin a sam ple 26 DPTO = =  1,000= 43 (sam plesize)(num berof defectsopportunities per unitin the sam ple) (200)(3 ) EVEN. Johnny's T's, a custom T-shirt company, has discovered some problems with a few of their recent orders. For every order, the company estimates there are three opportunities for defects to occur: a typo in the logo, incorrect coloration or general damage. They pull aside a sample of 100 T-shirts to inspect and find 12 total defects. The company typically ships a few thousand shirts a quarter, so they substitute in 1,000 for the 1,000,000 opportunities. and their calculation looks like this: a. What is the number of defect opportunities that may occur? b. Compute the Defects Per Unit DPU c. Compute the Defect Per Thousand Opportunity DPTO num berof defectsopportunities = 3 Total num berof defects foundin a sam ple 12 DPU = = = 0.12 sam plesize 100 Total num berof defects foundin a sam ple 12 DPTO = =  1,000= 40 (sam plesize)(num berof defectsopportunities per unitin the sam ple) (100)(3 ) 1. What are the primary differences in coursework and project requirements between the Six Sigma Green Belt (GB), Black Belt (BB), and Master Black Belt (MBB) certifications? The coursework hours vary significantly among the belt levels: - Green Belts (GBs) complete 40 to 160 hours of coursework and participate in at least one Six Sigma project. - Black Belts (BBs) require 160 to 360 hours of coursework and must provide evidence of at least one project completion. - Master Black Belts (MBBs) undertake extensive training, ranging from 500 to 1,000 hours, and must review completed projects to demonstrate their mastery of the subject. Additionally, as the belt levels increase, so do the technical requirements regarding the application of project management tools, statistics, and Lean principles. 2. How does the mentoring aspect differ among the various Six Sigma belt levels, specifically concerning whom they are expected to mentor? - Green Belts (GBs) are responsible for mentoring lower belt levels, specifically White Belts and Yellow Belts. - Black Belts (BBs) have a broader mentoring role as they mentor Green Belts, White Belts, and Yellow Belts, reflecting their advanced knowledge and experience. Page 21 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat - Master Black Belts (MBBs) mentor Black Belts, Green Belts, and Yellow Belts, and they typically have the highest level of expertise and leadership within the Six Sigma framework. 3. In what ways did organizations like Motorola influence the development and implementation of Six Sigma certification programs and the associated organizational structure? - Motorola pioneered the Six Sigma methodology in the 1980s, introducing a structured approach to quality management that emphasizes statistical analysis and process improvement. - They established a certification program that categorized skills into different belt levels, like martial arts, thus creating a clear hierarchy within Six Sigma roles. - Following Motorola's success, numerous organizations adopted and adapted Six Sigma practices and certification structures for their employees, leading to widespread implementation of Six Sigma methodologies across various industries and elevating the importance of quality management training. Certainly! Here are the questions along with their corresponding answers: 4. What are the key actions and expected outputs at each phase of the DMAIC improvement cycle in the context of continual improvement within Six Sigma? Answer: The DMAIC improvement cycle consists of five phases: - Define: Understand the problem and its scope. The expected outputs include a Problem Statement, Project Charter, SIPOC diagram, and the benefits expected from improvements. - Measure: Gather reliable data related to the problem. This phase results in inputs and outputs variables, Voice of the Customer (VOC) data, and a comprehensive dataset for analysis. - Analyze: Conduct root cause analysis to confirm problems and validate that the identified issues are indeed the root causes. Expected outputs include process capability metrics and statistical results from hypothesis testing. - Improve: Implement adjustments to input variables and eliminate root causes. The outputs from this phase include a list of improvements, charts illustrating results, and evaluation outputs documenting the outcomes of the initiatives. - Control: Ensure that improvements are sustained and properly implemented. The outputs are updated project descriptions, control charts, control plans, and Standard Operating Procedures (SOPs) to standardize successful changes. 5. How does the Design for Six Sigma (DFSS) methodology differ in its focus and application compared to the DMAIC process when developing new products or processes? Answer: The Design for Six Sigma (DFSS) methodology differs from DMAIC in that DFSS is primarily focused on creating new products and processes, while DMAIC is used to improve existing ones. DFSS emphasizes upfront planning and design validation during the development phase, using tools such as Quality Function Deployment (QFD) and Design of Experiments (DOE). It seeks to minimize defects and optimize performance before production begins, whereas DMAIC addresses problems and enhancements with a structured, iterative improvement process after a product or process is already in place. 6. In what ways do Lean and Six Sigma complement each other as improvement methodologies, particularly regarding their respective focuses on efficiency and effectiveness in business processes? Answer: Lean and Six Sigma complement each other by targeting different aspects of process improvement. Lean focuses on increasing the efficiency of production processes by eliminating waste and non-value-added activities, aiming for a streamlined operation. In contrast, Six Sigma aims to improve effectiveness by reducing defects and enhancing the quality of products and services. While Lean primarily seeks to achieve efficiency, Six Sigma addresses both efficiency and effectiveness, thereby ensuring that processes not only run smoothly but also meet quality standards. Together, they create a comprehensive approach to operational excellence, enhancing overall business performance. 7. How does the process capability index (Cpk) relate to the Sigma level, and what does a higher Sigma level indicate about process performance in terms of defects per million opportunities (DPMO)? Answer: The process capability index (Cpk) measures how centered the process output is within the specification limits. A Sigma level indicates the extent to which a process can produce defects: for instance, a one Sigma level Page 22 of 23 0906506 Lean and agile production systems 1st semester 2024/2025, date 11/01/2025 Prepared by Prof. Dr. Mohammad D. AL-Tahat corresponds to a Cpk of 2 (1/3), and an n Sigma level results in a capability equal to two (n/3). A higher Sigma level signifies better process performance, leading to fewer defects. For example, a six Sigma performance yields only 3.4 defects per million opportunities (DPMO), indicating a very reliable and highly capable process compared to lower Sigma levels that result in significantly more defects per million opportunities. 8. What is the significance of understanding both the Voice of the Customer (VOC) and the Voice of the Process (VOP) in achieving process improvement, and how can they impact customer satisfaction? Answer: Understanding both VOC and VOP is essential for effective process improvement and ensuring customer satisfaction. VOC captures customer requirements through specifications such as Lower Specification Limit (LSL), Upper Specification Limit (USL), and Target Value, while VOP reflects the actual performance of the process through control limits (LCL and UCL). If VOP remains within the VOC, the process meets customer expectations, leading to higher satisfaction. However, if VOP shifts outside the VOC (as seen in figure 12 in the handout papers), it will result in non-conformance and potential dissatisfaction. Thus, aligning VOP with VOC is critical to minimize variations and enhance the quality of products or services delivered to customers. 9. How did Motorola contribute to the development and popularization of the Six Sigma methodology? Answer: Motorola was pivotal in the development and popularization of Six Sigma in the late 1980s. Bill Smith and Mikhel Harry conceptualized the methodology to address product quality and reduce variation, initially using the principles of earlier quality control experts like Shewhart, Juran, and Deming. Motorola's implementation of Six Sigma not only led to significant improvements in their manufacturing processes but also earned them the Malcolm Baldrige Award. This success spurred other companies, such as General Electric, Ford, and Nissan, to adopt Six Sigma principles, showcasing its broader applicability across various industries. 10. What is the significance of the process sigma level and how does it relate to defect rates in a Six Sigma process? Answer: The process sigma level quantifies how far a process is from its target mean, with higher sigma levels indicating a lower likelihood of defects. When a process operates at a Six Sigma level, it is theoretically capable of producing fewer than 3.4 defects per million opportunities (ppm), corresponding to a near-perfect quality level. This measure emphasizes the importance of standard deviation in assessing process performance, as maintaining a sigma level of six means that the process continues to meet strict specifications even after accounting for potential shifts in the process mean. 11. What are the main components of quality control charts used in Six Sigma, and why are they important for process management? Answer: Quality control charts in Six Sigma consist of three main components: a central line (representing the process mean), an upper control limit (UCL), and a lower control limit (LCL), typically set at ±3 standard deviations from the mean. These charts are critical for monitoring process stability and performance, as they visually depict variations over time. By analyzing data points against the control limits, organizations can identify trends, shifts, or nonconformities, allowing for timely corrective actions to maintain quality standards. 12. How does the mapping of Critical to Quality (CTQ) needs to the Voice of the Customer (VOC) influence Six Sigma projects? Answer: Mapping Critical to Quality (CTQ) needs to the Voice of the Customer (VOC) is essential in Six Sigma projects as it helps ensure that customer requirements are translated into specific measurable process outputs. By identifying the relationship between input variables (x's) and output variables (Y), practitioners can focus on the critical influences affecting process performance. This alignment ensures that the process is optimized to deliver products or services that consistently meet or exceed customer expectations, ultimately enhancing customer satisfaction and reducing variations in quality. Page 23 of 23