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SIX SIGMA AN OVERVIEW
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COPQ Category Internal Failures External Failures Appraisal Prevention
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FIGURE 2-8. contributions.
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Six Sigma Measurements. A defect is defined as any attribute of a product that does not provide total customer satisfaction. The Six Sigma methodology measures defects in two key ways: Defects per Unit (DPU) and Defects per Million Opportunities (DPMO). A unit is defined as the output of a process. For example, a unit for the accounts payable department may be an invoice; for the assembly area it might be a subassembly; and for the packaging department, it may be a package that will be shipped to the customer. The DPU can be calculated as follows: DPU Total number of defects Total number of units inspected or verified
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The DPU measurement uses total defects instead of total defective units. For example, when a cell phone is inspected and five defects are found, all defects must be counted, recorded, and included in the DPU calculation. Once the DPU is calculated, the first-pass yield can be calculated according to the following formula: First-pass yield e
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Normally, the yield is calculated according to the number of good units produced over the total units started. If utilized correctly, the yield number will appear more accurate. However, because the focus for improvement is on defects or errors, the number of defects must be measured; they point to the opportunities for improvement.
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CHAPTER TWO
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When using measurement or variable data, one needs to look at the distributions of data and utilize an appropriate distribution to determine probabilities of producing good product within specifications. The following steps can be used to predict yields based on the variable data: 1. Gather variable data. STEP 2. Calculate the average and the standard deviation. STEP 3. Calculate the probability of producing the product within specification, using the Normal distribution table (in any business statistics book or software). STEP 4. Add probabilities of producing the product within specification on both sides of the target. STEP 5. Subtract from 100 to determine the defect rate. The defect rate can be converted to parts per million.
STEP
For example, if the process, as shown in Figure 2-9, demonstrates standard deviation such that the 3 Sigma distance is equal to the specification limits, then the 99.73 percent process output will be acceptable. If, however, the standard
Lower Specification Limit
68.26% 95.44% 99.73%
Upper Specification Limit
FIGURE 2-9. Probability of producing products within limits at specified standard deviations.
SIX SIGMA AN OVERVIEW
deviation is reduced through process improvement, or the limits are opened up after negotiations with customers, such that the tolerances are higher than the 3 Sigma around the mean, then the predictable yield will be 99.9 percent or higher. It is at this point that the benefits of reduced inspection and testing become visible.
ANALYZE
During the analyze phase, the focus is on searching for the root cause. Based on the data analysis, opportunities are prioritized according to their contribution to customer satisfaction and impact on profitability. Pareto Analysis. The Pareto chart (see Figure 2-10) is a graphic representation of the opportunities for improvement. It is used in identifying the critical opportunities that will have the greatest impact on customer satisfaction and profitability. The chart was developed by J. M. Juran and named after the Italian economist Vilferado Pareto, who observed that most of the world s wealth is owned by a few individuals. Juran likewise
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FIGURE 2-10.
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Defect
Pareto chart of opportunities for improvement.
Percent
Count
CHAPTER TWO
found that most events in nature are not equal. For example, most revenues of a company come from a few large accounts, most of the deaths occur due to a few diseases, and most problems in an organization stem from just a few causes. The Pareto chart is designed to help businesses identify opportunities for improvement that cost more than the others and thus should be attacked first. The Pareto chart shows opportunity categories based on their impact or frequency. People tend to work first on opportunities that are easier to attack rather than those most important to attack. The purpose of using the Pareto chart is to promote work on important opportunities rather than on the easy ones. Cause-and-Effect Analysis. Once the most significant opportunities have been identified, a root cause analysis is performed. The cause-and-effect diagram is one tool used to diagnose the causes of a selected problem. Most failures are caused by problems with the machine, material, method, or mind (skills). In addition, the environment and measurement devices may cause failures. The cause-and-effect diagram is a great way to list potential causes. Once causes are listed, a cross-functional team can prioritize various causes and select a few on which to work. The cause-and-effect diagram is also called the Fishbone or Ishikawa diagram. As shown in Figure 2-11, the main branches can be relabeled according to the categories of causes to be investigated. In the case of financial losses, categories such as machines, methods, and materials might not be the appropriate categories to represent potential causes. In such cases, other causes can be fitted into the standard branches, or the branches can be relabeled. Multivary Analysis. Multivary analysis is an excellent tool to apportion variance in the area where opportunities for improvement exist. It dissects the variance into positional, cyclical, and temporal categories. The positional variation is caused by the variables that affect the process performance at certain locations within the process or the product. The temporal variation is attributed to the changes between cycles of a process and represents trends over time, i.e., shift to shift, day
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