Six Sigma (6σ) Introduction There are lots of Six Sigma (6σ) definitions and interpretations. The Wikipedia definition: “Six Sigma is a set of tools and strategies for process improvement originally developed by Motorola in 1985.” is as good as any. Within the context of this definition, Six Sigma practitioners use a wide variety of tools (perhaps as many as 100 or more) to improve processes and/or identify and remove process defects. The Six Sigma Basic Tool Set This paper looks at a small subset of Six Sigma tools that appears to contain the most popular and widely used. The Component Engineer (CE) may on occasion want to use Six Sigma tools to identify a product problem or to improve a product process. Best Seven Tools (by popular acclaim) Each of the following tools references a American Society for Quality (ASQ) web site where more detailed explanations and Excel spreadsheet examples are available. Check sheet1 – The Check Sheet is used to gather data in a categorized way. The categoric data might be occurrences and the Check Sheet is used to tally the number of occurrences versus time or day or shift. The following list contains five different Check Sheet types. Figure 1 is a Frequency Check Sheet example. 1.Classification Check Sheet 2. Defect Location Check Sheet 3. Frequency Check Sheet 4. Measurement Scale Check Sheet 5. Check List Cause and Effect Diagram2 – The Cause and Effect Diagram (Ishikawa, Fishbone) derives its name from its structure which resembles a fish skeleton. Potential problem causes are listed along the fish bone lines. This tool is usually used by a group in a “brainstorming” session. The group might use the Five Whys8 as a mechanism for filling the skeleton with potential causes. Figure 2 shows two examples. Control Chart3 – The Control Chart was devised by Dr. Walter A. Shewhart in 1924. It’s purpose is to show in graphical form the behavior of a process over time. In addition to the process data, the Control Chart has two limit lines, an Upper Control Limit (UCL) and a Lower Control Limit (LCL). The limit lines represent process extremes within which the process data should be confined. Figure 3 presents a Control Chart that shows process data (randomly chosen resistor values from a normally distributed 1000 ohm 5% population). The LCL is 950 ohms (1000 – 5%) and the UCL is 1050 ohms (1000 + 5%). Pareto Chart4 – A Pareto chart is a Bar Chart of data usually used to rank occurrences that are plotted in decreasing order of relative frequency from left to right. Pareto charts find value in identifying the problems whose solution would provide the most “bang for the buck”. Figure 4 presents the Figure 1 data as a Pareto Chart. Scatter Diagram5 – A scatter plot or scatter diagram shows the distribution of data when both the x and y variables are numerical. This plot shows the correlation or lack of correlation between two numeric variables, one independent and the other dependent. Figure 5 shows a scatter plot. Stratification6 – Stratification takes a large data set and breaks it into smaller data groups that are homogeneous. For example, a process output may have wandered beyond specification limits. There may be data groupings that, looked at individually, would point to the most probable cause for the process going beyond specification limits. It is most frequently used to identity which of the smaller data groups most affect the process. Use stratification when data come from several sources or conditions, and when separating the sources or conditions helps to analyze the data.3 Data groups for potential stratification: Shifts Operators Days of the week Suppliers Departments Error codes Histogram7 – A Histogram is a Bar Chart that shows the frequency distribution of a data set. Figure 6 is a histogram of the Figure 1 data set. Figure 1 Check Sheet Frequency Type Occurrences Monday Tuesday Wednesday Thursday Friday Saturday Sunday Total Type 1 1 2 4 5 1 0 1 14 Type 2 1 1 3 0 2 2 1 10 Type 3 1 0 1 1 1 0 0 4 Type 4 1 2 2 2 0 0 0 7 Type 5 1 3 4 5 2 2 1 18 Type 6 1 0 1 0 1 0 1 4 Type 7 0 0 1 3 3 0 0 7 Type 8 1 2 2 4 2 2 0 13 Type 9 1 1 1 5 1 1 1 11 Type 10 1 0 0 3 1 0 0 5 Day Totals 9 11 19 28 14 7 5 93 The Figure 1 Check Sheet is a hypothetical collection of failure data over a seven day period. Each day is given a column. The first column contains ten failure types. From Figure 1 data one can create a Pareto chart as shown in Figure 4 and a Histogram as shown in Figure 6. The Pareto chart reflects the relative significance of failures by type with the most significant to the left and the least significant to the right. The Histogram plots the number of total occurrences by day. Figure 2 Cause and Effect Diagram – Two Examples As the two illustrations in Figure 2 show, problem categories have been identified and placed at the top of skeletal connections (ribs) to the central line (spine). Branching off each rib are specific possible causes unique to the main category. One might use the Five Whys8 to identify each major potential cause and again to further flesh out the skeleton. Figure 3 Control Chart Control Chart 1060 1040 1020 1000 UCL LCL Data 980 960 940 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 The Figure 3 Control Chart is a plot of 1000 ohm resistance values randomly selected from a normal distribution. The tolerance is 5% so one would expect all values to fall between the Lower Control Level (LCL) of 950 ohms and the Upper Control Level (UCL) of 1050 ohms. Any excursion above or below a control level signals an “out-of-spec” resistance value. Figure 4 Pareto Chart of Figure 1 Data Pareto Chart 30 25 20 Thursday Wednesday Friday 15 Tuesday Monday Saturday 10 Sunday 5 0 Pareto Distribution The Figure 4 Pareto Chart of Figure 1 data ranks the days from left to right in decreasing values. The “worst” day is Thursday, then Wednesday, then Friday. The Pareto Chart also often has a cumulative distribution line not included in the Figure 4 chart. The cumulative distribution values are calculated by adding each column’s value divided by the total number of incidents, i.e. 28/93, (28+19)/93, (28+19+14)/93, etc. The cumulative distribution line is usually expressed as a percent (%) of the total. So, the first three Pareto bars contain 61 of the 93 incidents or ~ 66% of the incidents. Figure 5 Scatter Diagram 8200 8150 8100 8050 8000 7950 7900 7850 7800 980 990 1000 1010 1020 1030 The Scatter Diagram is intended to show the existence or non-existence of correlation between two sets of data. In an Excel chart the chart type would be Scatter. There are methods for determining the level of correlation and whether or not the correlation is meaningful. Figure 6 Histogram of Figure 1 Data Histogram 20 18 16 Type1 Type2 14 Type3 12 Type4 Type5 10 Type6 Type7 8 Type8 Type9 6 Type10 4 2 0 Frequency Distribution The Figure 6 Histogram of Figure 1 data simply displays the frequency of occurrence by type. References: 1. http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/check-sheet.html 2. http://asq.org/learn-about-quality/cause-analysis-tools/overview/fishbone.html 3. http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/control-chart.html 4. http://asq.org/learn-about-quality/cause-analysis-tools/overview/pareto.html 5. http://asq.org/learn-about-quality/cause-analysis-tools/overview/scatter.html 6. http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/stratification.html 7. http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram.html 8. http://asq.org/healthcare-use/why-quality/five-whys.html .