Once sampling for the independent variables or Ys and dependent variables or Xs has been collected, analytical tools can be used to understand relationships between independent and dependent variables. Each method is designed to answer a very specific question and requires that the data be in a specific format. These tools and methods include process maps, histograms, Pareto charts, box plots, scatter plots, time series graphs, and many others that will answer the questions the data collection was created to answer.
There are several types of process maps. Each one provides insight into how a process works, but from different perspectives. We have already discussed SIPOC charts and value flow maps. The discussion will focus on functional process maps. These maps show how material and information flow operation by operation over time through a process. The operations are organized within workstreams or swim lanes that are usually functional in nature. An advantage of this approach is that rework loops and multiple hand-offs are easily seen as work moves between functions. The operational work tasks, inspection tasks, movement of materials and information, and other activities taking place within a process are shown.
There are three common versions of this type of process map. The first is the current state or as-is version of the process. This version, which may be how the process is expected to work, is often inaccurate. The team must verify the accuracy of the current-state process map by walking the process operation by operation with the people who do the actual work. The second version of a functional process map is the future state, or what the process should be. The future state map is an optimized process. All non-value-add operations and rework loops will be eliminated in the future-state process. This methodology is like that used in value flow mapping, except there is a focus on swim lanes by function. Portions of value flow maps are often broken into functional process maps to study them in detail. Table 9.14 provides useful ideas for building a functional map. Process maps, in different formats, are also used throughout the DMAIC process, depending on the required analytical questions. Figure 9.16 shows how different types of process maps are used in the DMAIC phases.
Histograms are graphical summarizations of continuously distributed data. The histogram shown in Figure 9.17 shows the central location and dispersion of the number of returns by month. Notice the distribution
Building Effective Process Maps
is highly skewed right. Subsequent statistical analysis of the population’s central location or median will require the use of non-parametric tools and methods because the data are not symmetrical around the mean (i.e., the data are not normally distributed). Non-parametric methods will test
Where are process maps used? SIPOC = supplier-input-process-output-customer.
Histogram of returned goods.
a continuous distribution’s median rather than its mean. The median is a better estimate of central location for a skewed distribution. The returns histogram shown in Figure 9.17 could be used to describe the project’s baseline prior to the starting an improvement project to reduce returns. After a project is completed, it is useful to compare the before and after returns distributions to see of the median returns or its variation was reduced over the baseline scenario.
Pareto charts are useful for ranking discrete categories of a variable by relative count or frequency. In Figure 9.18, a second-level Pareto chart classifies inventory classes by four machines. Notice the inventory classes having the highest observed counts by machine are placed first on the chart and the others in descending order. Pareto charts are useful for root-cause analysis because they focus attention on categories with the highest contribution to total observed count. Pareto charts are also useful communication vehicles to stakeholders because they are easy to interpret. The data required to construct a Pareto chart must include several categories with each having an observed count.
Box plots graphically depict the central location and range of a continuous variable for one or more discrete categories or levels. Figure 9.19 shows a three-level box plot of monthly sales at three price levels within two industries and two regions. Notice that the average monthly sales changes for price level, industry, and region. The variation also changes for each discrete level of the three variables. The advantage of using a box
Pareto chart of inventory type by machine type.
Box plot of sales vs region, industry, price level.
Scatter plot of margin vs sales.
plot is that it depicts sample data without assuming a specictc probability distribution. The ends of the whiskers of each box are calculated using the following formulas: lower limit = Q1 - 1.5 (Q3 - Q1), and upper limit = Q3 + 1.5 (Q3 - Ql). The cirst, second, and third quartiles are represented by horizontal bars as shown in Figure 9.19. Box plots are useful for qualitatively comparing several variations and at several levels for each variable.
Scatter plots describe qualitative relationships between two continuous variables. In F igure 9.20, g ross margin i s plotted a gainst m onthly s ales and s tratiaed b у p rice 1 evel, r egion, a nd i ndustry. I n t he p attern s hown in Figure 9.20, it appears that margin increases as monthly sales increase. Scatter plots are useful for qualitatively evaluating how the dependent variable changes in response to a second variable. They are useful for preliminary a nalysis and prior to developing more quantitative models. As an example, if a scatter plot shows a curvilinear pattern, a subsequent higher- level mathematical model may show its quantitative relationship as Y = a + b, x X,2.
Time series plots show changes in a continuous variable over time. They are like scatter plots except that the independent variable or X is ordered by t ime. The c ontinuous v ariable i s о n t he Y a xis a nd t he t ime i ndex i s
Time series plot of scrapped units for all machines.
the X axis. Figure 9.21 shows a time series graph of scrapped units per day for several machines and the day of the year independent variable is sequential. The average scrap rate appears constant over the time period, but scrap variation appears high. Examples of useful time series include forecasting models and control charts.