Analyze Phase 327

FIGURE 10.3 UPS racing team pit crew.

that occur sporadically under specific conditions. As discussed in the Measure stage, the response to each of these types of variation differs significantly.

The potential sources of process variation may be brainstormed by the Six Sigma team using a cause and effect diagram. These potential causes must then be analyzed for their significance using more advanced statistical tools, including designed experi­ments and their associated enumerative methods.

The basic statistical methods, including confidence intervals and hypothesis tests, are discussed in the sections that follow. While these rather simple statistical methods may be used to directly compare a sample to its desired properties, or one sample to another, designed experiments will build on these concepts in applying ANOVA (anal­ysis of variance) techniques to multiple sources of variation, allowing quantification of the relative contribution of each source to the total error. General regression and corre­lation analysis is presented as a precursor to the designed experiments, to aid in the understanding of the experimental analysis techniques.

Cause and Effect Diagrams With most practical applications, the number of possible causes for any given problem can be huge. Dr. Kaoru Ishikawa developed a simple method of graphically displaying the causes of any given quality problem. His method is called by several names, the Ishikawa diagram, the fishbone diagram, and the cause and effect diagram.

Cause and effect diagrams are tools that are used to organize and graphically dis­play all of the knowledge a group has relating to a particular problem.

Constructing the cause and effect diagram is very simple. The steps are:

1. Draw a box on the far right-hand side of a large sheet of paper and draw a horizontal arrow that points to the box. Inside of the box, write the description of the problem you are trying to solve.

328 C hap te r Ten

2. Write the names of the categories above and below the horizontal line. Think of these as branches from the main trunk of the tree.

3. Draw in the detailed cause data for each category. Think of these as limbs and twigs on the branches.

A good cause and effect diagram will have many "twigs," as shown in Fig. lOA. If your cause and effect diagram doesn' t have a lot of smaller branches and twigs, it shows that the understanding of the problem is superficial. Chances are that you need the help of someone outside of your group to aid in the understanding, perhaps someone more closely associated with the problem.

Cause and effect diagrams come in several basic types. The dispersion analysis type is created by repeatedly asking "why does this dispersion occur?" For example, we might want to know why all of our fresh peaches don't have the same color.

The production process class cause and effect diagram uses production processes as the main categories, or branches of the diagram. The processes are shown joined by the horizontal line. Figure 10.5 is an example of this type of diagram.

The cause enumeration cause and effect diagram simply displays all possible causes of a given problem grouped according to rational categories. This type of cause and effect diagram lends itself readily to the brainstorming approach we are using.

A variation of the basic cause and effect diagram, developed by Dr. Ryuji Fukuda of Japan, is cause and effect diagrams with the addition of cards, or CEDAC. The main difference is that the group gathers ideas outside of the meeting room on small cards, as well as in group meetings. The cards also serve as a vehicle for gathering input from people who are not in the group; they can be distributed to anyone involved with the process. Often the cards provide more information than the brief entries on a standard cause and effect diagram. The cause and effect diagram is built by actually placing the cards on the branches.

Boxplots A boxplot displays summary statistics for a set of distributions. It is a plot of the 25th, 50th, and 75th percentiles, as well as values far removed from the rest.

Figure 10.6 shows an annotated sketch of a boxplot. The lower boundary of the box is the 25th percentile. Tukey refers to the 25th and 75th percentile "hinges." Note that the 50th percentile is the median of the overall data set, the 25th percentile is the median of those values below the median, and the 75th percentile is the median of those values above the median. The horizontal line inside the box represents the median. Fifty per­cent of the cases are included within the box. The box length corresponds to the inter­quartile range, which is the difference between the 25th and 75th percentiles.

The boxplot includes two categories of cases with outlying values. Cases with val­ues that are more than 3 box-lengths from the upper or lower edge of the box are called extreme values. On the boxplot, these are designated with an asterisk (*). Cases with values that are between 1.5 and 3 box-lengths from the upper or lower edge of the box are called outliers and are designated with a circle. The largest and smallest observed values that aren't outliers are also shown. Lines are drawn from the ends of the box to these values. (These lines are sometimes called whiskers and the plot is then called a box-and-whiskers plot.)

Despite its simplicity, the boxplot contains an impressive amount of information. From the median you can determine the central tendency, or location. From the length

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330 C hap te r Ten

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FIGURE 10.6 Annotated boxplot.

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of the box, you can determine the spread, or variability, of your observations. If the median is not in the center of the box, you know that the observed values are skewed. If the median is closer to the bottom of the box than to the top, the data are positively skewed. If the median is closer to the top of the box than to the bottom, the opposite is true: the distribution is negatively skewed. The length of the tail is shown by the whis­kers and the outlying and extreme points.

Analyze Phase 331

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Boxplots are particularly useful for comparing the distribution of values in several groups. Figure 10.7 shows boxplots for the salaries for several different job titles.

The boxplot makes it easy to see the different properties of the distributions. The location, variability, and shapes of the distributions are obvious at a glance. This ease of interpretation is something that statistics alone cannot provide.

Statistical Inference This section discusses the basic concept of statistical inference. The reader should also consult the glossary in the Appendix for additional information. Inferential statistics belong to the enumerative class of statistical methods. All statements made in this sec­tion are valid only for stable processes, that is, processes in statistical control. Although most applications of Six Sigma are analytic, there are times when enumerative statistics prove useful. The term inference is defined as (1) the act or process of deriving logical conclusions from premises known or assumed to be true, or (2) the act of reasoning from factual knowledge or evidence. Inferential statistics provide information that is used in the process of inference. As can be seen from the definitions, inference involves two domains: the premises and the evidence or factual knowledge. Additionally, there are two conceptual frameworks for addressing premises questions in inference: the design-based approach and the model-based approach.

As discussed by Koch and Gillings (1983), a statistical analysis whose only assump­tions are random selection of units or random allocation of units to experimental condi­tions results in design-based inferences; or, equivalently, randomization-based inferences. The objective is to structure sampling such that the sampled population has the same

meeting room on small cards, as well as in group meetings. The cards also serveas a vehicle for gathering input from people who are not in the group; they canbe distributed to anyone involved with the process. Often the cards providemore information than the brief entries on a standard cause and effect diagram.The cause and effect diagram is built by actually placing the cards on thebranches.

7M TOOLSSince Dr. Shewhart launched modern quality control practice in 1931, the

pace of change in recent years has been accelerating. The 7M tools are an exam-ple of the rapidly changing face of quality technology. While the traditionalQC tools (Pareto analysis, control charts, etc.) are used in the analysis of quanti-tative data, the 7M tools apply to qualitative data as well. The ‘‘M’’ stands forManagement, and the tools are focused on managing and planning qualityimprovement activities. In recognition of the planning emphasis, these toolsare often referred to as the ‘‘7 MP’’ tools. This section will provide definitionsof the 7M tools. The reader is referred to Mizuno (1988) for additional informa-tion on each of these techniques.

Affinity diagramsThe word affinity means a ‘‘natural attraction’’ or kinship. The affinity dia-

gram is a means of organizing ideas into meaningful categories by recognizingtheir underlying similarity. It is a means of data reduction in that it organizes alarge number of qualitative inputs into a smaller number of major dimensions,constructs, or categories. The basic idea is that, while there are many variables,the variables aremeasuring a smaller number of important factors. For example,

264 PROBLEM SOLVING TOOLS

Figure 8.10. Production process class cause and e¡ect diagram.

if patients are interviewed about their hospital experience they may say ‘‘thedoctor was friendly,’’ ‘‘the doctor knew what she was doing,’’ and ‘‘the doctorkeptme informed.’’ Each of these statements relates to a single thing, the doctor.Many times affinity diagrams are constructed using existing data, such asmemos, drawings, surveys, letters, and so on. Ideas are sometimes generated inbrainstorming sessions by teams. The technique works as follows:

1. Write the ideas on small pieces of paper (Post-itsTM or 3� 5 cards workvery well).

2. The team works in silence to arrange the ideas into separate categories.Silence is believed to help because the task involves pattern recognitionand some research shows that for some people, particularly males, lan-guage processing involves the left side of the brain. Research also showsthat left-brain thinking tends to be more linear, which is thought to inhi-bit creativity and pattern recognition. Thus, by working silently, theright brain is more involved in the task. To put an idea into a category aperson simply picks up the Post-itTM and moves it.

3. The ¢nal groupings are then reviewed and discussed by the team.Usually, the grouping of ideas helps the team to develop a coherent plan.

Affinity diagrams are useful for analysis of quality problems, defect data, cus-tomer complaints, survey results, etc. They can be used in conjunction withother techniques such as cause and effect diagrams or interrelationship digraphs(see below). Figure 8.11 is an example of an affinity diagram.

Tree diagramsTree diagrams are used to break down or stratify ideas in progressively

greater detail. The objective is to partition a big idea or problem into its smallercomponents. By doing this you will make the idea easier to understand, or theproblem easier to solve. The basic idea behind this is that, at some level, a pro-blem’s solution becomes relatively easy to find. Figure 8.12 shows an exampleof a tree diagram. Quality improvement would progress from the right-mostportion of the tree diagram to the left-most. Another common usage of tree dia-grams is to show the goal or objective on the left side and the means of accom-plishing the goal, to the right.

Process decision program chartsThe process decision program chart (PDPC) is a technique designed to help

prepare contingency plans. It is modeled after reliability engineering methodsof failure mode, effects, and criticality analysis (FMECA) and fault tree analysis(see Chapter 16). The emphasis of PDPC is the impact of the ‘‘failures’’ (pro-

7M tools 265

266 PROBLEM SOLVING TOOLS

Figure 8.11. Software development process a⁄nity diagram.From ‘‘Modern approaches to software quality improvement,’’ ¢gure 3,Australian Organization for Quality: Qualcon 90.Copyright# 1990 by

Thomas Pyzdek.