Sampling Procedures for Extending the Use of
the Fishbone Diagram
Frank J. Matejcik
Industrial Engineering
South DakotaSchool of Mines and Technology
501 E. St. Joseph Street, Rapid City, SD 57701 -3901
Phone (605) 394-6066 e-mail:
Keywords: Fishbone; Ishikawa; capture; recapture
ABSTRACT
Procedures for creating a Fishbone diagram often assume all the possible participants are available. However, sampling among the participants may be required. The sampling problem is similar to a capture recapture. Methods for sampling decisions and experiences from classroom trials are discussed. Potential applications are mentioned, also.
I INTRODUCTION
The paper begins in the following section with a background discussion of how Ishikawa diagrams are currently used. The following section discuss the need for extending the method and the quality circle basic tool for gathering data to extend the method, which results in providing data as if we have a capture-recapture experiment. Accordingly, thefourth section discusses the state of the art of capture-recapture methods. Section five discusses how our problem is different than ecological experiments, which leads to section sixthat gives the details of a general procedure for applying the extended method. A relatively simple method computing estimates of completeness and suggestion follow up sample sizes is given in section seven.
The question of how an Ishikawa diagram may formally lead to further study is considered when section eight presents a complimentary procedure, a Pareto diagram related question set. Section nine discusses my current work. The article concludes with a summary section.
II ISHIKAWA DIAGRAM CURRENT STATE
The Ishikawa Diagram is also referred to as a fishbone diagram or a cause and effect diagram. Cause and effect describes the elements of the diagram. The diagram is begun by considering the effect, which may be a quality problem in a factory, a desired characteristic in an education system, or any clearly described condition. The diagram is drawn by applying a network of contributing causes. The completed network diagram (as show in figure 1) resembles a fishbone, in which the contributing causes branch from a main spine. Note that the sample graphics provided have fewer details than are typical in common use.
Figure 1 generic Ishikawa diagram
Figure 1 was prepared using Microsoft Visio, which is a chart tool which can be integrated with Microsoft Office. Visio has a special file request for the Cause and Effect diagrams. Of course, a Visio file can be e-mailed and used by all users with Visio. It can save to formats that can be read more generally. Visio has a free software/open source competitor Dia. There is no special file request for the Ishikawa diagram in Dia, but with the more general tools in Dia an Ishikawa diagram can be prepared. The format of the Dia file is open and can be used by other programs for further manipulations. The Draw tool in Open Office can also be used to create Ishikawa diagrams, and the format is of course open. The drawing tools in Microsoft Word can also be used to prepare an Ishikawa diagram.Pencil and paper can be used to create diagrams, and they can be readily scanned as a graphics file and e-mailed.
The Ishikawa diagram is part of the Quality Circle training that was developed in the 1960’s in Japan. All of these tools have been taught broadly and successfully since the 1960’s. Accordingly, many people are familiar with the method and teaching resources for the method are abundant. So, there is not reason to prevent the further teaching of the method.
The Ishikawa diagram is discussed beyond the Quality community. Some researchers have listed it among Qualitative Research tools. It is a competitor to other general qualitative research tools, such as focus groups. Much of my work here is inspired by a colleague’s suggestion that an Ishikawa diagram can be constructed to analyze a focus group transcript. My immediate response was “Why not just do anIshikawa diagram?”
Many sources (e.g. Ishikawa (1986), Juran and Godfrey (1998)) describe the Ishikawa diagram, but do not describe the procedure for getting the ideas from people’s minds to a diagram. Swanson (1995) does describe the process as beginning with a brainstorming session and continuing much like a brainstorming meeting. The drawing is constructed as a brainstorming notes record. Swanson (1995) mentions that frequently voting is done with the group, and the group making a recommendation of action for improving the situation described by the effect.
There are some implicit assumptions with this method. To run a brain storming session under conventional technology, everyone has to be in the same room. With additional technological enhancements everyone has to be working at the same time. Another assumption is that there enough people to state the causes that will help remedy the problem most effectively. There is a question that the people constructing the diagram have broad enough backgrounds to complete the task. Lastly, there is an assumption that there is no formal rule for deciding that the diagram is complete.
In the next section we describe procedures that extend the use the Ishikawa diagram both for situations where the people involved are at multiple sites and where sampling is required. The organization and additional documents required to deal with sampling also makes multiple site problems tractable.Fortunately, the use of e-mail makes transferring partially completed Ishikawa diagrams a relatively easy task, and by its nature e-mail is asynchronous.
IIIAPPLYING CAPTURE-RECAPTURE METHODS
In an overview, we assign individuals to complete Ishikawa diagrams and then the individual diagrams are combined. Combining the diagrams requires some discussion, because different terms may be used for the same object. Also, we have found from our trials with freshmen and work study students at the South Dakota School of Mines and Technology (SDSM&T) that having individuals begin with a common set of categories (see figure 1) for the Ishikawa diagram makes the task easier. We have not yet tried the procedure in a multi-site situation. The procedure can get quite detailed considering combining takes some work, sampling decisions are involved in the process, allowance for noting disagreement should be possible, and record keeping to aid the sampling needs to be done.
For record keeping we use a check sheet, another Quality Circle tool. Each cause on the Ishikawa diagram is listed vertically on the check sheet, and each individual involved being listed horizontally. See figure 2 for a generic example of a check sheet.
Figure 2 a generic check sheet
The data in this form has the same patterns as the results of animal abundance studies using capture- recapture methods. The causes in the extended Ishikawa procedure replace animals in animal abundance studies, and individuals in the extended Ishikawa procedure replace trapping sessions in animal abundance studies.
IV STATE OF THE ART OF CAPTURE-RECAPTURE METHODS
Capture-recapture methods are a mature area of Statistics with a long history. A particularly accessible recent book is Amstrup (2005). Additionally, the research is ongoing; Royle et al (2007) is a recent article describing Markov Chain Monte Carlo procedures for capture-recapture methods using WinBUGS. Anne Chao’s website ( ) includes numerous reference articles and softwarefor performing Capture-Recapture analysis. An extensive computer package with a 600 page free *.pdf file is MARK, which is available for free at
. Much of the best software in capture-recapture methods has been developed by government organizations and is available for free.
Royle et al (2007) describes other applications for capture-recapture methods. Most notably in software testing, where an error plays the role of animal, and tester replaces a capture session. Our application is similar in the sense that people replace capture sessions and observations replace the animals.
V DIFFERENCES IN OUR QUESTION
Many of themodels for capture-recapture studies involve continuous time sampling, which is not applicable in our setting. In fact, all trapping session are done at different times, whereas many Ishikawa diagrams are done at the same time. Additionally, the population of humans that may be sampled is finite. For example, we may be seeking opinions from students at one school or from workers for one company. This gives a finite sampling concern that does appear in ecological studies. Also, the causes in an Ishikawa diagram have a hierarchical nature, which animals do not have.
VI EXTENDED ISHIKAWA PROCEDURE
The procedure has a few layers. Stages contain steps; rounds are repeated sequences of steps. We work from the effect to a verified completed Ishikawa diagram.
Preliminary Setup
Phrase an effect statement to be studied. Select a team to begin the first chart, and manage the process. The team should represent the diversity of the entire population, and be at least five members to allow all common statistics to be computed. Our experience indicates that groups of nine or larger work more slowly.
Stage 0 Category Selection
Step 0.0 each team member is asked to write a list of categories.
Step 0.1 the team creates a combined list of the categories written in Step 0.0.
Step 0.2additional categories may be suggested by team members and added to the list created in Step 0.1.
Step 0.3 the team decides which categories will be included on the Ishikawa diagram. If a large number of categories are suggested for one diagram, multiple Ishikawa diagrams could be used with new effect statements that partition the original effect statement. Each of the multiple Ishikawa diagrams must follow the rest of the procedure separately.
Stage 1 Diagram Initiation
Step 1.0 team selects the locations of the categories on the Ishikawa diagram.
Step 1.1 each team member completes an individual Ishikawa diagram. A team member may add additional categories on the individual Ishikawa diagram at this time, if inspired by the work of constructing the diagram.
Step 1.2 the team members prepare a composite Ishikawa diagram based on Step 1.1 alone.
Step 1.3 each cause on the composite diagram should be labeled with a number. Label the corresponding causes on the individual Ishikawa diagrams. This step helps insure each item from the individual diagram is included on the composite diagram.
Step 1.4 the team members prepare a check sheet based on Steps 1.1-1.3 alone. Include labelsfrom Step 1.3 on the check sheet causes also.
Step 1.5 since viewing the work of others may inspire team members to observe additional causes (and possibly categories), team members may prepare an additions sheet which contains the new causes and/or categories.
Step 1.6 team members update the composite Ishikawa diagram from information on the additions sheets.
Step 1.7 team members update the Check Sheet from information on the additions sheets.
Step 1.8 Add label numbers to the revised diagram, the check sheets and the additions sheet analogous to Step 1.3
Repeat Steps 1.5 through 1.8 more as many rounds as required by the team.
Step 1.9 Compute Statistics from the Check Sheets if sampling is to be done. The next section describes procedures for these calculations.
Step 1.10 Determine whether a completion group is needed. If the group is not needed, go to Stage 3. If needed go to Step 1.9.
Step 1.11 Compute an additional sample size for a completion group.The next section describes procedures for these calculations. Sometimes for convenience or political concerns all possible people may be included in the completion group. Go to Stage 2
Stage 2 Diagram completion
Step 2.1 Select a completion group.
Step 2.2 Send each member of the completion group a copy of the currently updated Ishikawa and request that the additions be sent to the team.
Step 2.3 completion group makes additions (causes and possibly categories) and sends the results to the team.
Step 2.4 the team members prepare an updated Ishikawa diagram based on Step 2.3 alone.
Step 2.5 the team members prepare a Check Sheet based on Step 2.3 alone.
Step 2.6Add label numbers to the revised diagram, the check sheets and the additions sheet analogous to Step 1.3
Step 2.7 since viewing the work of others may inspire team members to observe additional causes (or possibly categories), team members now send updated Ishikawa diagrams to the group.
Step 2.8 group members may prepare an additions sheet which contains the new causes (or possibly categories), and return them to the team.
Step 2.9 team members update the composite Ishikawa diagram from information on the additions sheets.
Step 2.10 team members update the Check Sheet from information on the additions sheets.
Step 2.11Add label numbers to the revised diagram, the check sheets and the additions sheet analogous to Step 1.3
Repeat Steps 2.7 through 2.11 for as many rounds as required by the team.
Step 2.12 Compute Statistics from the Check Sheet began at Step 2.5. The next section describes procedures for these calculations.
Step 2.13 Determine whether anadditionalcompletion group is needed.If the group is not needed, go to Stage 3. If needed go to Step 2.14.
Step 2.14 Compute an additional sample size for a completion group and go to Step 2.1. The next section describes procedures for these calculations.
Stage 3 Follow Up Study
Stage 4 Reporting
Estimates of sample size and checks of completeness are introduced in the next section. A recommended follow up activity is included in section VIII. Reporting depends on the follow up training, the audience, and the team.
VII A COMPLETION CHECK RULE AND A COMPLETION SAMPLE SIZE ESTIMATE
We choose our notation to generally be consistent with Amstrup et al (2005). Let
Mk+1 = the number of causes found on the latest check sheet
MTOT = the total number of causes found since the end of stage 0.
= Estimated number of causes including only Mk+l, and the currently unobserved.
standard error of
=
C= from page 66,
Amstrup et al (2005)
d = portion of causes not observed
= an estimate of d
k= the number of users that have contributed to the most recent checksheet
p = the assumed probability of a cause being observed by an individual in the next check sheet
q = 1− p
r= the number required number causes to be observed so thatd will be as small as desired.
INT = an intermediate term, the mean of the geometric distribution order statistic based on r and p
= an intermediate term, the second moment of the geometric distribution order statistic based r and p
k+ = the number of users that we select to contribute to the next set of additions and be part of the next check sheet
To check the completion of the Ishikawa diagram begin by observingMk+land MTOT from the most recent check sheet data. Estimate and from the check sheet and calculations, which may be done using CARE-2 or another package. CARE-2 is easy to use, and computes many estimates of, and the Akaike Information Criteria. Judge appropriate values for both terms. Compute a point estimate of d, . Also, a 95% confidence interval for d is
If an interval estimate (NLB, NUB) for is given, an interval estimate of d, is
.
If both the point and interval estimates of d are as small as desired, no additional groups need be sampled.
Future work will likely use simulated check sheet data to decide an appropriate number of people to be selected for an additional group, k+. Here we use formulas based on approximate moments of the order statistics for the geometric distribution, which are listed in Evans et al (2006).
Select a value for p. You may choose the median probability of a cause in the previous check sheet. You may choose the average probability of a user selecting a cause from the previous check sheet.Other reasonable choices exist.
Choose a desired level of d, and then find the smallest integer r such that.
Finally, use the following three formulas to compute k+.
VIII EIPI
Once our work on the Ishikawa diagram (and possibly the check sheet) is completed, then we have a list of possible causes. Conventional quantitative analysis would lead to a survey with many questions. Our simplification is asking a few questions about the entire list of causes. Questions of this form include, “Which one cause is most important?”, “If you were to spend $10,000 to improve the situation, how much would you spend on each cause?”, and “Where on a scale of 1 to 6 would you rate each of the causes with 6 being the most important?”. The answers to our questions about the Ishikawa diagram causes can be summarized in a Pareto chart(shown in figure 3 below) (see e.g. Ishikawa (1986) or Juran and Godfrey (1998)). Pareto charts give direction for addressing problems.Hopefully, writing the questions will be simple enough for Quality Circles.
Figure 3 a generic Pareto Chart
The hybrid procedures are called Extended Ishikawa – Pareto Inspired (EIPI) procedures. Hopefully, the double rhyming acronym will be memorable and fun. A few people have mentioned that they are tempted to break into song upon hearing it.
We have an evolutionary Quality concept: expanding the use of Ishikawa diagrams by incorporating Quality Circle tools and sampling. Researchers that can print their instruments may call this is revolutionary. A qualitative tool is simple and cheap. A qualitative tool uses formal sampling and includes estimates of completeness. The quantitative tool is simple to prepare and leads to short, direct reports. In some cases (e.g. classroom assessmentand workplace multi-site problems with small populations) EIPI can be used with the completion group and the Pareto question group being the entire population, which simplifies the entire procedure to a Quality Circle level. Future work may lead to more convenient methods for estimating d and k+ , so most EIPI analyses to be performed at a Quality Circle level.