7QC Tools: Fish Bone or Ishikawa Diagram

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Once we have prepared the process flow diagram, we need to list down the possible causes of a problem graphically so that everyone can understand. The Fish Bone diagram is a graphic tool that helps in displaying the possible causes of a problem or quality characteristic.

Usually Fish Bone diagram is also called as Cause & Effect diagram, but I beg to differ here as Fish Bone diagram only gives the list of probable causes that may or may not affecting the quality parameter. Hence, I take it as a misnomer. The reason being, we need to establish the Cause & Effect relationship downstream using scatter plot or Design of Experiments and only after that we can say cause & effect relationship is established.

The Fish Bone diagram helps in listing down the possible causes of variation through group discussion. It presents the list in a pictorial form, which is easily understandable, it also increases process understanding and tells us to collect the data for possible causes of variation.

It also categorizes the all possible causes of variation in 5 broad categories known as 5M

Men (problem because of people)

Material (problem because of raw material)

Machine (Problem due to Machine)

Methods (problem due to the measurement system or the process)

Management (problem related to management)

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Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

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7QC Tools: How to Extract More Information from the Scatter Plot?

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We saw the use of scatter plot for understanding the correlation between two variables in earlier blogs.

Now let’s see what we can do to extract more information from the scatter plot. Let’s take the earlier example, X7 Vs, Y

Picture35The graph above indicates no correlation, which is also evident by the R2 value of 0.0465. However, if we look carefully, it appears that most of the observations (blue circle) is trying to show some trend but, the two points (outside the blue circle) is influencing that trend in their  direction!

Now question to be asked is whether these two outlier or influential points is because of typo error or there are some special causes associated with these observations? Let’s assume that an investigation was carried out and it was found that there was no typo error but these points appeared as exception because of some special causes. What we should do now?

Since these two observation are because of some special causes hence, it is appropriate to ignore these points and re-construct the scatter plot as shown below.

Picture36The re-constructed scatter plot starts showing a trend of negative correlation between the above two variables.

Another way of extracting information is by dividing the scatter plot into four quadrant by plotting the mean of X and Y. After that we can focus on the quadrant where there is maximum concentration of observations.

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Another way of analyzing scatter plot is by augmenting it by regression analysis, where we can have a quantitative equation describing the relationship between the variables. This can easily be done with excel sheet. This will be discussed in subsequent blog.

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

7QC Tools: How to Draw a Scatter Plot?

 

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Option-1: using Excel sheet

Select the columns whose scatter plot is to be constructed and then go to Menu bar and select “insert” followed by scatter plot as shown below

Picture28 Picture30For displaying R2 value

Picture31

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

 

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Let’s take the of scatter plot of X3 Vs. Y from the previous example

Picture26

We can see that there is a very weak correlation between  X3 Vs. Y as the scatter plot is almost horizontal to the X-axis. Now manipulate the Y-axis, instead of starting from zero, start the Y-axis from 20 and in another scatter plot start it from 37. See what happens

Picture27

This is called as misuse of statistics, initially there seems to be no correlation between X3 and Y, but as you change the Y-axis, there seems to be a strong correlation, even though R2 value remains constant.

It always better to quote the R2 values along with the scatter plot.

Second issue with Scatter Plot is that it represents the correlation between the two variables which may or may not have a cause and effect relationship. What we want to say is that, the two variables are correlated by chance but in reality, they don’t affect each other. Hence, after scatter plot we need to establish the cause and effect relationship between X and Y by deliberately varying X and measuring its effect on Y. This is done more systematically with the help of Design of Experiments (DoE).

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

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Car Parking & Six-Sigma

7QC Tools: Scatter Plot

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In general after preparing flow chart there is a brainstorming session, and the outcome of this brainstorming session is the fish-bone diagram which in-turn list down the probable parameters or causes that can affect your quality parameter. At this step all parameters thus collected are only suspects (unless proven guilty!) and their role in affecting the quality parameters needs to be proved in order to held them guilty. In this regard historical data of all suspects (probable parameters or causes) are collected and their effect on the quality parameter is evaluated using scatter plot.

This evaluation can be dome by expert using ANOVA, Regression etc. but a visual tool was required which can tell a shop-floor person that a given parameter is affecting the quality attributes or not? In this regard scatter plot comes handy where you plot a given parameter against the quality attributes.

In real case scenario, we end-up with huge data base as shown below, where X1 to X8 represents the process parameters (suspects) and y represents the quality attribute of interest.

Picture20

By visual inspection of the above data, it becomes difficult to analyze the effect of X on Y, situation becomes worse if data is larger. Hence, scatter plot is a visual tool that gives qualitative correlation between X and Y.

Let’s look at the scatter plot of X1 and X2 Vs. Y

Picture22X-Axis represents X and Y-axis represents Y. we can see that in scatter plot of X1 Vs. Y, as the value of X1 increases, Y also increases. Whereas in X2 Vs. Y, there is no apparent correlation. Hence, we can conclude that X1 is affecting the Y and there is no effect of X2 on Y. We can also quantify the effect by calculating R2 values. R2 values can vary from -1 to +1. The values close to +1 indicates strong positive correlation whereas values close to -1 indicates strong negative correlation.

Scatter plot of all X Vs. Y are given below along with R2 values.

Picture23Picture24

Looking at the scatter plot given above, any shop-floor person can tell that X1, X3 and X5 are affecting the Y in positive way whereas, X4 and X8 are affecting the Y in negative way. Also X2 and X6 doesn’t have any effect on Y.

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

Also See

Car Parking & Six-Sigma

 

7QC Tools — Pareto Chart, How to Prioritize Your Work?

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Pareto Principle: It has been found that 80% of the trouble (defects) are because of 20% of the reasons. Hence, 6sigma or continuous improvement program focuses on controlling these 20% of the causes so that 80% of the defects are under control. This helps in setting the priority (focus area) for a 6sigma project.

We have seen that the histogram provides the frequency (number of observations) in a given class. However, the classes are not arranged in descending order.

Picture9

If the bars of a histogram are arranged in descending order of the frequency then that type of sorted histogram is called as Pareto Chart. Also, cumulative frequency is also plotted along with the frequency on the Pareto Chart.

Picture12

Picture13

In above example, if we can control reasons C, D and G then we can reduce the failures by 82% (see cumulative frequency).

Hence, Pareto Chart helps you in simplifying the bigger problem by identifying the vital few significant variables and enables you identify the focus on them with your limited resources.

Cumulative Frequency:

Picture14

Picture15

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

Kindly do provide feedback for continuous improvement

7QC Tools — How to Interpret a Histogram?

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Different data set would give histograms of different shapes as shown below. However, always remember to draw the histogram of your dataset first before taking any decision or starting a continuous improvement.

Picture15

Symmetrical histogram: A given process is stable and is normally distributed around the mean. If this kind of histogram is seen during a six-sigma project then probably you are required to reduce the variance in the process to reduce the width of the histogram so that you move away from the customer’s specifications.

Left or right skewed histogram: In both of these case, maximum number of data is scattered around the median (caution:  not the mean!) which represents the real measure of central tendency instead of mean in these cases of skewed data. Efforts in six-sigma should be on identifying the cause of skewedness and eliminating those causes.

Picture11Taking mean as the measure of central tendency in these case would be misleading as mean is affected by the extreme values in the data set.

If you are supposed to work on this type of data, find the reasons for those extreme observations and eliminate them. These are the low hanging fruit which we must take advantage of.

Picture17

Let’s take an example of the yield if a process is represented by following left skewed histogram

Picture19

Median gives an estimate that 50% of the batches are having yield at some value (say 85%) however, if we present mean as the measure of central tendency and tell to management that mean yield of the process is just 80%. Is it the right approach? We then just found the reason for those extreme left values and tell the management that by applying 6sigma, you have increased the yield to 85%!

Bimodal histogram: It means that the data set contains observations from two different populations. If it happens during any process then it must be assumed that there are two processes are running or two operators are working differently (which they are not supposed to do).

Picture16Note: If number of classes are less (<5) you can’t see the bimodal histogram. Just increase the number of classes to 7, 9, 11 etc. it would be evident if bimodal process is running.

Picture16

Be it management or a 6sigma practitioner, always draw the histogram of your data OR by default take median as the measure of the central tendency as it is not affected by the extreme values. Also see the effect of increasing the number of classes on the shape of the histogram for any deviation in the standard operating procedure.

Lesson learnt: while analyzing your data, always ask?

Where is the center? Which measurement of the central tendency I should consider for my data set based on the histogram?

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

Kindly do provide feedback for continuous improvement

7QC Tools — How to Draw a Histogram?

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First approach is by using the readymade template from ASQ, Histogram

Second approach is by using Excel sheet, following are the steps involved

Excel → data → data analysis → Histogram

Picture1

Third approach is manually, it involves following steps

Step-1: Calculate the range (maximum-minimum)

Step-2: Divide range by number of classes you want (usually 5 or 7). This will give you class width.

Step-3: Defining class intervals. This is done starting from the minimum value in the data set and by adding the class width (step-2) to it. This will give you 1st class interval.

Second class interval is obtained by adding class width to the upper class limit of the first class interval.

Step-4: Step-3 is repeated 5 to 7 times depending on the number of class interval (step-2)

Step-5: segregate the data according to the class interval, this will give the frequency of each class.

Step-6: plot the bar graph between classes and the frequency to give histogram.

Fourth Approach: Using Minitab

Step-1: Go to Graph in menu section and then click histogram

Picture27

Step-2: Once you click the histogram, a menu will appear where you require to select the type of histogram desired.

Picture28

Step-3: After selecting the type of histogram, another menu will appear which needs to be filled

Picture29

After filling the above data, click OK to get the histogram

Picture30

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

Kindly do provide feedback for continuous improvement