7 Qc Tools Graphs: Significance and How to Use

7 Qc Tools Graphs

Histograms 

Purpose:  To determine the spread or variation of a set of data points in a graphical form.

Variation: It is always a desire to produce things that are equal to their design values.  For example, if we are producing several cylindrical objects having a certain diameter value, we wish that every part produced will have the same diameter value.  But this is not always the case.  We will always have variations in the values of the diameter between each produced part. Variation is everywhere.  It is found in the output of any process: manufacturing, service, or administrative.  But variation is not all bad.  One characteristic of variation is that it always displays a pattern, a distribution.  These patterns can tell us a great deal about the process itself and the causes of problems found in the process.  Histograms help us identify and interpret these patterns.

Figure 1

Histograms: A histogram is a tool for summarizing, analyzing, and displaying data.  It provides the user with a graphical representation of the amount of variation found in a set of data.  Histograms sort observations or data points, which are measurable data, into categories and describe the frequency of the data found in each category.

Constructing a Histogram: The following are the steps followed in the construction of a histogram: The following are the steps followed in the construction of a histogram: 

	Data collection:  To ensure good results, a minimum of 50 data points, or samples, need to be collected
	Calculate the range of the sample data:  The range is the difference between the largest and smallest data points. Range = Largest point – smallest point.
	Data points need to be divided on the X-axis into classes, look at Figure 1 above.  This is a very important step because how you select the class scale will determine the effectiveness of the histogram in interpreting the variation found in the data set.  Table 1 below lists some of the rules of thumb for determining the number of classes to use concerning the number of collected data points.

Table 1. Rules of thumb for class selection.

	Calculate the size of the class interval. The class interval is the width of each class on the X axis.  It is calculated by the following formula:  Class interval = Range / Number of classes.
	Determine the class boundary.  They are the largest and smallest data points that can be included in each class.
	Calculate the number of data points (frequency) that are in each class.  A tally sheet is usually used to find the frequency of data points in each interval.
	Draw the Histogram, as in Figure 1, and plot the data.

For example: Company X manufactures small resistors with a resistance value of 100 Ohms.  Recently, the company has been receiving numerous complaints from their customers about these resistors.  The value of the resistance has been deviating from the design value.  A team of workers was selected to investigate this deviation in the resistance values.  As a starting point, the team decided to construct a histogram to see the extent of variation in the resistance value.  A sample of 50 resistors from the production line was taken for the construction of the histogram.  The sample’s resistance values are listed in Table 2 below. 

Table 2. The resistance value for 50 resistors.

-The range of the fifty data points = 110 – 74 = 36.
-The Number of classes is 6 ( from Table 1).
-The class interval = range/number of classes= 36/6 = 6
-The class boundary and the frequency of each class are listed in Table 3 below. 

Figure 2

Table 3.

-Figure 2

above shows the histogram of the 50 resistor samples taken from the production line.  It is clear that the majority of resistors, about half, have a resistance value between 78 and 90 Ohms.  This makes us conclude that company X’s original assumption that the resistors have a resistance value of 100 Ohms is incorrect.  The next step is to look at the manufacturing process and determine the cause or causes of this deviation. 

Conclusion: Histograms are simple tools that allow the user to identify and interpret the variation found in a set of data points.  They are used to summarize and display data in a simple but clear manner.  It is important to remember that histograms do not give solutions to problems.  They only provide a starting point for the improvement process.  Also, the results obtained from any histogram will depend on the date on which the histogram is made.  If the data is inaccurate then any result obtained from the histogram is also inaccurate.

Flow Charts

Purpose:  Flow Charts visually illustrate the sequence of operations required to complete a task.

Flow Charts: Flowcharting is the first step we take in understanding a process.  Whether this process is an administrative or a manufacturing one, flow charts provide a visual illustration, a picture of the steps the process undergoes to complete its task.  From this picture, we can see how this process and the elements comprising it, fit into the overall picture of the business.  Every process will require input(s) to complete its task and will provide output(s) when the task is completed.  For example, an injection molding machine requires inputs in the form of raw material and proper machine settings to be able to produce a proper part.  The output of the injection molding process is the finished part. (See above picture)  Flow charts can be drawn in many styles.  They can be drawn by using pictures, engineering symbols, or just squares and rectangles.  Also, flow charts can be used to describe a single process, parts of a process, or a set of processes.  There is no right or wrong way to draw a flow chart.  The true test of a flow chart is how well those who create and use it can understand it.

 Construction of the Flow Chart (General guidelines): 

* Involving the right people in making the flow chart.  This includes people who do the work of the process, supervisors, suppliers to the process, and customers to the process.

* Flow charts usually require more time to construct than expected.  Therefore, enough time must be allotted to the group members to finish their work.

* Asking questions is the key to the flowcharting process.  The more questions everyone asks the better.  Here is a list of helpful questions to ask when constructing a flow chart:

1. What is the first thing that happens?
2.What is the next thing that happens?
3.Where does the output(s) of this operation go?
4.Where does the input(s) to the process come from?
5.How does the input(s) get to the process?
6.Is their anything else that must be done at this point?

A Special Benefit of Flow Charting:  People involved in constructing a flow chart begin to better understand the process.  They begin to identify areas for improving the process.  They also begin to realize how the process and all the people involved, including them, fit into the overall process or business.  Because of their involvement, they become enthusiastic supporters to quality and process improvement.  Finally, they all begin to understand the process in the same terms.

Conclusion:   Flow charts allow the user to have a visual illustration of a process.  They are the first step in the process of understanding manufacturing as well as administrative processes. They encourage team work and employee involvement.

Scatter Diagrams

Purpose:  To identify correlations that might exist between a quality characteristic and a factor that might be driving it.

Scatter Diagrams:  A scatter diagram is a nonmathematical or graphical approach for identifying relationships between a performance measure and factors that might be driving it.  This graphical approach is quick, easy to communicate to others, and generally easy to interpret.  Figure 1 below shows a commonly used structure for a scatter diagram.  The data needed to construct the scatter diagram must be collected in pairs (X,Y).  Almost always the performance characteristic, Y, is plotted on the vertical axis, while the suspected correlated factor, X, is plotted on the horizontal axis.  The point of intersection between the two axes is the average of each of the sets of data (i.e. the average of all the X’s and the average of all the Y’s).  The collected data is not for only observing the quality characteristic under investigation but also observing other factors or causes that might have an impact on the quality characteristic.  For example if we are taking measurements of the surface finish of a machined part, we will want to take measurements of other factors such as feed rate and tool condition that could have an effect on our surface finish quality characteristic.

Constructing the Scatter Diagram:

	Step 1:  Select the two items you wish to study.  The results of the cause-and-effect diagram could be very helpful in determining which items to select.  For example the two items could be an effect and a related cause.
	Step 2:  Collect the data.  The more data you have more accurate your conclusions will be.  Always remember that the type of data needed to construct the scatter diagram is paired.
	Step 3:  Draw the axis of the scatter diagram.  Remember that the performance characteristic in on the Y axis, and the suspected correlated factor on the X axis.  The point of intersection of the two axes is the average of each of the sets of data.  You can also make the origin point (0,0) your intersection point.
	Step 4:  Plot each set of paired data onto the graph (i.e. (Xo,Yo), (X1,Y1),(X2,Y2),……,(Xn,Yn), where n is the number of samples taken.

Interpreting the Results: Once all the data points have been plotted onto the scatter diagram, you are ready to determine whether their exists a relation between the two selected items or not. When a strong relationship is present, the change in one item will automatically cause a change in the other. If no relationship can be detected, the change in one item will not effect the other item. Their are three basic types of relationships that can be detected to on a scatter diagram:

Figure 1

1. Positive relationship; As the item on the X axis increases, the item on the Y axis also increases, and vice versa, look at Figure 1.

Figure 2

2. Negative relationship; As the item on the X axis increases, the item on the Y axis decreases, look at Figure 2.

Figure 3

3. No relationship; Changing the values of item X does not have any effect on the value of item Y, look at Figure 3.

Conclusion: Scatter diagrams allow the user to graphically identify correlations that could exist between a quality characteristic and a factor that might be driving it.  It is a quality tool that is simple, easy to communicate to others, and generally easy to interpret.

Pareto Charts

Purpose:

The purpose of the Pareto chart is to prioritize problems – to decide what problems must be addressed.  No company has enough resources to tackle every problem, so they must prioritize.  The purpose of this report is to inform the reader of the Pareto principles and how it can be applied to the manufacturing environment.  I will try to answer commonly asked questions regarding the Pareto process.

Pareto Principle:

The Pareto concept was developed by the Italian economist Vilfredo Pareto describing the frequency distribution of any given characteristic of a population.  Also called the 20-80 rule, he determined that a small percentage of any given group (20%) account for a high amount of a certain characteristic (80%).  For instance in the BYU Law parking lot, there are basically 9 different colors of cars: white, blue, red, black, tan, silver, brown, yellow, and green.  I decided to illustrate the Pareto principle by the different colors of cars. All colors are not created equally. Out of the nine different colors, three (red, blue, and white) make up about 64% of the cars.  The same principle can be applied to all aspects of manufacturing.  The Pareto chart is especially helpful in improving manufacturing processes.

Where do I begin?

The important thing is to begin.  Start somewhere.  Choose a process that is not producing the yields you would like it to produce.  Are there an excess amount of parts that you are having to rework or scrap?  Why?  What are the reasons for scrapping those parts?  Make a list of the causes of the problem.  Don’t worry about narrowing the list because it will narrow itself.  Keep track of the number of scrapped or reworked parts and what the reason is.  In the example above, I wanted to know what color of car was most popular.  I could have also

counted cars by their brand, or their type (compact, subcompact, etc.)  It doesn’t really matter.  As the data begins to come in, then you can make more decisions.

What do I do next?

After you have collected a sufficient amount of data, chart what you have.  In my example, I used the number of cars.  This is a great method.  However, you may want to keep track of the cost of each product failure.  For example, if you have a milling operation, and scratching the surface of the product causes the most reworks, but it only costs $2 to correct, whereas milling an uneven surface, while occurring less often, is actually more expensive to correct.  That is something that you must decide, whether to go by cost or total numbers.  If you don’t know which to choose, then do both.

There may be times where different products come off the same production line.  In this instance, it may be important to keep charts on the different products.  For instance, there may be 10 scraps out of 10,000 of product A; whereas with product B, there may be 8 scraps out of 100.  If you were to group the whole process together, the problem with product B might not be discovered.  Be aware of grouping products together that come from the same process.

Now you should have an idea of what problems are most troublesome.  There should be two or three problems that stick out.  Focus on those problems causing the greatest number of reworks or those problems which are the costliest.

After you feel you have improved the process, do another Pareto chart and find out if your improvements worked.  If they did, great! and your Pareto chart shows some new problems that must be worked on.  Continually improve on the problem that is causing the greatest harm.

Conclusion

You can’t choose the wrong process or the wrong problem to run a Pareto chart on.  The most important thing in improving quality is to start somewhere, doing something.  As you begin using the Pareto chart to decide where your problems are, you will discover many things about your processes and will come because you will know where to improve. 

Cause-and-Effect Diagrams

Purpose:

One important part of process improvement is continuously striving to obtain more information about the process and it’s output.  Cause-and-effect diagrams allow us to do not just that, but also can lead us to the root cause, or causes, of problems.  It is a tool that enables the user to set down systematically a graphical representation of the trail that leads ultimately to the root cause of a quality concern or problem.

Cause-and-Effect Diagram:

First developed in 1943 by Mr. Ishikawa at the University of Tokyo, the cause-and-effect diagram, also known as the fishbone diagram, relates the symptom or problem under question to the factors or causes driving it.  It accomplishes this through a hierarchical relationship between the effect, the main causes of this effect, and their subsequent relationship to the sub causes.  While a cause-and-effect diagram can be developed by an individual, it is best when used by a team.  A cause-and-effect diagram consists primarily of two sides.  The right side, effect side, lists the problem or the quality concern under question.  While the left side, cause side, lists the primary causes of the problem.  The right hand side can also include a desired effect the user wishes to achieve.  The picture below is an example of a eause-and-effect diagram.  The symptom or Quality Concern is the “Black Spots” that are occurring in an injection molding process.  The main causes that could give rise to the problem are the machine, the raw material, the method or process procedures, and the human element.  Each of these main causes is composed of sub causes that influence or effect the quality concern under question.  The selection of the headings for the main causes could be generic, such as Man or Method, or they can be specific such as Training or Wrong Speed.  The important thing is to continually define and relate causes to each other.

Constructing the Cause-and-Effect Diagram:

Step 1:  Select the team members.  It is preferable that the team members are knowledgeable about the quality concern under question.  One of the team members is selected as the team leader (Facilitator).  His job is to listen to the ideas presented by the other team members, capture those thoughts in simple words and write them on the chart.  Also to keep the team members focused on the problem under investigation.

Step 2:  Assuming that the quality concern has been identified, write this concern as a problem statement on the right hand side of the page, and draw a box around it with an arrow running to it.  This quality concern is now the effect.

Step 3:  Brain-storming.  The team members generate ideas as to what is causing the effect.  Main causes as well as sub causes are identified.  As indicated earlier, the team could choose generic or specific headings for describing the main causes.

Step 4:  This step could be combined with step 3.  Identify, for each main cause, its related sub-causes that might effect our quality concern or problem (our Effect).  Always check to see if all the factors contributing to the problem have been identified.  Start by asking why the problem exists.  If a cause is identified, repeat the question again.  When no other causes can be identified, you have likely identified all the possible causes to the problem.

Step 5:  Focus on one or two causes for which an improvement action(s) can be developed using other quality tools such as Pareto charts, check sheets, and other gathering and analysis tools.  This will depend on the team members themselves on where and how to start.  Agreement between the team members must be based on consensus.

Conclusion:

Improvement requires knowledge.  The more information we have about our processes the better we are at improving them.  Cause-and-effect diagrams are one quality tool that is simple yet very powerful in helping us better understand our processes.  They are a tool that fosters team work, helps to show the true picture, can be used on any issue of the business, and they are fun.

Check Sheets

Purpose:

Check sheets allow the user to collect data from a process in an easy, systematic, and organized manner.

Data Collection: 

Before we can talk about check sheets we need to understand what we mean by data collection.  Process improvement actions are always based on information obtained from data collected from the actual process.  This collected data needs to be accurate and relevant to the quality problem being analyzed if we wish for our information about this problem to also be accurate.  Information is based on data.  There are three primary steps that need to be taken before any data can be collected.  The first is to establish a purpose for collecting this data.  This is based on the quality problem that is going to be investigated.  Second, we need to define the type of data that is going to be collected.  Data can be collected in two ways: Measurable data such as length, size, weight, time,…etc., and countable data such as the number of defects.  Which type of data to use again depends on the quality problem being investigated.  The third step is to determine who is going to collect that data and when it should be collected.  Usually one can use statistical guides on when to take samples, or data points, from a process.  As for who is going to collect the data, what is important is that the person collecting the data understands the purpose of collecting this data and his role in the data collecting process.

Check Sheets: 

Check sheets are some of the most common tools used for collecting data.  They allow the data to be collected in an easy, systematic, and organized manner.  Also, data collected using check sheets can be used as input data for other quality tools such as Pareto diagrams. There are four main types of check sheets used for data collection (custom check sheets can also be designed to fit specific needs):

1.Defective Item Check Sheet:

This type of check sheet is used to identify what types of problems or defects are occurring in the process.  Usually these check sheets will have a list of the defects or problems that may occur in the process.  When each sample is taken, a mark is placed in the appropriate column whenever a defect or a problem has been identified.  The type of data used in the defective item check sheets is

countable data.  Table 1 below shows an example of a defective item check sheet for the wave solder manufacturing process.

Table 1.  Wave Solder Defect Count.

2. Defective Location Check Sheet:     

These type of check sheets are used to identify the location of the defect on the product.  They are used when the external appearance of the product is important.  Usually this type of check sheet consists of a picture of the product. On this picture, marks can be made to indicate were defects are occurring on the surface of the product. 

3. Defective Cause Check Sheet: 

This type of check sheet tries to identify causes of a problem or a defect.  More than one variable is monitored when collecting data for this type of check sheets.  For example, we could be collecting data about the type of machine, operator, date, and time on the same check sheet.  Table 2 below is an example of this type of check sheets.  As we can see most of the error is occurring at machine 2 and at the afternoon shift.  This could suggest that machine 2 has problems when it is run in the afternoon shift.

Table 2. Defect cause check sheet.

 X= Number of times the supervisor is called per day.

4. Checkup Confirmation Check Sheet: 

This type of check sheet is used to ensure that proper procedures are being followed. These check sheets usually will have a list of tasks that need to be accomplished before the action can be taken.  Examples of checkup confirmation check sheets are final inspection, machine maintenance, operation checks, and service performance check sheets.  

Conclusion: 

Check sheets are helpful tools for proper data collection.  They are easy to use and allow the user to collect data in a systematic and organized manner.  Many types of check sheets are available.  The most common are the defective item, defective location, defective cause, and checkup confirmation check sheets.

Control Charts

Purpose:

To ensure that the process is in control and to monitor process variation on a continuous basis.

Statistical Process Control:

The development and use of statistics and statistical theories about distributions and how they vary has become the corner stone of process improvement.  More known as statistical process control, SPC, this method allows the user to continuously monitor, analyze, and control the process.  It is based on the understanding of variation and how it effects the output of any process.  Variation is the amount of deviation from a design nominal value.  Not every product that is produced will exactly match it’s design nominal values.  That’s why we have tolerances on the nominal values to judge whether a product is acceptable or not.  But the closer we are to the nominal value the better the product is.  Control charts is one SPC tool that enables us to monitor and control process variation.

Common and Special Cause Variation: 

Variation in a process can be caused by, or related to, two types of causes.  They are common or system causes and special or local causes.  Special causes are problems that arise in a periodic fashion.  They are somewhat unpredictable and can be dealt with at the machine or operator level.  Examples of special causes are operator error, broken tools, and machine setting drift.  But this type of variation is not critical and only represents of small fraction of the variation found in the process.

Common causes are problems inherent in the system itself.  They are always present and effect the output of the process.  Examples of common causes of variation are poor training, inappropriate production methods, and poor workstation design.  As we can see, common causes of variation are more critical on the manufacturing process than special causes.  In fact Dr. Deming suggests that about 80 to 85% of all the problems encountered in production processes are caused by common causes, while only 15 to 20% are caused by special causes.

Control charts:

Developed in the mid 1920’s by Walter Shewhart of Bell labs, this SPC tool has become a major contributor to the quality improvement process.  It allows the

use to monitor and control process variation.  It also allow the user to make the proper corrective actions to eliminate the sources of variation.  Even though they require the user to have some statistical background, the are relatively easy to construct.  There are two basic types of control charts, the average and range control charts.  The first deals with how close the process is to the nominal design value, while the range chart indicates the amount of spread or variability around the nominal design value.  A control chart has basically three line: the upper control limit UCL, the center line CL, and the lower control limit LCL.  These lines are computed from samples taken from the production line.  Each sample represents a point on the control chart.  A minimum of 25 points is required for a control chart to be accurate.  To better understand the use of a control chart and how it is constructed we present the following example:

Construction of a Control Chart:

A manufacturing process produces gasket material blanks.  In order to better understand the manufacturing process, it was suggested to the manufacturing engineer to construct a control chart.  After meeting with his team, he decides to construct a control chart for the thickness of the gasket material blanks.  The team decides to take a sample size of n=4 every have hour and measure the thickness of each gasket material blank.  The average of the four thicknesses is then measured as well as the range for the four parts.  Table 1 below has a list of the X-bar, or average, of each sample and it’s range.

The average= Sum of the thickness for each measured part/ number of parts.
The range= The biggest value in the sample – the lowest value in the sample.

Table 1. The X-bar And Range of Each Sample.

The next step is to construct the three lines of each of the average and range control charts:

Where the constants D3, D4, and A2 are based on the sample size of each sample. Any text on the subject will have a table for these values with respect to the sample size n. Now we are ready to draw the two control charts: The X-bar control chart:

                       X-bar Chart for Thickness

         –

         –

         ———————————————UCL=1.486

S   1.400+

a        –                                   +

m        – +                           +

p        –               +

l        –         +             +             +      =

e   1.050+—————–+———————–+-+X=1.043

         –   +   +   + +     +       +   + +     +

M        –                     +

e        –                         +

a        –     +

n   0.700+

         ———————————————LCL=0.5999

         –

         –

         –

         +———+———+———+———+———+

0         5        10        15        20        25

                          Sample Number

The range control chart:

                         R Chart for thickness

     1.50+

         –

S        –

a        –

m        –

p    1.00+

l        ——————————————–UCL=0.97

e        –

         –

R        –               +           +

a    0.50+ +   +     +       +     +   + +   +   +    _

n        —-+———+———+—————–+-+R=0.0.425

g        –                     +           +   +       

e        –         +

         –                 +

     0.00+——-+————————————LCL=0.000

         –

         +———+———+———+———+———+

         0         5        10        15        20        25

                          Sample Number

Interpretation of the X-bar and Range charts: Variation reveals it self through recognizable patterns on the control charts.  A process is said to be under the influence of common causes only if all the data points lie within the upper and lower control limits.  If a point falls out side the control limits then the process is said to be out of control or under the influence of special causes.  Remember that special causes are sporadic and in most cases we can eliminate what is causing them.  Process improvement can only start with the process being in control.  Then we look at the control charts to see if any pattern or trend exists in the graph.  Control charts can detect several basic patterns that can occur in a process.  These patterns are:

	Runs:  A series of consecutive points on the control chart that fall on one side of the central Line. This indicates that the mean or average of the process has shifted.
	Trends:  A series of points continues to rise or fall in one direction.  This is an indication that an abnormal condition is operating within the process.  An example of causes of trends is tool or equipment wear.
	Cycles:  A series of points displaying a similar or repeatable pattern.
	Jumps:  Occurs when a large shift has occurred between two consecutive points.
	Hugging:  A series of points are very close to the central line or the two control limits.

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