Posts Tagged ‘x chart’

Control Charts; A last resort control system.

Wednesday, May 23rd, 2012


Control charts are the most difficult of the seven basic quality tools to use. They are seldom the method of choice. When a process step is important, we would prefer that the step not vary at all. ONLY when this can not be accomplished in an economical way does one choose to use a control chart.

 

 

 

In any process, pieces vary from each other.


But as they vary, they form a pattern.

And if that pattern is stable, it can be described as a distribution.  These distributions can differ in location, spread, and shape.

If this variation that is present is, only common caused variation the process output forms a distribution that is stable and predictable over time.

If this variation that is present is special caused variation, the process is unstable over time producing varying distributions and thus is not predictable.

Control charts are only useful if the step (operation or function), over time, exhibits measurable random variation. Control charts display the data over time.

 

The Control Chart above (Time is on the x axis above listed as sample). Control Limits (the red lines) are displayed on control charts, where data falling within the control limits are considered common caused or  “normal” variation. Any point outside the control limits are considered “special caused” variation and need to be look at and corrected through an action plan. If you create a control chart, you must also have with it an action plan.

Besides control limits for control charts, there are several other type of trends (runs) that can indicate an out-of-control process before any defective parts are produced.  Remember that with common cause I can predict what will happen next. This means that if I have several things happen in a row it could tell me something has changed.

What I have shown above is only one type a control chart and one of the simplest to use but there are several others types of control charts available.

As mentioned in other articles, there are two types of data and we have control charts for both. There is what we call variables data and attribute data. Variables data is data that you can measure and attribute data is data that we count. So let me give you a brief description of the most commonly used Control Charts we have for each data type.

Variables Data Control Charts (Measurable)

The Individuals and Moving Range Chart (X-MR)

Individual and Moving range charts are used when taking more than one is expensive  or the data is collected in a  destructive test. If this is not your situation use one of the other types of variable control charts. One of the main reasons why you should use a different variables control chart is that with individual control charts the data need to be normally distributed. If it is not normally distributed, the chart will not work properly for you. The other charts below use averages and the distribution of averages are normal (Central Limit Theorem).

Average and Range Chart ( Xbar – R)

This is the most popular of the variables control charts. This is because it is uses a small sample size and the range of that sample. With this chart, it is easiest to calculate the average (Xbar) of the sample and Range of the sample by hand. As mentioned above using the averages of samples in this chart assures you that the data plotted will be normal and all the trends can be predicted.

Average and Standard Deviation Chart (Xbar – s)

This chart is used a lot when there is a computer associated with the work area that can calculate and plot the statistics needed for this chart (Xbar and s). Here we have to calculate and plot the sample average (Xbar) and the sample standard deviation (s).

 Other Variable Control Charts

There are several other types of variables control charts all used for very special conditions. These are the three that are used 95% of the time.

Attribute Data Control Charts (Count)

Proportion Defective (p)

p charts measure the proportion defective over time. It is important that each item (part, component or document) being check is either conforming (good) or defective (bad) as a whole. This means even if an item has several defects in it, it is still counted as 1 defective item. It is also important that the inspection of these items is grouped in some meaningful way. In this chart, the groups do not always have to be equal, but because of the varying group sizes, the control limits vary for group to group. This way the defective items can be expressed as a decimal fraction (percentage) of the grouping.

 

Number Defective (np)

np charts also measure the proportion defective over time. It is important that each item (part, component or document) being check is either conforming (good) or defective (bad) as a whole. This means even if an item has several defects in it, it is still counted as 1 defective item.

The difference between the p and the np chart is in the grouping. Here in the np charts all of the groups being inspected need to always be the same size and never vary. This having the grouping (sample size) always the same make the control limits always the same an easier to calculate. These groupings, like the p chart, should be grouped in some meaningful way. This way the defective items can be expressed as a decimal fraction (percentage) of the grouping

Number of Defects (c)

c charts measure the number of defects over time. Here we are counting defect in each item (part, component or document), so an item can have more than one defect in it.  It is also important that the inspection of these items is grouped in some meaningful way. In this chart, the groups do not always have to be equal, but because of the varying group sizes, the control limits vary for group to group. This way the defective items can be expressed as a decimal fraction (percentage) of the grouping.

Defects per unit (u)

u charts also measure the number of defects over time. . Here, just like c charts, we are counting defect in each item (part, component or document), so an item can have more than one defect in it.  The difference between the c and the u chart is in the grouping. Here in the u charts all of the groups being inspected need to always be the same size and never vary. This having the grouping (sample size) always the same make the control limits always the same an easier to calculate. These groupings, like the p chart, should be grouped in some meaningful way. This way the defective items can be expressed as a decimal fraction (percentage) of the grouping.

Selecting the Correct Control Chart

Below is a Decision Tree Diagram of the different type and there use. In this chart “n” is your grouping size or what is called sample size. Be sure you understand the application of each control chart or get help if you plan to use one of these.

 

The Control Systems

I have talked to you about control charts, but to make them useful and not just a pretty picture on the wall you have to have a “Reaction Plan”. What is a Reaction Plan; a plan so when an out-of-control condition does occur you have a plan of action for the operator (person that plots the points) to follow to correct the condition NOW before another item is produced. Without this, the chart is a waste of time to build and maintain.

Well there you have a short article on Control Charts. Check back on my website blog to find videos on how to build each one of these in Minitab. If, you have questions or comments please feel free to contact me by leaving a comment below, emailing me, calling me, or leaving a comment on my website.

Bersbach Consulting
Peter Bersbach
Six Sigma Master Black Belt
http://sixsigmatrainingconsulting.com
peter@bersbach.com
1.520.829.0090

 

The Seven Basic Quality Control Tools

Saturday, November 26th, 2011

Product or service quality is everyone’s responsibility, from a “Mom and Pop Shop” to an international corporation. So I thought I give those who don’t know how to look at the quality of what they do, a set of basic tools. Quality professional have all heard of “The Seven Basic Quality Control Tools” so here they are.

The Seven Basic QC (Quality Control) Tools are a given set of graphical techniques identified as being helpful in troubleshooting issues related to quality[1]. These seven are called basic because they can be used easily by anyone to solve the vast majority of quality-related issues. Many quality professional believe these were originated by Dr. Ishikawa, a world renowned quality professional.  But, he would tell you that he was inspired by the “Seven Famous Weapons of Benkei[2] . The designation as the “Seven Basic Tools of Quality” arose in postwarJapan.

The Tools

  1. 1.      Cause and Effect Diagrams: (Fishbone Diagrams, Ishikawa Diagrams)

These diagrams are tools that organize a group or persons knowledge about the causes of a problem or issue and display the information graphically.

 

It was originally created and used by Dr. Kaoru Ishikawa and is sometimes called an Ishikawa Diagram. Also, because of its shape it is called a Fishbone Diagram. In general what you do is brainstorm ideas (causes) then group them in to categories. Those categories become the many branches of the Cause and Effect diagram.

  1. 2.      Check Sheets:

This is another simple but powerful tool. Check Sheets are lists of items and the frequency that the item occurs. They can be made in so many different ways that many times, we don’t think of them as a list, but they are. below are two, one that kind of looks like a list the other not so much. On the shoe the defects are marked with an “x” in the location it was found.

They are use to answer many important questions such as:

  • Has all the work been done?
  • Has all the inspection been done?
  • How frequently a problem occurs?

They are often used to remind individuals doing complex tasks of what to do and in what order. They are also used many times in conjunction with other tools to help quantify or validate information.

  1. 3.      Control Charts:

Control charts are the most difficult of the seven tools to use. They are seldom the method  of choice. When a process step is important, we would prefer that the step not vary at all. ONLY when this can not be accomplished in an economical way does one choose to use a control chart. Below is an “XBar-R Chart” also called an “Average and Range Control Chart”.

Control charts are only useful if the step (operation or function), over time, exhibits measurable random variation. Control charts display the data over time (Time is on the x axis above listed as sample). Control Limits (the red lines) are displayed on control charts, where data falling within the control limits are considered “normal” variation. Any point outside the control limits are considered “special caused” variation and need to be look at and corrected through an action plan. If you create a control chart, you must also have with it an action plan.

Besides control limits for control charts, there are several other type of trends (runs) that can indicate an out-of-control process.

What I have shown above is only one type a control chart and one of the simplest to use but there are several others (not so simple to use). Below is a Decision Tree Diagram of the different type and there use. Be sure you understand the application of each control chart or get help if you plan to use one of these.

  1. 4.      Histograms:

Histograms are a “picture” of a set of data (or information). It is created by grouping the data you collect in to “Cells” or “Bins” (Bars in the chart below).

Histograms take your data and give it a shape (Distribution). With this, you can see the data sets spread, central tendencies, and if it meets requirements. As you can see, it is a valuable troubleshooting tool. You can take it a compare differences between machines, people, suppliers etc. Never use a histogram alone always also plot it in a time ordered  plot (run chart).

  1. 5.      Pareto Charts:

Pareto Charts are a specialized Histogram of count data. It arranges the Bins or Cells in largest to smallest counts and gives you an accumulation line as seen below.

The Pareto Chart gets its name from the use of the Pareto Principle which states “ 80% of the effect comes from 20% of the causes”. Vilfredo Pareto, an Italian economist, originated this principle by determining that 80% of the land inItalyis owned by 20% of the population. Later it was found to hold true in many things and help us focus on the critical few. With a chart like this a team can decide where to place its priority and focus ( the big hitters). This is extremely helpful when time and money is limited as it is in most cases.

  1. 6.      Scatter Diagrams:

Scatter plot are a very simple tool to use to see if there is a correlation between two things (i.e. does one thing lead to another). I always before going into any major analysis of data, plot the data in some way to get a “gut feel” of what is happening. This tool lets you create a simple picture showing how two or more variables change “together”.

As one can see in the chart above the fruit on the tree increase in weight the longer it is on the tree. In scatter charts we see if one thing relates (correlates) with another. Below is a set of chart that shows some of the relationships you might find with this tool.

  1. 7.      Stratification: (Flow Charts, Run Charts, etc.)

To me Stratification is a catch-all for summarizing, picturing, or applying some tool to data so you can understand what is happening. Stratification is the process of dividing members of a population into homogeneous subgroups before using it. The data (strata) should be mutually exclusive: every element in the population must be assigned to only one subgroup (stratum). The data should also be collectively exhaustive: no population element (data) can be excluded.

That’s a mouthful, but if you look at above six tools all of them do this stratification of the data. In many texts they list either flow charts or run charts under this seventh tool area. A run chart is just the “Individuals Chart” of the above control chart without control limits. A flow chart takes a group of steps in a process and summaries them into a map of the way the process works. They are sometimes called a Process Map or a Process Flow Map.

They are created to:

  • Create a common understanding of the process flow
  • Clarify steps in a process
  • Uncover problems and misunderstanding in a process
  • Reveal how a process operates (good and bad)
  • Helps you ID places for improvement.

Well there you have a short description of the Seven Basic Quality Tools. Stay in touch as I go into each tool with details of how to construct and interpret them. If, you have questions or comments please feel free to contact me by leaving a comment below, emailing me, calling me, or leaving a comment on my website.

Bersbach Consulting
Peter Bersbach
Six Sigma Master Black Belt
http://sixsigmatrainingconsulting.com
peter@bersbach.com
1.520.829.0090



[2] Ishikawa, Kaoru (1990), Introduction to Quality Control (1 ed.), Tokyo: 3A Corp, p. 98, ISBN 9784906224616, OCLC 23372992

 

The Element of Time

Friday, September 24th, 2010

As we all know there is variation everywhere and in everything. This includes people pencils, traffic at an intersection, customer needs, goods, services, and of course processes. If you can not predict this variation, I can bet you are compensating for it and that compensation is costing you money!!

In Six Sigma we use statistics to recognize and thus assess and understand that variation so we can predict it ahead of time. This reduces our costs and increases customer satisfaction. Statistics can help you “Picture” variation. Many times we look at data that we gather in various ways but some times we forget about the element of time. At any given point things may look great but over time many times things vary. This variation can not be seen in what we call a histogram of all the data or any other kind of plot that does not use time on one of the axis. For example below (Figure 1) is a plot of Systolic blood pressure of one individual over four months. This plots shows where the average Systolic Blood Pressure would be if it was Normal, Marginally High, or High. In this individuals case it does not look that great.

As you can see this individuals Systolic pressure is all over the place and does not look like a normal distribution. It may be Bi or Multi modal (two or more things effecting the results making several peaks in the Histogram).  From this we can not draw to much of a conclusion but to tell him to see a doctor. Or should we??

If I take that same data and plot over time we get the following graphic.

Now clearly you can see a shift in the blood pressure over the 4 months. All for the better. We might not want the person to see the doctor but find out what might have cause this improvement. A different solution just because we looked at the data in a time sequence chart.

What these two graphs tell us is that if you have collected data over any given time period I’d suggest that you plot it in what is called an x or individuals chart (Figure 2 above) over time and see what you see in patterns there. In fact many times I plot the data in several different ways just to see what I can find. What kinds of patterns I see that can lead me to why the data varies so much.

If, you have questions or comments please feel free to contact me by leaving a comment below, emailing me, calling me, or leaving a comment on my website.


Bersbach Consulting
Peter Bersbach
Six Sigma Master Black Belt
http://sixsigmatrainingconsulting.com
peter@bersbach.com
1.520.829.0090