Control chart

Control charts, also known as Shewhart charts or process-behavior charts, in statistical process control are tools used to determine if a manufacturing or business process is in a state of statistical control.


If analysis of the control chart indicates that the process is currently under control (i.e., is stable, with variation only coming from sources common to the process), then no corrections or changes to process control parameters are needed or desired. In addition, data from the process can be used to predict the future performance of the process. If the chart indicates that the monitored process is not in control, analysis of the chart can help determine the sources of variation, as this will result in degraded process performance.A process that is stable but operating outside of desired limits (e.g., scrap rates may be in statistical control but above desired limits) needs to be improved through a deliberate effort to understand the causes of current performance and fundamentally improve the process.

The control chart is one of the seven basic tools of quality control. Typically control charts are used for time-series data, though they can be used for data that have logical comparability (i.e. you want to compare samples that were taken all at the same time, or the performance of different individuals), however the type of chart used to do this requires consideration.


The control chart was invented by Walter A. Shewhart while working for Bell Labs in the 1920s. The company’s engineers had been seeking to improve the reliability of their telephony transmission systems. Because amplifiers and other equipment had to be buried underground, there was a business need to reduce the frequency of failures and repairs. By 1920, the engineers had already realized the importance of reducing variation in a manufacturing process. Moreover, they had realized that continual process-adjustment in reaction to non-conformance actually increased variation and degraded quality. Shewhart framed the problem in terms of Common- and special-causes of variation and, on May 16, 1924, wrote an internal memo introducing the control chart as a tool for distinguishing between the two. Dr. Shewhart’s boss, George Edwards, recalled: “Dr. Shewhart prepared a little memorandum only about a page in length. About a third of that page was given over to a simple diagram which we would all recognize today as a schematic control chart. That diagram, and the short text which preceded and followed it set forth all of the essential principles and considerations which are involved in what we know today as process quality control.”[5] Shewhart stressed that bringing a production process into a state of statistical control, where there is only common-cause variation, and keeping it in control, is necessary to predict future output and to manage a process economically.

Dr. Shewhart created the basis for the control chart and the concept of a state of statistical control by carefully designed experiments. While Dr. Shewhart drew from pure mathematical statistical theories, he understood data from physical processes typically produce a “normal distribution curve” (a Gaussian distribution, also commonly referred to as a “bell curve“). He discovered that observed variation in manufacturing data did not always behave the same way as data in nature (Brownian motion of particles). Dr. Shewhart concluded that while every process displays variation, some processes display controlled variation that is natural to the process, while others display uncontrolled variation that is not present in the process causal system at all times.

In 1924 or 1925, Shewhart’s innovation came to the attention of W. Edwards Deming, then working at the Hawthorne facility. Deming later worked at the United States Department of Agriculture and became the mathematical advisor to the United States Census Bureau. Over the next half a century, Deming became the foremost champion and proponent of Shewhart’s work. After the defeat of Japan at the close of World War II, Deming served as statistical consultant to the Supreme Commander for the Allied Powers. His ensuing involvement in Japanese life, and long career as an industrial consultant there, spread Shewhart’s thinking, and the use of the control chart, widely in Japanese manufacturing industry throughout the 1950s and 1960s.

Chart details

A control chart consists of:

  • Points representing a statistic (e.g., a mean, range, proportion) of measurements of a quality characteristic in samples taken from the process at different times [the data]
  • The mean of this statistic using all the samples is calculated (e.g., the mean of the means, mean of the ranges, mean of the proportions)
  • A centre line is drawn at the value of the mean of the statistic
  • The standard error (e.g., standard deviation/sqrt(n) for the mean) of the statistic is also calculated using all the samples
  • Upper and lower control limits (sometimes called “natural process limits”) that indicate the threshold at which the process output is considered statistically ‘unlikely’ and are drawn typically at 3 standard errors from the centre line

The chart may have other optional features, including:

  • Add MediaUpper and lower warning limits, drawn as separate lines, typically two standard errors above and below the centre line
  • Division into zones, with the addition of rules governing frequencies of observations in each zone

Annotation with events of interest, as determined by the Quality Engineer in charge of the process’s qualitycontrol chart

Chart usage

If the process is in control (and the process statistic is normal), 99.7300% of all the points will fall between the control limits. Any observations outside the limits, or systematic patterns within, suggest the introduction of a new (and likely unanticipated) source of variation, known as a special-cause variation. Since increased variation means increased quality costs, a control chart “signaling” the presence of a special-cause requires immediate investigation.

This makes the control limits very important decision aids. The control limits provide information about the process behavior and have no intrinsic relationship to any specification targets or engineering tolerance. In practice, the process mean (and hence the centre line) may not coincide with the specified value (or target) of the quality characteristic because the process’ design simply cannot deliver the process characteristic at the desired level.

Control charts limit specification limits or targets because of the tendency of those involved with the process (e.g., machine operators) to focus on performing to specification when in fact the least-cost course of action is to keep process variation as low as possible. Attempting to make a process whose natural centre is not the same as the target perform to target specification increases process variability and increases costs significantly and is the cause of much inefficiency in operations. Process capability studies do examine the relationship between the natural process limits (the control limits) and specifications, however.

The purpose of control charts is to allow simple detection of events that are indicative of actual process change. This simple decision can be difficult where the process characteristic is continuously varying; the control chart provides statistically objective criteria of change. When change is detected and considered good its cause should be identified and possibly become the new way of working, where the change is bad then its cause should be identified and eliminated.

The purpose in adding warning limits or subdividing the control chart into zones is to provide early notification if something is amiss. Instead of immediately launching a process improvement effort to determine whether special causes are present, the Quality Engineer may temporarily increase the rate at which samples are taken from the process output until it’s clear that the process is truly in control. Note that with three-sigma limits, common-cause variations result in signals less than once out of every twenty-two points for skewed processes and about once out of every three hundred seventy (1/370.4) points for normally distributed processes. The two-sigma warning levels will be reached about once for every twenty-two (1/21.98) plotted points in normally distributed data. (For example, the means of sufficiently large samples drawn from practically any underlying distribution whose variance exists are normally distributed, according to the Central Limit Theorem.)


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Posted by on 19/01/2013 in Uncategorized


Scatter plot

A scatter plot or scattergraph is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data.

The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. This kind of plot is also called a scatter chart, scattergram, scatter diagram or scatter graph.



A scatter plot is used when a variable exists that is under the control of the experimenter. If a parameter exists that is systematically incremented and/or decremented by the other, it is called the control parameter or independent variable and is customarily plotted along the horizontal axis. The measured or dependent variable is customarily plotted along the vertical axis. If no dependent variable exists, either type of variable can be plotted on either axis and a scatter plot will illustrate only the degree of correlation (not causation) between two variables.

A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval. For example, weight and height, weight would be on x axis and height would be on the y axis. Correlations may be positive (rising), negative (falling), or null (uncorrelated). If the pattern of dots slopes from lower left to upper right, it suggests a positive correlation between the variables being studied. If the pattern of dots slopes from upper left to lower right, it suggests a negative correlation. A line of best fit (alternatively called ‘trendline’) can be drawn in order to study the correlation between the variables. An equation for the correlation between the variables can be determined by established best-fit procedures. For a linear correlation, the best-fit procedure is known as linear regression and is guaranteed to generate a correct solution in a finite time. No universal best-fit procedure is guaranteed to generate a correct solution for arbitrary relationships. A scatter plot is also very useful when we wish to see how two comparable data sets agree with each other. In this case, an identity line, i.e., a y=x line, or an 1:1 line, is often drawn as a reference. The more the two data sets agree, the more the scatters tend to concentrate in the vicinity of the identity line; if the two data sets are numerically identical, the scatters fall on the identity line exactly.

One of the most powerful aspects of a scatter plot, however, is its ability to show nonlinear relationships between variables. Furthermore, if the data is represented by a mixture model of simple relationships, these relationships will be visually evident as superimposed patterns.

The scatter diagram is one of the seven basic tools of quality control.


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Posted by on 19/01/2013 in Uncategorized


Defect concentration diagram

The defect concentration diagram is a graphical tool that is useful in analyzing the causes of the product or part defect. It is a drawing of the product (or other item of interest), with all relevant views displayed, onto which the locations and frequencies of various defects are shown.

defect concentration


Defect concentration diagram is used effectively in the following situations:

  1. During data collection phase of problem identification.
  2. Analyzing a part or assembly for possible defects.
  3. Analyzing a product (or a part of a product) being manufactured with several defects.


There are a number of steps that are needed to be follow when constructing the defect concentration diagram:

  1. Define the fault or faults (or whatever) being investigated.
  2. Make a map, drawing, or picture.
  3. Mark on the diagram each time a fault (or whatever) occurs and where it occurs.
  4. After a sufficient period of time, analyze it to identify where the faults occur.

resources :

Montgomery, Douglas (2005). Introduction to Statistical Quality Control. John Wiley & Sons, Inc. ISBN 978-0-471-65631-9


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Posted by on 18/01/2013 in Uncategorized


Cause-and-Effect diagrams

Ishikawa diagrams (also called fishbone diagrams, herringbone diagrams, cause-and-effect diagrams, or Fishikawa) are causal diagrams created by Kaoru Ishikawa (1968) that show the causes of a specific event. Common uses of the Ishikawa diagram are product design and quality defect prevention, to identify potential factors causing an overall effect. Each cause or reason for imperfection is a source of variation. Causes are usually grouped into major categories to identify these sources of variation. The categories typically include:

  • People: Anyone involved with the process
  • Methods: How the process is performed and the specific requirements for doing it, such as policies, procedures, rules, regulations and laws
  • Machines: Any equipment, computers, tools, etc. required to accomplish the job
  • Materials: Raw materials, parts, pens, paper, etc. used to produce the final product
  • Measurements: Data generated from the process that are used to evaluate its quality
  • Environment: The conditions, such as location, time, temperature, and culture in which the process operates

fish bone


Causes in the diagram are often categorized, such as to the 6 M’s, described below. Cause-and-effect diagrams can reveal key relationships among various variables, and the possible causes provide additional insight into process behavior.

Causes can be derived from brainstorming sessions. These groups can then be labeled as categories of the fishbone. They will typically be one of the traditional categories mentioned above but may be something unique to the application in a specific case. Causes can be traced back to root causes with the 5 Whys technique.

The 6 Ms (used in manufacturing industry)

  • Machine (technology)
  • Method (process)
  • Material (Includes Raw Material, Consumables and Information.)
  • Man Power (physical work)/Mind Power (brain work): Kaizens, Suggestions
  • Measurement (Inspection)
  • Milieu/Mother Nature (Environment)

The original 6Ms used by the Toyota Production System have been expanded by some to include the following and are referred to as the 8Ms. However, this is not globally recognized. It has been suggested to return to the roots of the tools and to keep the teaching simple while recognizing the original intent; most programs do not address the 8Ms.

  • Management/Money Power
  • Maintenance

The 7 Ps (used in marketing industry)

  • Product=Service
  • Price
  • Place
  • Promotion
  • People/personnel
  • Process
  • Physical Evidence

The 5 Ss (used in service industry)

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Posted by on 17/01/2013 in Uncategorized


Pareto Chart

A Pareto chart, named after Vilfredo Pareto, is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line.

The left vertical axis is the frequency of occurrence, but it can alternatively represent cost or another important unit of measure. The right vertical axis is the cumulative percentage of the total number of occurrences, total cost, or total of the particular unit of measure. Because the reasons are in decreasing order, the cumulative function is a concave function. To take the example above, in order to lower the amount of late arriving by 78%, it is sufficient to solve the first three issues.

The purpose of the Pareto chart is to highlight the most important among a (typically large) set of factors. In quality control, it often represents the most common sources of defects, the highest occurring type of defect, or the most frequent reasons for customer complaints, and so on. Wilkinson (2006) devised an algorithm for producing statistically based acceptance limits (similar to confidence intervals) for each bar in the Pareto chart.


These charts can be generated by simple spreadsheet programs, such as Calc and Microsoft Excel and specialized statistical software tools as well as online quality charts generators.

The Pareto chart is one of the seven basic tools of quality control.


Resource :

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Posted by on 16/01/2013 in Uncategorized


Check Sheet

The check sheet is a form (document) used to collect data in real time at the location where the data are generated. The data it captures can be quantitative or qualitative. When the information is quantitative, the check sheet is sometimes called a tally sheet.

The check sheet is one of the seven basic tools of quality control.

check sheet


The defining characteristic of a check sheet is that data are recorded by making marks (“checks”) on it. A typical check sheet is divided into regions, and marks made in different regions have different significance. Data are read by observing the location and number of marks on the sheet.

Check sheets typically employ a heading that answers the Five Ws:

  • Who filled out the check sheet
  • What was collected (what each check represents, an identifying batch or lot number)
  • Where the collection took place (facility, room, apparatus)
  • When the collection took place (hour, shift, day of the week)
  • Why the data were collected Read the rest of this entry »
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Posted by on 16/01/2013 in Uncategorized



In statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson. A histogram consists of tabular frequencies, shown as adjacent rectangles, erected over discrete intervals (bins), with an area equal to the frequency of the observations in the interval. The height of a rectangle is also equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval. The total area of the histogram is equal to the number of data. A histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases that fall into each of several categories, with the total area equaling 1. The categories are usually specified as consecutive, non-overlapping intervals of a variable. The categories (intervals) must be adjacent, and often are chosen to be of the same size. The rectangles of a histogram are drawn so that they touch each other to indicate that the original variable is continuous.

Histograms are used to plot density of data, and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot.

An alternative to the histogram is kernel density estimation, which uses a kernel to smooth samples. This will construct a smooth probability density function, which will in general more accurately reflect the underlying variable.

The histogram is one of the seven basic tools of quality control


The U.S. Census Bureau found that there were 124 million people who work outside of their homes. Using their data on the time occupied by travel to work, Table 2 below shows the absolute number of people who responded with travel times “at least 15 but less than 20 minutes” is higher than the numbers for the categories above and below it. This is likely due to people rounding their reported journey time.The problem of reporting values as somewhat arbitrarily rounded numbers is a common phenomenon when collecting data from people.





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Posted by on 15/01/2013 in Uncategorized