- ISHIKAWA KAORU, Professor Emeritus, University of Tokyo-
Problem solving should follow a logical, systematic method. This will place emphasis on locating and eliminating the root or real cause of the problem. Other, less systematic attempts at problem solving run the risk of attempting to eliminate the symptoms associated with the problem rather than eliminating the problem at its cause. Organized problem-solving efforts utilize a variety of quality tools for problem analysis.
The QC 7 Tools are proven scientific management tools, which are basic and easy to understand. They form the fundamental foundation for all problem solving and quality control activities.
The benefits of applying QC 7 Tools should not be limited to only below:
The QC 7 Tools consist of below:
Histogram
In statistics, a histogram is a graphical display of tabulated frequencies, shown as bars. It shows what proportion of cases fall into each of several categories. The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent. The intervals (or bands) should ideally be of the same size.
The word histogram is derived from Greek: histos 'anything set upright' (as the masts of a ship, the bar of a loom, or the vertical bars of a histogram); gramma 'drawing, record, writing'. The histogram is one of the seven basic tools of quality control, which also include the Pareto chart, check sheet, control chart, cause-and-effect diagram, flowchart, and scatter diagram. A generalization of the histogram is kernel smoothing techniques. This will construct a very smooth probability density function from the supplied data.
Examples
As an example we consider data collected by the U.S. Census Bureau on time to travel to work. The census found that there were 124 million people who work outside of their homes. This rounding is a common phenomenon when collecting data from people.
Histogram of travel time. Area under the curve equals the
total number of cases. This diagram uses Q/width from the table
This histogram shows the number of cases per unit interval so that the height of each bar is equal to the proportion of total people in the survey who fall into that category. The area under the curve represents the total number of cases (124 million). This type of histogram shows absolute numbers.
Histogram of travel time. Area under the curve equals 1. This diagram uses Q/total/width from the table.
Useful Links
Cause and Effect Diagram
Ishikawa diagrams were proposed by Kaoru Ishikawa in the 1960s, who pioneered quality management processes in the Kawasaki shipyards, and in the process became one of the founding fathers of modern management.
It was first used in the 1960s, and is considered one of the seven basic tools of quality management, along with the histogram, Pareto chart, check sheet, control chart, flowchart, and scatter diagram. See Quality Management Glossary. It is known as a fishbone diagram because of its shape, similar to the side view of a fish skeleton.
Mazda Motors famously used an Ishikawa diagram in the development of the Miata sports car, where the required result was "Jinba Ittai" or "Horse and Rider as One". The main causes included such aspects as "touch" and "braking" with the lesser causes including highly granular factors such as "50/50 weight distribution" and "able to rest elbow on top of driver's door". Every factor identified in the diagram was included in the final design.
Causes in a typical diagram are normally grouped into categories, the main ones of which are:
Machine, Method, Materials, Maintenance, Man and Mother Nature (Environment) (recommended for the manufacturing industry).
Note: a more modern selection of categories used in manufacturing includes Equipment, Process, People, Materials, Environment, and Management.
Price, Promotion, People, Processes, Place / Plant, Policies, Procedures, and Product (or Service) (recommended for the administration and service industries).
Surroundings, Suppliers, Systems, Skills (recommended for the service industry).
A generic Ishikawa diagram showing general (red) and more refined (blue) causes for an event.Most Ishikawa diagrams have a box at the right hand side, where the effect to be examined is written. The main body of the diagram is a horizontal line from which stem the general causes, represented as "bones". These are drawn towards the left-hand side of the paper and are each labeled with the causes to be investigated, often brainstormed beforehand and based on the major causes listed above.
Off each of the large bones there may be smaller bones highlighting more specific aspects of a certain cause, and sometimes there may be a third level of bones or more. These can be found using the '5 Whys' technique. When the most probable causes have been identified, they are written in the box along with the original effect. The more populated bones generally outline more influential factors, with the opposite applying to bones with fewer "branches". Further analysis of the diagram can be achieved with a Pareto chart.
The Ishikawa concept can also be documented and analyzed through depiction in a matrix format.
The check sheet is a simple document that is used for collecting data in real-time and at the location where the data is generated. The document is typically a blank form that is designed for the quick, easy, and efficient recording of the desired information, which can be either quantitative or qualitative. When the information is quantitative, the checksheet is sometimes called a tally sheet.
A defining characteristic of a checksheet is that data is recorded by making marks ("checks") on it. A typical checksheet is divided into regions, and marks made in different regions have different significance. Data is read by observing the location and number of marks on the sheet.
5 Basic types of Check Sheets:
Example
(i) An example of a simple quality control checksheet
(ii) The figure below shows a check sheet used to collect data on telephone interruptions. The tick marks were added as data was collected over several weeks.
Useful Links
- http://en.wikipedia.org/wiki/Check_sheethttp://www.asq.org/learn-about-quality/data-collection-analysis-tools/overview/check-sheet.html
- http://www.asq.org/learn-about-quality/data-collection-analysis-tools/overview/check-sheet.html
Pareto Chart
A Pareto chart is a special type of bar chart where the values being plotted are arranged in descending order. The graph is accompanied by a line graph which shows the cumulative totals of each category, left to right. The chart is named after Vilfredo Pareto, and its use in quality assurance was popularized by Joseph M. Juran and Kaoru Ishikawa.
Simple example of a Pareto chart using hypothetical data showing the relative frequency of reasons for arriving late at work.
The Pareto chart is one of the seven basic tools of quality control, which include the histogram, Pareto chart, check sheet, control chart, cause-and-effect diagram, flowchart, and scatter diagram. These charts can be generated in Microsoft Office or OpenOffice as well as many free software tools found online.
Typically on the left vertical axis is frequency of occurrence, but it can alternatively represent cost or other 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. The purpose is to highlight the most important among a (typically large) set of factors. In quality control, the Pareto chart often represents the most common sources of defects, the highest occurring type of defect, or the most frequent reasons for customer complaints, etc.
The Pareto chart was developed to illustrate the 80-20 Rule — that 80 percent of the problems stem from 20 percent of the various causes.
Useful Links
Flow Chart
A flowchart is common type of chart, that represents an algorithm or process, showing the steps as boxes of various kinds, and their order by connecting these with arrows. Flowcharts are used in analyzing, designing, documenting or managing a process or program in various fields.
Flowcharts are used in designing and documenting complex processes. Like other types of diagram, they help visualize what is going on and thereby help the viewer to understand a process, and perhaps also find flaws, bottlenecks, and other less-obvious features within it.
There are many different types of flowcharts, and each type has its own repertoire of boxes and notational conventions. The two most common types of boxes in a flowchart are:
A flowchart is described as "cross-functional" when the page is divided into different swimlanes describing the control of different organizational units. A symbol appearing in a particular "lane" is within the control of that organizational unit. This technique allows the author to locate the responsibility for performing an action or making a decision correctly, showing the responsibility of each organizational unit for different parts of a single process.
Flowcharts depict certain aspects of processes and they are usually complemented by other types of diagram. For instance, Kaoru Ishikawa defined the flowchart as one of the seven basic tools of quality control, next to the histogram, Pareto chart, check sheet, control chart, cause-and-effect diagram, and the scatter diagram. Similarly, in UML, a standard concept-modeling notation used in software development, the activity diagram, which is a type of flowchart, is just one of many different diagram types.
History
The first structured method for documenting process flow, the "flow process chart", was introduced by Frank Gilbreth to members of ASME in 1921 as the presentation “Process Charts—First Steps in Finding the One Best Way”. Gilbreth's tools quickly found their way into industrial engineering curricula. In the early 1930s, an industrial engineer, Allan H. Mogensen began training business people in the use of some of the tools of industrial engineering at his Work Simplification Conferences in Lake Placid, New York.
A 1944 graduate of Mogensen's class, Art Spinanger, took the tools back to Procter and Gamble where he developed their Deliberate Methods Change Program. Another 1944 graduate, Ben S. Graham, Director of Formcraft Engineering at Standard Register Corporation, adapted the flow process chart to information processing with his development of the multi-flow process chart to displays multiple documents and their relationships. In 1947, ASME adopted a symbol set derived from Gilbreth's original work as the ASME Standard for Process Charts.
According to Herman Goldstine, he developed flowcharts with John von Neumann at Princeton University in late 1946 and early 1947.
Flowcharts used to be a popular means for describing computer algorithms. They are still used for this purpose; modern techniques such as UML activity diagrams can be considered to be extensions of the flowchart. However, their popularity decreased when, in the 1970s, interactive computer terminals and third-generation programming languages became the common tools of the trade, since algorithms can be expressed much more concisely and readably as source code in such a language. Often, pseudo-code is used, which uses the common idioms of such languages without strictly adhering to the details of a particular one.
Symbols
A typical flowchart from older Computer Science textbooks may have the following kinds of symbols:
Start and end symbols
Represented as lozenges, ovals or rounded rectangles, usually containing the word "Start" or "End", or another phrase signaling the start or end of a process, such as "submit enquiry" or "receive product".
Arrows
Showing what's called "flow of control" in computer science. An arrow coming from one symbol and ending at another symbol represents that control passes to the symbol the arrow points to.
Processing steps
Represented as rectangles. Examples: "Add 1 to X"; "replace identified part"; "save changes" or similar.
Input/Output
Represented as a parallelogram. Examples: Get X from the user; display X.
Conditional or decision
Represented as a diamond (rhombus). These typically contain a Yes/No question or True/False test. This symbol is unique in that it has two arrows coming out of it, usually from the bottom point and right point, one corresponding to Yes or True, and one corresponding to No or False. The arrows should always be labeled. More than two arrows can be used, but this is normally a clear indicator that a complex decision is being taken, in which case it may need to be broken-down further, or replaced with the "pre-defined process" symbol.
A number of other symbols that have less universal currency, such as:
- A Document represented as a rectangle with a wavy base
- A Manual input represented by parallelogram, with the top irregularly sloping up from left to right. An example would be to signify data-entry from a form;
- A Manual operation represented by a trapezoid with the longest parallel side at the top, to represent an operation or adjustment to process that can only be made manually
- A Data File represented by a cylinder
Flowcharts may contain other symbols, such as connectors, usually represented as circles, to represent converging paths in the flow chart. Circles will have more than one arrow coming into them but only one going out. Some flow charts may just have an arrow point to another arrow instead. These are useful to represent an iterative process (what in Computer Science is called a loop).
A loop may, for example, consist of a connector where control first enters, processing steps, a conditional with one arrow exiting the loop, and one going back to the connector. Off-page connectors are often used to signify a connection to a (part of another) process held on another sheet or screen. It is important to remember to keep these connections logical in order. All processes should flow from top to bottom and left to right.
Examples
A simple flowchart for computing factorial N (N!)
A flowchart for computing factorial N (N!) Where N! = 1 * 2 * 3 *...* N. This flowchart represents a "loop and a half" — a situation discussed in introductory programming textbooks that requires either a duplication of a component (to be both inside and outside the loop) or the component to be put inside a branch in the loop.
Types of flow charts
· Document flowcharts, showing a document flow through system
· Data flowcharts, showing data flows in a system
· System flowcharts showing controls at a physical or resource level
· Program flowchart, showing the controls in a program within a system
However there are several of these classifications. For example Andrew Veronis (1978) named three basic types of flowcharts: the system flowchart, the general flowchart, and the detailed flowchart. That same year Marilyn Bohl (1978) stated "in practice, two kinds of flowcharts are used in solution planning: system flowcharts and program flowcharts...". More recently Mark A. Fryman (2001) stated that there are more differences. Decision flowcharts, logic flowcharts, systems flowcharts, product flowcharts, and process flowcharts are "just a few of the differnt types of flowcharts that are used in business and government.
Useful Links
Scatter Chart
A scatter plot is a type of display 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. A scatter plot is also called a scatter chart, scatter diagram and scatter graph.
A scatter plot only specifies variables or independent variables 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 experimenter, 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 level. 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. Unfortunately, no universal best-fit procedure is guaranteed to generate a correct solution for arbitrary relationships.
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.
For example, to display values for "lung capacity" (first variable) and how long that person could hold his breath (second variable), a researcher would choose a group of people to study, then measure each one's lung capacity (first variable) and how long that person could hold his breath (second variable).
The researcher would then plot the data in a scatter plot, assigning "lung capacity" to the horizontal axis, and "time holding breath" to the vertical axis. A person with a lung capacity of 400 cc who held his breath for 21.7 seconds would be represented by a single dot on the scatter plot at the point (400, 21.7) in the Cartesian coordinates. The scatter plot of all the people in the study would enable the researcher to obtain a visual comparison of the two variables in the data set, and help to determine what kind of relationship there might be between the two variables.
Example
Waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA. This chart suggests there are generally two "types" of eruptions: short-wait-short-duration, and long-wait-long-duration.
Useful Links
- http://en.wikipedia.org/wiki/Scatter_chart
- http://office.microsoft.com/en-us/excel/HA102274781033.aspx
Control Chart
The control chart, also known as the Shewhart chart or process-behaviour chart, in statistical process control is a tool used to determine whether a manufacturing or business process is in a state of statistical control or not.
If the chart indicates that the process is currently under control then it can be used with confidence to predict the future performance of the process. If the chart indicates that the process being monitored is not in control, the pattern it reveals can help determine the source of variation to be eliminated to bring the process back into control. A control chart is a specific kind of run chart that allows significant change to be differentiated from the natural variability of the process.
This is key to effective process control and improvement. On a practical level the control chart can be seen as part of an objective disciplined approach that facilitates the decision as to whether process performance warrants attention or not.
The control chart is one of the seven basic tools of quality control (along with the histogram, Pareto chart, check sheet, cause-and-effect diagram, flowchart, and scatter diagram).
History
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 they 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." 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 never 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 then 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 of 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.
More recent use and development of control charts in the Shewhart-Deming tradition has been championed by Donald J. Wheeler.
Chart Details
A control chart consists of the following:
- Points representing measurements of a quality characteristic in samples taken from the process at different times [the data]
- A centre line, drawn at the process characteristic mean which is calculated from the data
- Upper and lower control limits (sometimes called "natural process limits") that indicate the threshold at which the process output is considered statistically 'unlikely'
The chart may contain other optional features, including:
- Upper and lower warning limits, drawn as separate lines, typically two standard deviations 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 quality
However in the early stages of use the inclusion of these items may confuse inexperienced chart interpreters.
Chart Usage
If the process is in control, all points will plot within 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 tell you about process behaviour 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 can't deliver the process characteristic at the desired level.
Control charts omit 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, one expects to be signaled approximately once out of every 370 points on average, just due to common-causes.
Choice of Limits
Shewhart set 3-sigma limits on the following basis.
· The coarse result of Chebyshev's inequality that, for any probability distribution, the probability of an outcome greater than k standard deviations from the mean is at most 1/k2.
· The finer result of the Vysochanskii-Petunin inequality, that for any unimodal probability distribution, the probability of an outcome greater than k standard deviations from the mean is at most 4/(9k2).
· The empirical investigation of sundry probability distributions reveals that at least 99% of observations occurred within three standard deviations of the mean.
Shewhart summarised the conclusions by saying:
... the fact that the criterion which we happen to use has a fine ancestry in highbrow statistical theorems does not justify its use. Such justification must come from empirical evidence that it works. As the practical engineer might say, the proof of the pudding is in the eating.
Though he initially experimented with limits based on probability distributions, Shewhart ultimately wrote:
Some of the earliest attempts to characterise a state of statistical control were inspired by the belief that there existed a special form of frequency function f and it was early argued that the normal law characterised such a state. When the normal law was found to be inadequate, then generalised functional forms were tried. Today, however, all hopes of finding a unique functional form f are blasted.
The control chart is intended as a heuristic. Deming insisted that it is not a hypothesis test and is not motivated by the Neyman-Pearson lemma. He contended that the disjoint nature of population and sampling frame in most industrial situations compromised the use of conventional statistical techniques. Deming's intention was to seek insights into the cause system of a process ...under a wide range of unknowable circumstances, future and past .... He claimed that, under such conditions, 3-sigma limits provided ... a rational and economic guide to minimum economic loss... from the two errors:
1. Ascribe a variation or a mistake to a special cause when in fact the cause belongs to the system (common cause). (Also known as a Type I error)
2. Ascribe a variation or a mistake to the system (common causes) when in fact the cause was special. (Also known as a Type II error)
Calculation of Standard Deviation
As for the calculation of control limits, the standard deviation required is that of the common-cause variation in the process. Hence, the usual estimator, in terms of sample variance, is not used as this estimates the total squared-error loss from both common- and special-causes of variation.
An alternative method is to use the relationship between the range of a sample and its standard deviation derived by Leonard H. C. Tippett, an estimator which tends to be less influenced by the extreme observations which typify special-causes .
Performance of Control Charts
When a point falls outside of the limits established for a given control chart, those responsible for the underlying process are expected to determine whether a special cause has occurred. If one has, then that cause should be eliminated if possible. It is known that even when a process is in control (that is, no special causes are present in the system), there is approximately a 0.27% probability of a point exceeding 3-sigma control limits. Since the control limits are evaluated each time a point is added to the chart, it readily follows that every control chart will eventually signal the possible presence of a special cause, even though one may not have actually occurred.
For a Shewhart control chart using 3-sigma limits, this false alarm occurs on average once every 1/0.0027 or 370.4 observations. Therefore, the in-control average run length (or in-control ARL) of a Shewhart chart is 370.4.
Meanwhile, if a special cause does occur, it may not be of sufficient magnitude for the chart to produce an immediate alarm condition. If a special cause occurs, one can describe that cause by measuring the change in the mean and/or variance of the process in question. When those changes are quantified, it is possible to determine the out-of-control ARL for the chart.
It turns out that Shewhart charts are quite good at detecting large changes in the process mean or variance, as their out-of-control ARLs are fairly short in these cases. However, for smaller changes (such as a 1- or 2-sigma change in the mean), the Shewhart chart does not detect these changes efficiently. Other types of control charts have been developed, such as the EWMA chart and the CUSUM chart, which detect smaller changes more efficiently by making use of information from observations collected prior to the most recent data point.
Types of Charts
Useful Links
- http://en.wikipedia.org/wiki/Control_chart
- http://www.asq.org/learn-about-quality/data-collection-analysis-tools/overview/control-chart.html
