what is statistical process control?

What is SPC?

What is SPC?

(/ stə-ˈti-sti-kəl  ˈprä-ˌses  kən-ˈtrōl /)noun —  a statistical method that aids in detection of process problems

Statistical Process Control, commonly referred to as SPC, is a method for monitoring, controlling and, ideally, improving a process through statistical analysis.

The result of SPC is reduced scrap and rework costs, reduced process variation, and reduced material consumption.

SPC states that all processes exhibit intrinsic variation. However, sometimes processes exhibit excessive variation that produces undesirable or unpredictable results. SPC, in a manufacturing process optimization context, is used to reduce variation to achieve the best target value.

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In the mid-1920s, Dr. Walter A. Shewhart developed the fundamentals of Statistical Process Control (though that was not what it was called at the time) and the associated tool of the Control Chart. His reasoning and approach were practical, sensible and positive. In order to be so, he deliberately avoided overdoing mathematical detail. In later years, significant mathematical attributes were assigned to Shewhart’s thinking with the result that this work became better known than the pioneering application that he had worked up.

The crucial difference between Shewhart’s work and the inappropriately perceived purpose of SPC that emerged, that typically involved mathematical distortion and tampering, is that his developments were in context, and with the purpose, of process improvement, as opposed to mere process monitoring; that is, they could be described as helping to get the process into that “satisfactory state” which one might then be content to monitor. Note, however, that a true adherent to Deming’s principles would probably never reach that situation, following instead the philosophy and aim of continuous improvement.

Suppose that we are recording, regularly over time, some measurements from a process. The measurements might be lengths of steel rods after a cutting operation, or the lengths of time to service some machine, or your weight as measured on the bathroom scales each morning, or the percentage of defective (or non-conforming) items in batches from a supplier, or measurements of Intelligence Quotient, or times between sending out invoices and receiving the payment, etc., etc.

A series of line graphs or histograms can be drawn to represent the data as a statistical distribution. It is a picture of the behaviour of the variation in the measurement that is being recorded. If a process is deemed as “stable” then the concept is that it is in statistical control. The point is that, if an outside influence impacts upon the process, (e.g., a machine setting is altered or you go on a diet, etc.) then, in effect, the data are of course no longer all coming from the same source. It therefore follows that no single distribution could serve to represent them. If the distribution changes unpredictably over time, then the process is said to be out of control. As a scientist, Shewhart knew that there is always variation in anything that can be measured. The variation may be large, or it may be imperceptibly small, or it may be between these two extremes; but it is always there.

What inspired Shewhart’s development of the statistical control of processes was his observation that the variability which he saw in manufacturing processes often differed in behavior from that which he saw in so-called “natural” processes – by which he seems to have meant such phenomena as molecular motions.

Wheeler and Chambers combine and summarize these two important aspects as follows: “While every process displays variation, some processes display controlled variation, while others display uncontrolled variation.”

In particular, Shewhart often found controlled (stable) variation in natural processes and uncontrolled (unstable) variation in manufacturing processes. The difference is clear. In the former case, we know what to expect in terms of variability; in the latter we do not. We may predict the future, with some chance of success, in the former case; we cannot do so in the latter.

Shewhart gave us a technical tool to help identify the two types of variation: the control chart.

What is important is the understanding of why correct identification of the two types of variation is so vital. There are at least three prime reasons.

First, when there are irregular large deviations in output because of unexplained special causes, it is impossible to evaluate the effects of changes in design, training, purchasing policy, etc. which might be made to the system by management. The capability of a process is unknown, whilst the process is out of statistical control.

Second, when special causes have been eliminated, so that only common causes remain, improvement then has to depend upon management action. For such variation is due to the way that the processes and systems have been designed and built – and only management has authority and responsibility to work on systems and processes. As Myron Tribus, Director of the American Quality and Productivity Institute, has often said:

“The people work in a system. The job of the manager is to work on the system to improve it, continuously, with their help.”

Finally, something of great importance, but which has to be unknown to managers who do not have this understanding of variation, is that by (in effect) misinterpreting either type of cause as the other, and acting accordingly, they not only fail to improve matters – they literally make things worse.

These implications, and consequently the whole concept of the statistical control of processes, had a profound and lasting impact on Dr. Deming. Many aspects of his management philosophy emanate from considerations based on just these notions.

So why SPC?

The plain fact is that when a process is within statistical control, its output is indiscernible from random variation: the kind of variation which one gets from tossing coins, throwing dice, or shuffling cards. Whether or not the process is in control, the numbers will go up, the numbers will go down; indeed, occasionally we shall get a number that is the highest or the lowest for some time. Of course we shall: how could it be otherwise? The question is – do these individual occurrences mean anything important? When the process is out of control, the answer will sometimes be yes. When the process is in control, the answer is no.

So the main response to the question “Why SPC?” therefore this: It guides us to the type of action that is appropriate for trying to improve the functioning of a process. Should we react to individual results from the process (which is only sensible, if such a result is signaled by a control chart as being due to a special cause) or should we instead be going for change to the process itself, guided by cumulated evidence from its output (which is only sensible if the process is in control)?

The key to any process improvement program is the Plan-Do-Study-Act cycle described by Walter Shewhart.


Plan involves using SPC tools to help you identify problems and possible causes.

Do involves making changes to correct or improve the situation.

Study involves examining the effect of the changes (with the help of control charts).

Act involves, if the result is successful, standardizing the changes and then working on further improvements or, if the outcome is not successful, implementing other corrective actions.

by Roger Edgell with an excerpt from Statit Software, Inc. 

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SPC FAQ

SPC FAQ

Just getting started? Here are answers to some of the most common SPC questions asked by those who have heard about SPC and want to learn more.

What is Statistical Process Control?

Statistical Process Control, commonly referred to as SPC, is a method for monitoring, controlling, and improving a process through statistical analysis. The philosophy states that all processes exhibit natural variation, or randomness. However, sometimes processes exhibit excessive variation that produces undesirable or unpredictable results. In a manufacturing context, the less consistent and predictable a process is, the higher its costs are. SPC is used to reduce variation and lower costs.

What is real-time SPC?

Today’s manufacturers rely heavily on a combination of automation, machinery, devices and technology in an effort to produce products faster. As manufacturing capacity increases, manufacturers require a method to increase their quality control capacity while shrinking the organization’s overall cost-of-quality. Traditional SPC allows manufacturers to understand what products and processes were in-control or out-of-control. However, for some manufacturers this information comes too little, too late.

Real-time or in-line SPC is defined as the technique of applying SPC on the shop floor at the time of production. Real-time SPC gathers product and process information in real-time and provides operators and plant managers with alerts, triggers, and other event management tools to quickly contain and fix defects before they leave the shop floor.

Most continuous improvement, Six Sigma and lean manufacturing initiatives require some form of SPC. While some programs focus on quality assurance, others focus on process optimization. Both real-time SPC and SPC are viable programs for improving manufacturing product and process quality. However, real-time SPC offers manufacturers a method to concurrently improve product and process quality and lower the cost-of-quality. Similar to the benefits that a calculator offers the mathematician, automated, real-time SPC provides manufacturers with a leaner method to continuously improve their product and process quality.

Where did SPC originate?

The foundation for Statistical Process Control was laid by Dr. Walter Shewhart working in the Bell Telephone Laboratories in the 1920s conducting research on methods to improve quality and lower costs. He developed the concept of control with regard to variation, and came up with Statistical Process Control charts which provide a simple way to determine if the process is in control or not. Dr. W. Edwards Deming built upon Shewhart’s work and took the concepts to Japan following WWII. There, Japanese industry adopted the concepts whole-heartedly.  The resulting high quality of Japanese products is world-renowned. Dr. Deming is famous throughout Japan. Today, SPC is used in manufacturing facilities around the world.

What is a histogram?

A histogram is a bar graph. Each bar shows the number of data points that fall within its measurement range. The relative heights of the bars offer clues to the health of a process.

 

What are control charts?

Control charts consist of product or process measurements over time and are a graphical representation of the variation between those measurements (or between subgroups of those measurements). Some additional horizontal lines representing the average measurement and control limits are frequently drawn across a control chart. Also, notes about data points and limit violations are commonly displayed.

Control charts have four key features: 1. Data points are either averages of subgroup measurements or individual measurements plotted on the x/y axis and joined by a line. Time is always on the x-axis. 2. The Average or Center Line is the average or mean of the data points and is drawn across the middle section of the graph, usually as a heavy or solid line. 3. The Upper Control Limit (UCL) is drawn above the centerline and often annotated as “UCL”. This is sometimes called the “+3 sigma” line. 4. The Lower Control Limit (LCL) is drawn below the centerline and often annotated as “LCL”. This is sometimes called the “-3 sigma” line.

What is the purpose of a control chart?

It helps quality teams monitor how a process is performing and identify special or assignable causes for factors that impede peak performance.

How do they work?

Control charts show if a process is in control or out of control. They show the variance (or variation) of process output over time. Control charts compare this variance against upper and lower limits to see if it fits within the expected, specific, predictable and normal variation levels. If so, the process is considered in control and the variance between measurements is considered normal random variation that is inherent in the process. If, however, the variance falls outside the limits, or has a run of non-natural points, the process is considered out of control.

What’s this relationship between variation and assignable causes?

Variation is the key to statistical process control charts. The extent of variation in a process indicates whether a process is working as it should. When the variation between the points is large enough for the process to be out of control, the variation is determined to be due to non-natural or assignable (special) causes.

So how are these normal, predictable, variance levels determined?

The process itself determines the control limits. The control limits are automatically calculated from the data produced by the process.  Control limits are the “voice of the process”. They are not specifications, corporate goals, or the “voice of the customer”. These two concepts must never be confused.

What about rule violations for determining if a series of points within the control limits is unnatural?

The work done by Shewart and his colleagues gave them a base of empirical knowledge on which to base rule violations. An example of a rule violation is six points in a row steadily increasing or decreasing. Rules such as this have been codified and are contained in the AT&T Statistical Quality Control Handbook. SPC software can be used to automatically check for violations of these time-tested and industry proven rules.

What’s the significance of in-control and out-of-control?

If a process is in-control, the outcomes of the process can be accurately predicted.  In an out-of-control process, there is no way of predicting whether the results will meet the target. An out-of-control process is like driving a bus with brakes that may or may not work. If a process is out-of-control, you look for the assignable causes that make it so and attempt to eliminate them.

What does process capability mean?

Process capability simply refers to what a process is capable of producing. Some processes might be capable of producing 100% of their output within spec, others considerably less. Sometimes an organization’s requirements, specifications, or goals are beyond what the process is actually capable of producing. In this case, either the process must be made more capable or the requirements, specifications, or goals relaxed.

Can any type of process data be judged using control charts?

Processes which produce data that exhibits natural or common-cause variation will form a distribution that looks like a bell-curve. For these types of processes, control charts will provide useful information. If the data is not normally distributed, does not form a bell-curve, the process is already out-of-control so it is not predictable. In this case we must look for ways to bring the process into control. For example, the data may be too broad, using measurements from different work shifts that have different process outcomes. Organizing the data collection into rational subgroups, each of which could be in control, is the first step to using control charts.

How do I make a control chart?

In the past, creating control charts was a difficult process requiring statisticians and mathematicians to remember the formulas and actually calculate the various data points and control limits. Today, using SPC software and computers, control charts can be constructed quickly and accurately, freeing you to investigate and remedy the situations exposed by control charts.

When is the best time to start SPC?

Now! The key to SPC is action. Rather than trying to discover the perfect methodology or waiting until you are an SPC expert, it is best to dive in and get started. You can always make adjustments as you go along. In most circumstances, the cost of poor quality and non-conformance is too great to do otherwise.

What are the Western Electric Rules that determine whether or not a process is in-control?

The relevant Western Electric Rules and the charts to which they apply are detailed in the below table.

CHARTS Western Electric Rules
  • X-bar, Individual, Median, R (when subgroup size is equal to or greater than 4)
  • 1 point above upper spec
  • 1 point below lower spec
  • 1 point above Zone A
  • 1 point below Zone A
  • 2 of 3 successive points in upper Zone A or beyond
  • 2 of 3 successive points in lower Zone A or beyond
  • 4 of 5 successive points in upper Zone B or beyond
  • 4 of 5 successive points in lower Zone B or beyond
  • 8 points in a row above centerline
  • 8 points in a row below centerline
  • 15 points in a row in Zone C (above and below center)
  • 8 points on both sides of center with 0 in Zone C
  • 14 points in a row alternating up and down
  • 6 points in a row steadily increasing or decreasing
  • R (when subgroup size is less than 4)
  • 1 point above upper spec
  • 1 point below upper spec
  • 1 point above Zone A
  • 2 successive points in or above upper Zone A
  • 3 successive points in or above upper Zone B
  • 7 successive points in or above upper Zone C
  • 10 successive points in or below lower Zone C
  • 6 successive points in or below lower Zone B
  • 4 successive points in lower Zone A
  • s, Moving Average, Moving Range
  • 1 point above upper spec
  • 1 point below lower spec
  • 1 point above Zone A
  • 1 point below Zone A
  • p, np, c, u
  • 1 point above upper spec
  • 1 point below lower spec
  • 1 point above Zone A
  • 1 point below Zone A
  • 9 points in a row above centerline
  • 9 points in a row below centerline
  • 6 points in a row steadily increasing or decreasing
  • 14 points in a row alternating up and down

by Statit Software, Inc.

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SPC Glossary

SPC Glossary

Unsure of a certain SPC term? Use this page to find the technical definition you’re after.

Accuracy
Accuracy of measurements refers to the closeness of agreement between observed values and a known reference standard. Any offset from the known standard is called bias.

 

Assignable Cause
A cause of process variation that isn’t random or inherent and that is attributable to some identifiable and controllable influence. A dulled cutting tool, for example, could be an assignable cause for a cutting process’s increased variation.

 

Attribute data
Qualitative data that can be counted for recording and analysis. Examples include: number of defects, number of errors in a document, number of rejected items in a sample, presence of paint flaws. Attribute data are analyzed using the p-, np-, c- and u-charts.

 

Average
See mean.

 

Average Run Length (ARL)
Short for average run length, ARL is the interval between out-of-control events that can be expected. For example, is a common out-of-control event chosen to determine a process’ ARL. When an out-of-control event appears on a control chart, an analyst can examine the interval between that event and the previous out-of-control event. If the interval matches or exceeds the process’ ARL value: a) the process can probably be classified as still in-control, b) the violation can probably be attributed to typical process variation, and c) a search for an assignable cause can probably be considered unwarranted. The inverses of these statements are likely true if the interval between out-of-control events is smaller than the ARL value.

 

Bias
The offset of a measured value from the true population value.

 

Binomial Distribution
A discrete probability distribution used for counting the number of successes and failures, or conforming and nonconforming units. This distribution underlies the p-chart and the np-chart.

 

Box and Whisker Plot
A graphical display of data tat shows the median and upper and lower quartiles, along with extreme points and any outliers.

 

Brainstorming
In the field of SPC as it is applied to manufacturing, a recognized strategy for identifying manufacturing problems and solutions.

 

Capability
A measure of the amount of variation inherent in a stable process. Capability can be determined using data from control charts and histograms and is often quantified using the Cp and Cpk indices. A process is said to be capable when all of its output is in-spec.

 

Cause-and-Effect Diagram
A quality-control tool used to analyze potential causes of problems in a product or process. It organizes potential problems into four groups: man, method, machine, and material. It is also called a fishbone diagram or an Ishikawa diagram, after its developer.

 

c-Chart
A control chart based on counting the number of defects per constant size subgroup. Also known as a Count of Nonconformities chart. The c-chart is based on the Poisson distribution.

 

Center Line (CL)
The line on the control chart that represents the long-run expected, or average value, of the quality characteristic that corresponds to the in-control state which occurs when only chance causes are present.

 

Central Limit Theorem
An important statistical theorem that states that subgroup averages tend to be normally distributed even if the output as a whole is not. This allows control charts to be widely used for process control, even if the underlying process is not normally distributed.

 

Check Sheet
In the field of SPC, a simple user-friendly form for collecting data over a period of time. Originally, it was a paper form but today it is often found integrated into SPC software.

 

Coefficient of Correlation
See Correlation below.

 

Common Causes
Problems with the system itself that are always present, influencing all of the production until found and removed. These are “common” to all manufacturing or production output. Also called chance causes, system causes, or chronic problems. Compare common causes to special causes.

 

Continuous Improvement
The ongoing improvement of products, services, or processes through incremental and breakthrough improvements.

 

Control Chart
A graphical mechanism for deciding whether the underlying process has changed based on sample data from the process. Control charts help determine which causes are “special” and thus should be investigated for possible correction. Control charts contain the plotted values of some statistical measure for a series of samples or subgroups, along with the upper and lower control limits for the process.

 

Control Limits
Numerical limits, often represented on control charts as horizontal lines, which indicate whether the process is statistically in control. There is typically an upper control limit (UCL) and a lower control limit (LCL). If the process is in control and only common causes are present, and nearly all of the sample points fall within the control limits.

 

Correlation
A measure of the relationship between two variables. If both variables grow larger (or smaller) together, they have a positive correlation. If one variable becomes smaller as the other grows larger, they have a negative correlation. Correlation values range from -1 to 1, with -1 indicating a negative correlation and 1 indicating a positive correlation.

 

Count Data
See attribute data.

 

Cp
A measure of the capability of a process to produce output within the specifications. The measurement is made without regard to the centering of the process.

 

Cpk
A measure of the capability of the process to produce output within the specifications. The centering of the process is taken into consideration by looking at the minimum of the upper specification limit capability and the lower specification limit capability. Cpk = min (Cpu, Cpl).

 

CUSUM
A control chart designed to detect small process shifts by looking at the Cumulative SUMs of the deviations of successive samples from a target value.
Design of Experiments
A branch of applied statistics dealing with planning, conducting, analyzing, and interpreting controlled tests which are used to identify and evaluate the factors that control a value of a parameter of interest.

 

Defect
An occurrence of a defect type (see below) in a manufactured part. A part can have multiple defect types and each type can have multiple occurrences.

 

Defective Unit
A part that is determined to be defective, without detailing what makes the part defective.

 

Defect Type
A type of defect that may be observed in a part; for example, scratched. Each defect type may have multiple occurrences.

 

Detection Model
A method of quality control that only inspects a process’s output. It is considered inferior to a prevention method, as it tends to result in more output needing to be scrapped or reworked. In contrast, a prevention method anticipates scrap and rework and makes process adjustments accordingly.

 

Distribution
A mathematical model that relates the value of a variable with the probability of the occurrence of that value in the population.

 

EWMA charts
An Exponentially Weighted Moving Average control chart that uses current and historical data to detect small changes in the process. Typically, the most recent data is given the most weight, and progressively smaller weights are given to older data.

 

Histogram
A bar graph representing the frequency of different measurements in a set of data. The graph is divided into ranges, such as 1-5, 6-10, 11-15, 16-20, and 21-25. Each range is represented by a bar, the height of which indicates the number of measurements in the set of data fall within that range.

 

Hypothesis Testing
A procedure that is used on a sample from a population to investigate the applicability of an assertion (inference) to the entire population. Hypothesis testing can also be used to test assertions about multiple populations using multiple samples.

 

In-Control Process
A process in which the quality characteristic being evaluated is in a state of statistical control. This means that the variation among the observed samples can all be attributed to common causes, and that no special causes are influencing the process.

 

Individual
A single unit or a single measurement of a quality characteristic, usually denoted as X. This measurement is analyzed using an individuals chart, CUSUM or EWMA chart.

 

Individuals Chart
A control chart for processes in which individual measurements of the process are plotted for analysis. Also called an I-chart or X-chart.

 

Kurtosis
The degree of peakedness, or flatness, of a histogram’s distribution curve.

 

Mean
The average of the individual values in a subgroup.

 

Median
The “middle” value in a group of values. If the number of values is even, by convention, the median is determined by averaging the two middle values.

 

Mixture
A pattern on a control chart that indicates data is coming from different systems or processes. The pattern consists of 8 consecutive points that occupy both sides of the center line in Zone B or beyond but not Zone C.

 

Mixing
A generally improper sampling technique that arises in practice when the output from several processes is first thoroughly mixed and then random samples are drawn from the mixture. This may increase the sample variability and make the control chart less sensitive to process changes. This action violates the fundamental rule of rational sampling.

 

Mode
The observation that occurs most frequently in a sample. The data can have no mode, be unimodal, bimodal, etc.

 

Moving Range
A measure used to help calculate the variance of a population based on differences in consecutive data. Two consecutive individual data values are compared and the absolute value of their difference is recorded on the moving range chart. The moving range chart is typically used with an Individuals (X) chart for single measurements.

 

Non-conforming Unit
A unit with one or more nonconformities or defects. Also called a reject or defective unit.

 

Non-conformity
A defect or an occurrence of something that violates a requirement, such as a scratch or dent.

 

Normal Distribution
A continuous, symmetrical, bell-shaped frequency distribution for variables data that is the basis for control charts for variables, such as x-bar and individuals charts. For normally distributed values, 99.73% of the population lies within ± 3 standard deviations of the mean. According to the Central Limit Theorem, subgroup averages tend to be normally distributed even if the output as a whole is not.

 

np-Chart
A control chart that plots the number of defective units in a lot. Only used when the lot size is fixed. The np-chart is based on the binomial distribution.

 

Outliers
Unusually large or small observations relative to the rest of the data.

 

Over-control
An element often introduced into a process by a well-meaning operator or controller who considers any appreciable deviation from the target value as a special cause. In this case, the operator is incorrectly viewing common-cause variation as a fault in the process. Over control of a process can actually increase the variability of the process and is viewed as a form of tampering.

 

Pareto Chart
A problem-solving tool that involves ranking all potential problem areas or sources of variation according to their contribution to cost or total variation. Typically, 80% of the effects come from 20% of the possible causes, so efforts are best spent on these “vital few” causes, temporarily ignoring the “trivial many” causes.

 

Pareto Principle
The principle that 80% of the problems are due to 20% of the causes. Also known as the 80/20 rule.

 

p-Chart
A control chart that plots the proportion of nonconforming units per lot.

 

Percentiles
Percentiles divide the ordered data into 100 equal groups. The kth percentile pk is a value such that at least k% of the observations are at or below this value and (100-k)% of the observations are at or above this value.

 

Poisson Distribution
A probability distribution used to count the number of occurrences of relatively rare events. The Poisson distribution is used in constructing the c-chart and the u-chart.

 

Precision
Precision of measurements refers to their long-run variation (s2). It is a measure of the closeness between several individual readings.

 

Prevention Model
A method of quality control that proactively adjusts a process using SPC so that scrap and rework are prevented. It is considered superior to a detection model, which only inspects a process’s output.

 

Process Capability
A measure of the ability of a process to produce output that meets the process specifications.

 

Quartile
Quartiles divide the ordered data into 4 equal groups. The second quartile (Q2) is the median of the data.

 

Random Sampling
A subset of the population chosen such that each member of the population has an equal probability of being included in the sample.

 

Range
The difference between the highest and lowest values in a subgroup. For example, if a subgroup contains the values 1, 2, 6, 4, and 5, the range is the difference between 6 and 1, which is 5.

 

Rational Subgroups
A principle of sampling which states that the variation between subgroups or samples should be solely attributable to the common causes in the system rather than the sampling method. Rational subgroups are usually chosen so that the variation represented within each subgroup is as small as feasible for the process, so that any changes in the process, or special causes, appear as differences between subgroups. Rational subgroups are typically made up of consecutive pieces, although random samples are sometimes used.

 

R-Chart
A control chart based on the range (R) of a subgroup, typically used in conjunction with an x-bar chart.

 

Run
A consecutive number of points consistently increasing or decreasing, or above or below the centerline. A run can be evidence of the existence of special causes of variation that should be investigated.

 

Run Chart
A simple graphic representation of a characteristic of a process which shows plotted values of some statistic gathered from the process. The graphic can be analyzed for trends or other unusual patterns.

 

S-Chart
A control chart based on the standard deviation, s, of a subgroup. The s-chart is typically used in conjunction with an x-bar chart.

 

Sample
A subset of data from a population that can be analyzed to make inferences about the entire population.

 

Sampling Distribution
The probability distribution of a statistic. Common sampling distributions include t, chi-square (c2), and F.

 

Scatter Plots
A graphical technique used to visually analyze the relationship between two variables. Two sets of data are plotted on a graph, with the y-axis being used for one variable and the x-axis being used for the other.

 

Sensitizing Rules
Control chart interpretation rules that are designed to increase the responsiveness of a control chart to out-of-control conditions by looking for patterns of points that would rarely happen if the process has not changed.

 

Short-run Techniques
Adaptations made to control charts to help determine meaningful control limits in situations when only a limited number of parts are produced or when a limited number of services are performed. Short-run techniques usually look at the deviation of a quality characteristic from a target value.

 

Sigma
The Greek letter used to designate a standard deviation.

 

Six Sigma
A high-performance, data-driven approach to analyzing the root causes of business problems and solving them. Six-sigma techniques were championed by Motorola.

 

Skewness
The tendency of the data distribution to be non-symmetrical. Skewness can be positive or negative and may affect the validity of control charts and other statistical tests based on the normal distribution.

 

SPC
Statistical Process Control, a proven and comprehensive methodology for achieving and maintaining manufacturing quality.

 

Special Causes
Causes of variation which arise periodically in a somewhat unpredictable fashion. Also called assignable causes, local faults, or sporadic problems. Contrast to common causes. The presence of special causes indicates an out-of-control process.

 

Specification Limits
The upper and lower limits within which a process’s output must fall in order for that output to be acceptable.

 

Spread
The amount of variability in a sample or population.

 

Stability
A process is considered stable if it is free from the influences of special causes. A stable process is said to be in control.

 

Standard Deviation
Deviation is the distance far process measurements deviate from the process mean. Standard deviation is a standardized distance that is calculated from process data.

 

Statistic
A value calculated from, or based on, sample data which is used to make inferences about the population from which the sample came. Sample mean, median, range, variance, and standard deviation are commonly calculated statistics.

 

Statistical Control
The condition describing a process from which all special causes of variation have been removed and only common causes remain.

 

Statistical Process Control (SPC)
A collection of problem solving tools useful in achieving process stability and improving capability through the reduction of variability. SPC includes using control charts to analyze a process to identify appropriate actions that can be taken to achieve and maintain a state of statistical control and to improve the capability of the process.

 

Statistical Quality Control (SQC)
Another name commonly used to describe statistical process control techniques.

 

Stratification
Stratification arises in practice when samples are collected by drawing from each of several processes, for example machines, filling heads or spindles. Stratified sampling can increase the variability of the sample data and make the resulting control chart less sensitive to changes in the process.

 

Subgroup
Another name for a sample from the population. Subgroups consist of individual measurements or readings and the number of measurements or readings is referred to as the subgroup size. A common subgroup size is 5, which means each subgroup consists of 5 measurements or readings.

 

Tampering
An action taken to compensate for variation within the control limits of a stable system. Tampering increases rather than decreases variation.

 

Target
The ideal or aimed-for measurement of a process. It is typically mid-way between the upper and lower specification limits but does not have to be.

 

Type I Error
Occurs when a true hypothesis about the population is incorrectly rejected. Also called false alarm. The probability of a Type I error occurring is designated by a.

 

Type II Error
Occurs when a false hypothesis about the population is incorrectly accepted. Also called lack of alarm. The probability of a Type II error occurring is designated by b.

 

u-Chart
A control chart that plots the number of non-conformities or defects per inspection unit. It is used when the lot size is not fixed.

 

Variable Data
Measurements, such as diameter or weight, that are taken from a measuring instrument, such as calipers or a scale. It contrasts with attribute data, which consists of defects that are observed by a human. An example of attribute data is scratches or dents.

 

Variation
The differences among individual results or output of a machine or process. Variation is classified in two ways: variation due to common causes and variation due to special causes.

 

X Chart
A control chart used for process in which individual measurements of the process are plotted for analysis, as opposed to being grouped into subgroups and averaged. Also called an individuals chart or I-chart.

 

Xbar Chart
A control chart for variable data that plots the average of each subgroup.

 

Xbar-R Chart
Two control charts that are viewed together. Usually, the X-bar chart is positioned above the R chart. Both charts are for variable data. The X-bar chart plots the average of each subgroup. The R chart plots the range of each subgroup and is typically used when the subgroup size is 7 or less.

 

Xbar-S Chart
Same as Xbar-R but typically used when the subgroup size is 8 or more.

 

Zone A
The outermost one-third of the area between the center line and the upper and lower limits on a control chart.

 

Zone B
The center one-third of the area between the center line and the upper and lower limits on a control chart.

 

Zone C
The innermost one-third of the area between the center line and the upper and lower limits on a control chart.

 

 

Bibliography

Nelson, Loyd S. (1985), “Interpreting Shewhart X Control Charts”, Journal of Quality Technology, 17:114-16.
Steel, R. G. D. and J. H. Torrie (1980), Principles and Procedures of Statistics.New York: McGraw-Hill.
Western Electric Company (1956), Statistical Quality Control Handbook, available from ATT Technologies, Commercial Sales Clerk, Select Code 700-444, P.O. Box 19901, Indianapolis, IN 46219, 1-800-432-6600.
 
by Statit Software, Inc.

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What is SPC?

What is SPC?

(/ stə-ˈti-sti-kəl  ˈprä-ˌses  kən-ˈtrōl /) noun —  a statistical method that aids in detection of process problems

Statistical Process Control, commonly referred to as SPC, is a method for monitoring, controlling and, ideally, improving a process through statistical analysis.

The result of SPC is reduced scrap and rework costs, reduced process variation, and reduced material consumption.

SPC states that all processes exhibit intrinsic variation. However, sometimes processes exhibit excessive variation that produces undesirable or unpredictable results. SPC, in a manufacturing process optimization context, is used to reduce variation to achieve the best target value.

Considering SPC? The posters and slides available on our SPC Training Materials page contain practical information on SPC benefits and fundamentals. 

In the mid-1920s, Dr. Walter A. Shewhart developed the fundamentals of Statistical Process Control (though that was not what it was called at the time) and the associated tool of the Control Chart. His reasoning and approach were practical, sensible and positive. In order to be so, he deliberately avoided overdoing mathematical detail. In later years, significant mathematical attributes were assigned to Shewhart’s thinking with the result that this work became better known than the pioneering application that he had worked up.

The crucial difference between Shewhart’s work and the inappropriately perceived purpose of SPC that emerged, that typically involved mathematical distortion and tampering, is that his developments were in context, and with the purpose, of process improvement, as opposed to mere process monitoring; that is, they could be described as helping to get the process into that “satisfactory state” which one might then be content to monitor. Note, however, that a true adherent to Deming’s principles would probably never reach that situation, following instead the philosophy and aim of continuous improvement.

Suppose that we are recording, regularly over time, some measurements from a process. The measurements might be lengths of steel rods after a cutting operation, or the lengths of time to service some machine, or your weight as measured on the bathroom scales each morning, or the percentage of defective (or non-conforming) items in batches from a supplier, or measurements of Intelligence Quotient, or times between sending out invoices and receiving the payment, etc., etc.

A series of line graphs or histograms can be drawn to represent the data as a statistical distribution. It is a picture of the behaviour of the variation in the measurement that is being recorded. If a process is deemed as “stable” then the concept is that it is in statistical control. The point is that, if an outside influence impacts upon the process, (e.g., a machine setting is altered or you go on a diet, etc.) then, in effect, the data are of course no longer all coming from the same source. It therefore follows that no single distribution could serve to represent them. If the distribution changes unpredictably over time, then the process is said to be out of control. As a scientist, Shewhart knew that there is always variation in anything that can be measured. The variation may be large, or it may be imperceptibly small, or it may be between these two extremes; but it is always there.

What inspired Shewhart’s development of the statistical control of processes was his observation that the variability which he saw in manufacturing processes often differed in behavior from that which he saw in so-called “natural” processes – by which he seems to have meant such phenomena as molecular motions.

Wheeler and Chambers combine and summarize these two important aspects as follows: “While every process displays variation, some processes display controlled variation, while others display uncontrolled variation.”

In particular, Shewhart often found controlled (stable) variation in natural processes and uncontrolled (unstable) variation in manufacturing processes. The difference is clear. In the former case, we know what to expect in terms of variability; in the latter we do not. We may predict the future, with some chance of success, in the former case; we cannot do so in the latter.

Shewhart gave us a technical tool to help identify the two types of variation: the control chart.

What is important is the understanding of why correct identification of the two types of variation is so vital. There are at least three prime reasons.

First, when there are irregular large deviations in output because of unexplained special causes, it is impossible to evaluate the effects of changes in design, training, purchasing policy, etc. which might be made to the system by management. The capability of a process is unknown, whilst the process is out of statistical control.

Second, when special causes have been eliminated, so that only common causes remain, improvement then has to depend upon management action. For such variation is due to the way that the processes and systems have been designed and built – and only management has authority and responsibility to work on systems and processes. As Myron Tribus, Director of the American Quality and Productivity Institute, has often said:

“The people work in a system. The job of the manager is to work on the system to improve it, continuously, with their help.”

Finally, something of great importance, but which has to be unknown to managers who do not have this understanding of variation, is that by (in effect) misinterpreting either type of cause as the other, and acting accordingly, they not only fail to improve matters – they literally make things worse.

These implications, and consequently the whole concept of the statistical control of processes, had a profound and lasting impact on Dr. Deming. Many aspects of his management philosophy emanate from considerations based on just these notions.

So why SPC?

The plain fact is that when a process is within statistical control, its output is indiscernible from random variation: the kind of variation which one gets from tossing coins, throwing dice, or shuffling cards. Whether or not the process is in control, the numbers will go up, the numbers will go down; indeed, occasionally we shall get a number that is the highest or the lowest for some time. Of course we shall: how could it be otherwise? The question is – do these individual occurrences mean anything important? When the process is out of control, the answer will sometimes be yes. When the process is in control, the answer is no.

So the main response to the question “Why SPC?” therefore this: It guides us to the type of action that is appropriate for trying to improve the functioning of a process. Should we react to individual results from the process (which is only sensible, if such a result is signaled by a control chart as being due to a special cause) or should we instead be going for change to the process itself, guided by cumulated evidence from its output (which is only sensible if the process is in control)?

The key to any process improvement program is the Plan-Do-Study-Act cycle described by Walter Shewhart.


Plan involves using SPC tools to help you identify problems and possible causes.

Do involves making changes to correct or improve the situation.

Study involves examining the effect of the changes (with the help of control charts).

Act involves, if the result is successful, standardizing the changes and then working on further improvements or, if the outcome is not successful, implementing other corrective actions.

 
by Roger Edgell with an excerpt from Statit Software, Inc. 

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