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Statistical Process Control Chart Basics

Many companies employ SPC throughout various operations in their facility. Individuals who manage the SPC programs may be familiar with the formulas required to calculate control chart limits, but they are not always aware of the basic requirements or "rules" for control charts that must be followed in order to obtain valid results. There are many prerequisites or considerations for all control charts. These general requirements are specific as to whether you have variable or attribute data, whether or not the subgroup sizes are constant or changing, and how much sensitivity for variation detection is desired. A facility using SPC that is unaware of these requirements can be making mistakes, or errors in judgment, without knowing they have violated the general rules and in return may be actually harming the process rather than improving it. The analysis of control chart requirements and rules can be somewhat extensive. The following text illustrates just a sample of the basics of different types of control charts and their associated rules.

View The Top Seven Run Rules for control charts...Click Here

DL SPC Chart Basics  The Statistical Solutions SPC Charts Basic Document*

VARIABLES CONTROL CHARTS (XBAR/S, XBAR/R and I charts for example)
 
Variables control charts for subgroup data are powerful and simple visual tools for determining whether a process may be in or out of control.
  • An in-control process exhibits only random variation any will remain within the control chart limits.
  • An out-of-control process exhibits non-random variation due to the presence of special-causes. (special-cause is sometimes referred to assignable-cause)
 
Control charts can help you determine whether the process average (center) and process variability (spread) are operating at normal levels. Control charts help you focus problem-solving efforts by distinguishing between common and special-cause variation.
 
A variables control chart for subgroup data will consist of the following:
  • Plotted points, each of which represents a rational subgroup of data sampled from the process, such as a subgroup mean or average.
  • A center line, which represents the expected value of the characteristic for all subgroups.
  • Upper and lower control limits (UCL and LCL), which are set at the distance of 3 sigma above and below the center line. These control limits provide a visual display, or "zone", for the expected amount of variation. Control limits predict how the process should behave. The control limits are based on probability and the actual behavior of the process, not the desired behavior. Control chart limits are different from specification limits. A process can be in control and still not be capable of meeting the specification limit requirements.
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A graphical example of a basic control chart is shown at the right with a center line (green) and upper/lower control limits (red).
SPC Chart
Control charts evaluate the patterns of variation for stability through the use of tests for special causes. If you detect special cause variation, you should seek out the factors that contribute to this variation so that you can implement corrective actions.
 
XBAR/S CHART vs. XBAR/R CHART
 
Both XBar/S charts and XBar/R charts measure subgroup variability. The S chart uses the "standard deviation" to represent the spread in the data and the R chart uses the "range". Both charts lead to a similar estimate of the process standard deviation and similar control limits for the charts. The calculation of the range uses only two data points - the largest and smallest values - while the calculation of the standard deviation uses all the data from the sub-group. R charts are not as sensitive to small amounts of variation as the S chart. You must decide what is most important for your specific requirements when deciding between an S chart and an R chart.
 
XBar Chart (Averages)
The Xbar chart is where the sub-group averages or mean values are plotted. Probability shows us that the averages of our processes tend to stay constant unless special-cause is present. A process can be behaving normally for the averages and at the same time be considered out-of-control for the R and S charts. The reverse is also true, R and S charts can remain in-control while the averages become out-of-control.
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S Chart (Standard Deviations)
Use the S chart when the subgroup sizes are nine or greater. S charts use all the data collected to calculate the subgroup and process standard deviations. S charts provide a more accurate indication of the process variation and result in a chart that is very sensitive to small changes in the process average. You should consider using S charts for processes with a high rate of production, when data collection is quick and inexpensive, or when increased sensitivity to variation is desired. S charts can detect smaller amounts of variation when compared to R charts. The only negative aspect in managing an S chart is the need to perform the more difficult calculations for the standard deviation which typically are accomplished by using a computer.
 
R Chart (Ranges)
Use the R chart when your subgroup sizes are eight or less. R charts are efficient for small subgroup sizes and are easier to manage due to basic shop math calculations that need to be performed. R charts can be highly influenced by a single data value from the sub-group.
 
I Charts (Individuals)
When collecting samples to learn about a process, it is sometimes easier to combine the samples into subgroups, if it makes sense to group the samples together. When grouping is not appropriate, then a subgroup size of one (1) provides a method for evaluating the process. Samples that cannot logically be grouped together are good candidates for individuals (I) and moving range (MR) charts.
 
Examples of conditions that make using subgroups unfeasible or undesirable could be similar to the following:
  • When each sample is unique with respect to a specific period of time.
  • When each sample represents one distinct batch or group.
  • When there are extremely long time intervals between each sample or production cycle time is extended.
  • When sampling or testing is destructive or may be cost prohibitive due to expense.
  • When the output is continuous and homogenous.
  • When the measurements (results) are not necessarily related in time to each other.
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ATTRIBUTES CONTROL CHARTS (P and NP charts for example)
 
Attributes control charts represent a rational sample of data sampled from the process and are either counts (n) of the number of defectives or defects per sample, or proportions of the defectives or defects per sample (%).
  • An in-control process exhibits only random variation any will remain within the control chart limits.
  • An out-of-control process exhibits non-random variation due to the presence of special-causes. (special-cause is sometimes referred to assignable-cause)
 
Control charts can help you determine whether the process average (center) and process variability (spread) are operating at normal levels. Control charts help you focus problem-solving efforts by distinguishing between common and special-cause variation.
 
An attributes control chart for subgroup data will consist of the following:
  • Plotted points, each of which represents a rational subgroup of data sampled from the process, such as a subgroup mean or average.
  • Center line, which is the average number (NP Chart) or average proportion (P Chart) of defectives or defects.
  • Control limits, which are set at a distance of 3 sigma on either side of the center line and provide a visual display for the expected number or proportion of defectives or defects. These control limits provide a visual display, or "zone", for the expected amount of variation. Control limits predict how the process should behave. The control limits are based on probability and the actual behavior of the process, not the desired behavior. Control chart limits are different from specification limits. A process can be in control and still not be capable of meeting the specification limit requirements.
 
P CHART vs. NP CHART
An attribute defect is a product or service in which a nonconformity (or flaw) renders the product or service unusable. Examples of this type of defect include broken articles, late deliveries, unanswered calls, scratched paint, and flat tires. Attributes can have only one of two outcomes, pass/fail, good/bad, go/no-go, etc.
 
P Chart (Proportion Defective..%)
Use P charts to study the proportion of defectives in each sample and determine whether or not the process is in control. Use P charts when your sub-group sample sizes vary.
 
NP Chart (Number Defective..n)
Use NP charts to examine the number of defectives in each sample and determine whether or not the process is in control. You should not use an NP chart when your sub-group sample sizes vary because the control limits and center line change when sample size changes. This variation in sub-group sample sizes and changing limits would make the NP chart difficult to manage and interpret.
 
View The Normal Distribution - An Illustration of Basic Probability...Click Here
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