In business, there is a natural variation in nearly every business-related activity or process. For example, in manufacturing, the number of substandard or defective items per million produced will likely vary with each production run. In customer service, the number of complaints may be higher one month than they were the month before. A school district may discover that SAT scores in one high school are higher than another.

The challenge with business variation is that it is not always clear, for a given data set or time period, if the reported results are significant enough to warrant management’s attention.

SPC, or Statistical Process Control, is a method for determining when the variation in a given business process has exceeded “normal” behavior and is considered “out of control”. SPC calculations are applied to raw data, and the results are then graphed for easy viewing. Once identified, out of control processes can command the appropriate level of management’s time and attention, and strategies can be devised to address them.

In NetCharts Analytics, the functions described in the following section perform the necessary SPC calculations and generate data for easy graphing.

There are two main types of SPC charts. Control charts for variables, and control charts for attributes.

Control charts for variables are based on a periodic sampling of real data values (weight, cost, height, location, etc) in order to determine the behavior of the process. They are considered to be preventative; identifying problems before they occur. The SPC control charts for variables are:

• Run Chart
• XBar – R Control Charts
• XBar – s Control Charts
• Median – R Control Charts
• Median – s Control Charts
• Individuals Chart or Moving Range (MR) Chart
• Exponentially Weighted Moving Average (EWMA) Charts
• Histogram
• Probability Chart

Control charts for attributes are used to identify samples in a given set of data that conform to a defined standard versus those that do not. The SPC control charts for attributes are:

• p Charts
• np Charts
• c Charts
• u Charts

Following are general guidelines for Control Chart selection:

1. If the data is of type measurable then use Control charts for variablesTo view raw data and make general observations use Run Chart.

   To derive statistical analysis:
   If the sample size is 1 then use MR Chart
   If the sample size is greater than 1 and number of samples is less than 10 then use Range Charts – Xbar R or Median R.
   If the sample size is greater than 1 and number of samples is greater than 10 then use s (Standard Deviation) Charts – XBar s or Median s.
   EWMA chart is an alternative to XBar charts when sample size is greater than 1. EWMA chart is an alternative to MR charts when sample size is equal to 1. This chart has a build in mechanism for incorporating information from all previous samples, weighting the information from the closest sample with a higher weight.
   Histogram can be used to check if a process is normally distributed and centered.
   Probability chart is used to determine the normality of a distribution.

2. If the data is of type countable then use Control charts for AttributesIf the number of nonconformities is less than the items checked use p Chart, when the sample sizes are not the same, or np Chart, when the sample sizes are the same for each sample.

   If the number of nonconformities is greater than the items checked use u Chart when the sample sizes are not the same, or c Chart, when the sample sizes are the same for each sample.

SPC Run Rules

In most of the Variables SPC charts, a set of run rules will be applied to the data with the results posted in the last column of output data. These rules may be used in concert with NetCharts Designer’s Conditional Colors process module in order to highlight one or more out-of-control conditions.

Consider the results below of an XBAR-s function (NOTE: All XDBBar columns have been removed from the table below because of space):

 
Note that in row 15 and 19, the Rules Check column (at the end) identifies a rule as having been met. The value of the Rules Check result distinguishes between which rule(s) were met. In the following manner:

 
Note that if a point meets more than one rule, the values will be combined. For example, if the point exceeds the UCL and is part of a six-point trend, then the Rules Check value would be 101.

Conditional Colors

As previously mentioned, developers may wish to identify out-of-control conditions on the graph by leveraging the Rules Check data. This can be done in the following steps: (This assumes the SPC function has already been applied to the data)

1. From the Process Modules listbox in the data editor, select Add
2. Choose the Conditional Colors process module (this is a default process module within the Visual Mining group).
    
   
    
3. In the “Configure Process Module” dialog, set the Base Value Column to be the index of the Rules Check column. Note that all column numbers start at 0 (in our example above, the column index is 14).
4. Next to the “Expressions” listbox, select the Add button. Set up one or more expressions that you’d like to identify individual colors for.
    
   
    
5. After configuring the parameters, an additional column will be added to the data set called “Colors“.
6. From the chart editor, configure the SPC chart per the instructions given in the document. In the Data Source binding tab, map the Line Color Tables data to the new column. This will cause any non-null color values to override the default color of the line symbol.
    
   
    

SPC Attributes Chart – c

The c chart is used to measure the number of defects for a given item. It implies that each sample has an equal size.

Parameter Set

 
Applications

Determine statistically normal number of accidents per month, defects per square yard of cloth, oil spills per year, etc.

Data Sample

 
Chart Sample
The following chart shows the number of unfavorable responses per 1000 customer surveys on a given day.
 

 

SPC Attributes Chart – np

The np Attribute chart displays the number of non-conforming items within a defined sample size.

Parameter Set

 
Applications

Use to determine errors per 1000/lines of software, on-the-job accidents per 2000 man-hours, many other uses.

Data Sample

 
Chart Sample
The following chart shows a non-conformance (late arrivals) plot per 1000 (sample size) packages for a given day.
 

 

SPC Attributes Chart – p

The p SPC Attribute chart is used to evaluate non-conforming units by comparing the proportion of defective elements to the number sampled. It may be used for any sample size and inconsistent sample sizes.

Parameter Set

 
Applications

Test and report results on between 300 – 900 computer chips/day to determine approximate quality levels. Many more uses.

Data Sample

 
Chart Sample
The following chart shows the proportion of defective LCD’s produced on a given day.
 

 

SPC Attributes Chart – u

The u chart is used when there can be more than one defect per item tested and the sample size varies. It shows the proportion of defects per item.

Parameter Set

Applications

Use to determine number of defective items on a circuit board, number of unfavorable responses on a customer survey, many more uses.

Data Sample

 
Chart Sample
The following chart shows the results of daily customer surveys. Each point represents the proportion of negative responses for each survey, for a given day.
 

 

SPC Variables Chart – EWMA

The Exponentially Weighted Moving Average (EWMA) chart is used for fast detection of out of control processes and no run rules are required. It gives less emphasis, or weight, to the data as the data ages.

Parameter Set

 
Applications

Used in many manufacturing quality applications measuring the precision of the manufactured products.

Data Sample

 
Chart Sample
 

 

SPC Variables Chart – Histogram

Shows the frequency of elements in the data sample. Also allows specification of USL/LSL.

Parameter Set

 
Applications

Use to show software errors found per test segment, many other uses.

Data Sample

 
Chart Sample
 

 

SPC Variables Chart – MR

Moving Range chart. Helps amplify sudden changes in data.

Parameter Set

 
Applications

Note increase in product defects, days late, many more uses.

Data Sample

 
Chart Sample
 

 

SPC Variables Chart – Median-R

The Median-R, or “median range” chart determines the median value and range of each subgroup. It controls the centering of a process as well as the process variability. Typically used when the samples in the subgroup are 10 or less.

Parameter Set

 
Applications

Use for controlling energy use, product output, much more.

Data Sample

 
Chart Sample
 

 

SPC Variables Chart – Median-s

The Median-s, or “median standard deviation” chart determines the median value and standard deviation of each subgroup. Typically used when the samples in the subgroup are 10 or more.

Parameter Set

 
Applications

Use for controlling energy use, product output, much more.

Data Sample

 
Chart Sample
 

 

SPC Variables Chart – Probability

Determines the “normality” of a given distribution and the likelihood of a particular process result.

Parameter Set

 
Applications

Help determine expected results for task completion, many other uses.

Data Sample

Chart Sample
 

 

SPC Variables Chart – XBar-R

Displays variation occurring in a set of data points. It helps to examine the variation of a process (but not necessarily a product). It computes the average value and range for each subgroup. Typically used when the samples in the subgroup are 10 or less.

Parameter Set

Applications

May be used to examine the stability in a manufacturing process, software development process, and much more.

Data Sample

Chart Sample
 

 

SPC Variables Chart – XBar-s

The XBAR-s chart determines the average value and standard deviation of each subgroup. Typically used when the samples in the subgroup are 10 or more.

Parameter Set

Applications

May be used to examine the stability in a manufacturing process, software development process, and much more.

Data Sample

Chart Sample