Integrating SPC and SQC with DataLyzer® Spectrum
Keywords: attribute, analysis, priority, defect, AQL, sample, defect, category, ranking, control limit, alarm, subgroup
SQC and SPC are both powerful techniques, but they both have disadvantages. In this document a methodology is presented which will overcome the disadvantages of the separate systems by integrating the techniques. This methodology is implemented in DataLyzer Spectrum.
SQC is short for statistical quality control and deals with the statistics used for acceptance sampling. Based on consumer, producer risks, lot sizes and acceptable reject levels a specific sampling plan and acceptance numbers are chosen to take samples of a lot.
Well known and often used techniques based on SQC are Mil standards 105D also known as ABC standard.
Although the statistics used in SQC will bring the quality of delivered goods to a predictable level there are some negative points about SQC.
SQC is always at the end of a process, when the problems already have occurred. SQC in itself will not improve the process and give proper signs when a problem has appeared. It will only inform the inspector whether the lot is good enough to be shipped.
When inspecting during the process to find possible problems as soon as they appear the technique of SPC is often used.
The advantage of SPC is that sampling is done with a high frequency which will increase the chance of finding a process problem in the early stages. The technique used when applying SPC are attribute control charts.
Attribute control charts have a few disadvantages:
1. Different defects are combined in an attribute chart. This means that no distinction is made between major and minor errors and especially if the number of minor errors is bigger than the number of major errors this will influence the statistics. The solution in this case could be to make separate charts for minor and major defects but that will increase the amount of administrative work.
2. Attribute charts assume that the data can be treated as coming from a normal distribution which is only true if the number of errors is so high that np > 2.5. A solution can be to calculate the limits based on X moving Range instead of normal calculations. This approach will give good results as long as the number of errors in the subgroup is 1 or higher. In most attribute processes the number of errors is lower. This means you need to combine subgroups to get subgroups big enough to get an average of 1 or higher.
3. The attribute control charts will give the operator information when the process is out of control but it will not give proper information when the lot should be blocked based on chosen consumer and producers risks. This means in case of an out of control SQC should be applied to verify whether the lot can be shipped.
The problems presented above can be overcome by integrating the two techniques.
DataLyzer is using the attribute charts so we have implemented solutions which will overcome the problems presented applying SPC.
The solution to the problem of different type of errors is to introduce categories in DataLyzer. These categories can have a reject limit. If the number of errors in a category exceed the reject limit an alarm will be given. The reject limit can be set by the user.
The solution to problem 2 and 3 is to combine subgroups and summarize the defects in these subgroups. In the setup of DataLyzer you can enter a Sampling Plan Size for a category and an acceptance number related to that Sampling Plan. When entering a new subgroup, DataLyzer will go back in the chart and combine subgroups until the number inspected for combined subgroups exceeds the Sampling Plan Size. The number of errors found in the Sampling Plan will be compared with the acceptance number and an alarm will be given if the acceptance number is exceeded. This alarm implicates the lot should be blocked and should not be shipped.
How to establish Sampling Plan Sizes and acceptance numbers is not supported in DataLyzer. DataLyzer assumes you come up with the numbers based on mil. Standards 105D or any other system used in your company.
A program which can assist in establishing the correct sample sizes and acceptance numbers is sampling plan analyzer. A demo version can be downloaded from www.spc-itk.com.
The technique implemented in DataLyzer will not support double sampling plans.
To implement extended attribute category analysis, select SETUP/DEFINE DEFECT CATEGORIES from the main DataLyzer® Spectrum screen. To add a defect category, press the “add” button. A window will appear. Enter the name of the defect category in the window and press “ok”.
The category you created will appear in the “Define Defect Categories” window. Continue this procedure of adding categories until you are satisfied with your category selections and fill out the associated fields for each category.
Each defect category has an associated row of user-defined data that must be filled out before data entry. In the order column, enter the importance of the defect category. For example, the most important category should be rated with a “1”, and less important categories should have higher numbers.
In the limit field, enter the maximum number of defects for each category allowed per subgroup entered. This includes all defects within the defect category. For example, if the “minor” category contains the defects “blistered”, “scratched”, and “discolored”, the total number of defects of blistered, scratched, and discolored combined must not exceed five defects. .
The acceptance number field allows users to track defects over a specific period rather than just one subgroup. In the Sampling Plan Size, enter the number of pieces you wish to track. In the acceptance number field, enter the number of defects allowed in the given Sampling Plan Size. If any subgroup’s number of defects exceeds this limit, the subgroup will be considered out of specification and labeled as such on the HUB status screen. If a negative number is entered into a limit cell, it means no limit is in effect.
Notice that if the Sampling Plan Size is the same size as the subgroup size, the Limit field and acceptance number field may have the same values.
The “Combine” field gives the option of creating a category to hold a cumulative count of all previous categories combined. There are three possible settings for the “Combine” field. The default setting is an unchecked box. This means that no additional category will be displayed. If you click the box once, a checked box appears with the word “only”. This setting displays the cumulative category only, and does not display the individual category. If you click the box again, a box appears with the word “both”. This setting displays the cumulative category as well as the individual category.
In the “Combined Name” field, enter a title label to correspond with the combined categories. The combined name cannot exceed twelve characters. If the “Combine” field is left blank, the “Combined Name” field may be left empty as well.
How it works:
If no entries are made in the combined column, only the main defect categories appear in the defect category table below the attribute graph during data entry. They tally individually with a total defects option. You can see a graph for each category and the total by clicking the category button for each one.
In some cases you may wish to combine categories together and name the combination separately. In those cases, you can use options in the “Combine” column. These options include “Only” and “Both”.
“Only” replaces the associated main category row with a row labeled from the “Combined Name” column in the table below the control chart. This row contains a cumulative tally of all rows above it. The main category it replaced will continue to be tallied behind the scenes. “Both” leaves the main defect category in the table and adds a row for the cumulative tally in the table.
The graphic below shows the setup for the category table that will appear below the control chart during data entry. When viewing control charts for an attribute, a separate count will be kept of critical defects, major defects, and minor defects. Since the “Only” setting is selected in the “Major” category, however, the “Major” category will not appear on the control chart, never the less an internal count for it will be maintained. The “Major” category will be replaced in the table by a cumulative tally of the rows above displaying the totals for “critical” and “major” defects. This row will be labeled “Important”, as designated in the “Combined Name” column.
Since “Both” appears in the “Combined” column for the “Minor” defects row, it causes both the minor defects and a cumulative row to be inserted. The cumulative row will be labeled “All Defects”. Example data entry and control chart windows for this example are shown later in this document.
Once you are satisfied with the changes you made to the “Define Defect Categories” window, press the “Ok” button to save your changes and exit to the main DataLyzer® Spectrum screen. Press the “Cancel” button to exit to the main DataLyzer® Spectrum screen without saving your changes. To delete a category, place the cursor in the row of the category you wish to delete and press the “Delete” button. Categories in use by a characteristic may not be deleted. To rename a characteristic, place the cursor in the row of the category you wish to rename and press the “Rename” button. A window similar to the “add category” will appear. Enter the name you want in this window and press “Ok’.
This is what the control chart looks like before entering data:
Attribute characteristics with defect categories should be created the same way as normal attribute characteristics. Once the attribute is created, press the “Use Categories” checkbox located in the middle right-hand area of the characteristic creation window. A new column named “Type” will appear in the defect definition area of the attribute window. In this column, use the drop down box for each defect to select a previously defined category for each defect. Press File/Save & Exit to save the changes you made. If some characteristics do not have a category selected, they are automatically assigned to the defect category in the “define categories” window.
Enter data for the extended attribute analysis in the usual manner of data entry. Notice that the defect category of each defect is listed next to its name. In the bottom of the control chart screen, there is a table showing how many defects were found in each subgroup by category. Pressing any of the category buttons to the left of the table will show the control chart for the given category instead of displaying the total number of defaults, which is the default. The title bar at the top of the data entry window will identify which category is being viewed.
This is how the window appears during data entry:
When creating the defect categories, specifications were set for number of defects allowed per Sampling Plan Size and Subgroup size. If either of these limits are exceeded, DataLyzer® Spectrum gives the operator an error message before saving the data values. The specific block for the subgroup out of control and defect category out of control is saved in the color red in the category table below the control chart graph. When using combined categories, if the subgroup limit or AQL is exceeded for the cumulative associated categories, the combined category box will be shown in red. When the subgroup limits are exceeded, DataLyzer® Spectrum interprets it as data entered out of specification limits. The point is saved in red on the control chart. When the
The following graph is an example of the total attribute count. It shows the total number of defects for all categories at once. To view the total attribute chart from a category’s chart, press the “all” button that is located below the minor column. To view the chart for any specific category, press the button in the lower left hand corner with the category’s name on it.
The following graph is a graph of the “critical” category. Notice that the only points shown are points shown in the “critical” category.
The following graph is an example of the “Minor” graph.
The following graph is an example of the “Important” combined Critical and Major categories graph.
The following graph is an example of the “All Defects” combined Critical, Major, and Minor categories graph.
SQC:
Statistical Quality Control
By Eugene L. Grant, Richard S. Leavenworth
McGraw-Hill, ISBN: 0-07-024117-1
SPC:
Advanced Topics in Statistical Process Control
By Donald J. Wheeler, Ph.D.
SPC Press, ISBN: 0-945320-45-0
DataLyzer® Spectrum Application Note
Compliments of DataLyzer International, Inc.