Statistical Process Control (SPC) Background Information

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Statistical Process Control (SPC) Background Information

This topic deals with the subset of SPC that is incorporated into M.O.L.E.® MAP Software. It does not address general SPC principals. A working knowledge of general statistical principals and SPC terms is assumed and is not addressed here. There are many good basic SPC books where this information may be obtained.

 

Reflow and Wave Solder operators, engineers and production managers are expected to understand their soldering process so as to deliver quality products cost effectively. This is a continuous process.

 

First, the machine must be checked for consistency. A standard or typical set up should be routinely checked prior to any process set point determinations, or actual production run machine checks. Only after the machine has been determined to be operating correctly and not experiencing abnormal variation, should data from the machine be utilized. SPC is all about identifying common or normal variation from abnormal variation.

 

Second, the correct process set points must be determined for a particular product. Utilizing the M.O.L.E. Profiler, the correct set points for a particular product may be determined. These set points, if selected correctly and followed, should deliver the maximum throughput of quality product.

 

Third, the machine must consistently deliver the correctly determined set points. SPC will help identify common or normal variation from abnormal variation. Checking the machine using your M.O.L.E. Profiler and the M.O.L.E.® MAP Software with its SPC capability will help ensure that the machine is consistently performing to its set points and your expectations.

 

Fourth, repeat the above three steps. Continuous improvement is a never-ending cycle. Check the long-term variation of the machine by graphing typical set point samples. Using the M.O.L.E. Profiler, recheck/adjust part number specific set points to maximize your quality throughput. Check the machine during a part number run to control the machine variation from that part number’s actual ideal set points.

While SPC had its start in high volume repetitive operations, SPC is applicable to many other types of operations as well. However, SPC can be difficult to apply to short runs. Short runs may be runs that take a long time to process, runs in which multiple samples are difficult to collect, and runs where samples are difficult to place into subgroups or runs where small quantities are run.

 

The M.O.L.E.® MAP Software charts will be more meaningful to the user if SPC charts are generated based on data sets that have the same set points each time.

 

There are several basic short run SPC techniques:

1.Nominals Charts

2.Individuals/Moving Range Charts

3.Moving Average/Moving Range Charts

4.Standardized Formula Charts

The Moving Average/Moving Range Chart technique is particularly well suited for situations where control information is desired as soon as possible and there is a relatively long time between sample collections. After considering the nature of solder operations and the machine sampling process, the Moving Average/Moving Range Chart technique was incorporated into M.O.L.E.® MAP Software.

 

Moving Average/Moving Range Chart Technique:

M.O.L.E.® MAP Software utilizes the standard Moving Average/Moving Range Charting technique with a subgroup size of 2-6 that is selected by the user. The following steps and figure illustrates the Moving Average/Moving Range calculations (using a group size of two) that are used to construct the SPC chart.

 

Steps for Creating a Moving Average Moving Range Control Chart:

1.Select the key variable to monitor.

2.Select the moving average group size. (We will use two in our example.)

3.Obtain your first sample and record it as sample 1 (X1).

4.Obtain your second sample and record it as sample 2 (X2).

5.Determine the x-bar and R values.

Equation

Moving Average formulas:

6.Plot this value on the chart as subgroup 1.

7.Carry forward sample 2 into subgroup 2’s calculation. Obtain your third sample and record it as sample 3. The averages of sample 2 and sample 3 form subgroup 2.

8.Plot this value on the chart as subgroup 2.

9.Repeat for all the samples.

10.Calculate control limits using standard x-bar and R formulas for the appropriate sample sizes. M.O.L.E.® MAP Software uses range-based calculations for LCL and UCL.

11.Continue monitoring the process.

 

SAMPLE #

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

SAMPLE MEASUREMENTS

3

4

5

3

2

9

5

2

6

8

4

8

5

6

3

3

SUBGROUP VALUE

x

3.5

4.5

4

2.5

5.5

7

3.5

4

7

6

6

6.5

5.5

4.5

3

 

R

1

1

2

1

7

4

3

4

2

4

4

3

1

3

0

Moving Average/Moving Range Subgroup Size 2 Calculations Chart

 

Process Capability

A process capability index is a standard measure of how a process compares with its specification limits—how a process is performing relative to how it is supposed to perform. As opposed to the control chart, which shows detailed information about how the data compares with control limits, a capability index is a summary of how the data compares with the specification limits.

 

Two common capability indicators are Cp and Cpk.  These values are shown in the Statistics Box on the SPC Page Tab.  

For both of the index values, the data used to determine them is dictated by the subgroup size (N) chosen by the user. In the case where N=1, individual data is used—for N>1, average data is used (x bar).

 

The charts on the next page give a graphical representation of the concept of Cp and Cpk. Notice that in each graph, the same upper and lower specification limits (USL, LSL) are used.  The values of Cp and Cpk will differ according to the data that is compared with those specifications.

 

Depending on the particular process being monitored, the desired value for Cp and Cpk may differ. In general, however, a Cp and Cpk of 1.33 or above is desired. This assures that the process is not only capable of meeting the required specification limits, but also has a built-in margin for error that may be needed in special circumstances. In addition to targeting a certain minimum Cp and Cpk, it is also desirable to have these two values equal one another. This indicates that the process is well-centered between the specification limits.

 

Cp-Cpk_Sample

Cp1.33: Data tightly distributed.

 

Cpk 1.33: Data well inside spec limits.

Cp = 1.00: Data fills entire spec range.

 

Cpk = 1.00: Data fills entire spec range.

Cp > 1.00: Data tightly distributed. If it were centered between the spec limits, no data would lie beyond those limits.

 

Cpk < 1.00: Some data is outside the spec limits.

Cp < 1.00: Data not tightly distributed. If it were centered between the spec limits, some data would still lie outside those limits.

 

Cpk < 1.00: Some data is outside the spec limits.





 

The equations used to calculate the index values are as follows:

Equation

 

 


OR

, whichever is less

As can be interpreted from the above equations, Cp gives an indication of how narrow the data distribution is relative to the width of the specification limits. Essentially, it indicates how well the process would be able to stay within the specified limits if the data were perfectly centered between those limits.

 

Cpk compares the widest half of the data distribution to the appropriate specification limit.  It indicates whether the process is capable of meeting the specification as indicated by the “worst half” of the measurements.  Unlike Cp, the Cpk index measures process capability without assuming the data is well-centered.