The Most Important QM Tool: Statistical Process Control (SPC)

The Most Important QM Tool: Statistical Process Control (SPC)

By Werner Bergholz, QTEAM and Jacobs University Bremen

The Need for Predictable Quality

In two previous contributions to the Grid in Dec 2014 and in March 2015, it was pointed out that for photovoltaics manufacturing and installation, quality management (QM) is a key success factor, and that the implementation of a QM system is actually less complex and involved, if you follow a simple recipe.

One of the cornerstones of an effective QM system is managing manufacturing processes in such a way that predictable quality is produced. To manufacture predictable quality goes along with manufacturing reliable products (and vice versa!), which is of highest relevance since PV products must be functional for 20 years or more if they are to be attractive to buyers and investors.

Natural and Extraordinary Variability of Processes

At first glance, PREDICTABLE quality in manufacturing seems unrealistic since any technical process is subject to an unavoidable and “natural” VARIABILITY (such as the scatter of the thickness of PV wafers cut from a brick by a wire saw). In addition, extraordinary events can lead to exceptionally large excursions from the natural variability. In the case of the wire saw, this could be a wire or slurry that does not conform to the material specification, or the clogging of valve which controls the flow of slurry etc.

It is the distinction of Common Causes1) (which causes the natural variability) and Special Causes1) (which are responsible for the extraordinary variability) which is the first building block of statistical process control (SPC). 

A process is defined to be “under control,” if only common causes are active. There is a well-defined quantitative relationship between the technical specification and the process variability, which will be explained later. Under such conditions, the process will turn out products with predictable quality, provided the variation is small enough so that the technical specification is fulfilled.

In the event that a special cause of variability starts to impact the process results, then the process is considered “out of control” and must be stopped. The special cause of variation must be identified and eliminated before the process is allowed to be restarted.

How to Distinguish between Common Causes and Special Causes for Variation

So the question about whether the process produces predictable quality or not is reduced to the question: Is a special cause present? This is where statistical analysis is needed and can provide the answer:

  • Process results are all the information that is needed
  • From a sufficient number of process runs, the distribution and the standard deviation σ of the process results can be calculated
  • From the σ value determined in this way and the process average AVE the control limits for the process can be calculated:

Upper control limit: UCL = AVE + 3σ

Lower control limit: LCL = AVE - 3σ

  • The simplest rule to tell you whether or not a special cause is present is whether there is a value outside the control limits or not, point 22 in figure 1 is an example for an “out of control” situation. That point signals that the process is out of control due to the influence of a special cause of variation. The process must be stopped and can only be resumed after the special cause has been identified and eliminated.

Example of an SPC chart

Figure 1: Example of an SPC chart. The values are arbitrarily chosen values and could be the efficiency of solar module batches. The black line is the average, the red horizontal line above and below the average line are the 3 sigma limits, the dashed and the dotted lines are the two and one sigma limit (created with an excel chart that can be downloaded from the website of the American Society for Quality). The out of control point could e.g. be caused by a malfunctioning firing furnace.

There are a number of rules which indicate the onset of a special cause, and they can be found in any publication on SPC (note: usually called “Western Electric (WE) Rules”).

If there is no special cause operative, i.e. none of the Western Electric Rules is violated, there is a surprising consequence: You must NOT change any of the process settings, “hands off” the process!

It is completely counter intuitive, but if one tries to reduce the variability of the process by adjusting the target value of the process after each run to compensate for the difference between the target value and the process result, the variability will go up, not down ─ in fact, it will increase by a factor of 2! This is convincingly demonstrated by a process simulator (marbles dropping from a funnel), available at:


Control Limits and Specification Limits: Is the Process Capable?

So far we have only considered the process itself, and whether it is under control. Now we turn to the question: Is the process capable of fulfilling the specification limits for the product it manufactures. For this, we have to compare the control limits (as described in the previous section) with the technical specification limits for the product. In figure 2a, an example is shown, in which the control limits UCL and LCL are well within the specification limits USL and LSL. (if you are not too interested in mathematics, you can skip this and move to the next section: when is cpk good enough? )

This state of affair obviously calls for the following metric, of how capable the process is relative to the specification, namely

Capability index of the process cp

cp = (USL – LSL) / 6σ

The rationale is, the larger this number, the more stable the process is relative to the technical specification limits. In figure 2a, cp is approximately 1.67.

In practice, processes are rarely exactly centered, so there is an offset of the center of the specification limits (= [USL – LSL]/2 and the process average. Obviously, for the probability that a process run is out of the specification limit, the closer of the 2 specification limit is the more relevant one. Therefore a second more useful capability cpk is defined as

cpk = min[(USL- AVE),(AVE – LSL) / 3σ

cpk is always smaller than cp, in the example of fig 2b, cpk = 1,33.

Figure 2: Representation of the control and specification limits


Figure 2: Representation of the control and specification limits.
USL = upper specification limit
UCL = upper control limit
AVE = process average
LCL = lower control limit
LSL = lower specification limit

When is cpk Good Enough?

For any process, a metric can be determined regarding the capability of the process, the cpk value. A cpk value of 1.33 at first sight might look sufficient, but according to established quality standards, it is not good enough. By definition a process is called capable, if cpk >1.67.

The value of 1.67 implies that there is a probability of only 3.4x10-6 that the process will violate the specification limit. (This can be calculated from the distribution function of the process results; details of the calculations are omitted, since they are not relevant for the application of SPC).

Now it is plausible, that predictive quality can be produced: Only 3-4 out of 1 million process runs lead to a violation of the specification limits.

According to the automotive standard ISO 16949, any cpk value below 1.67 for processes critical to quality must be improved until that value is reached, and additional product tests have to be implemented to detect any misprocessed material. So even, in such a situation, which is e.g. typical for ramping up a production facility, the quality level can be maintained, however at the expense of more product checks, i.e. additional cost, and lower factory yield.

The Dashboard for Quality

A large PV manufacturing facility has hundreds of individual pieces of equipment, with a corresponding number of SPC charts. How can an auditor or the director of quality or production keep an an eye on the stability and capability of all these processes?

One solution is to create a monthly stacked bar graph of all the cpk values of all processes. Just one look provides data on the maturity of the process in that factory, and whether the process is getting more capable or not (see figure 3).

The example below is representative of a factory which is in the ramp-up phase, where a relatively small percentage of the process meets the 1.67 criterion, and where an equal share of processes has a capability index below 1, which means a probability of 3 or more out of 1,000 processes are out of specification (so a factor of 2 in cpk means a factor of 1000 in the defect rate!).

Stacked Chart


Figure 3: Stacked bar graph of a factory during ramp-up. The vertical scale is a percent scale.
Dark green = percent of process with cpk>1.67
Light green = percent of process with 1.67>cpk>1.33
Pink = percent of process with 1.33>cpk>1.00
Red = percent of process with 1.00>cpk


For an industry like the PV industry, where the financial health of an investment for the customer hinges on the durability and reliability of the product, an effective QM system is absolutely critical.

To manufacture reliable PV modules is only possible if individual processes produce PREDICTABLE quality. The central tool to achieve this is SPC, the pivotal metric is a cpk value for each process critical to quality.


1) Deming, W. Edwards, 1993, The New Economics for Industry, Government, Education, Cambridge, MA: MIT Center for Advanced Engineering Study.