Why Use Control Charts?

In everyday language, “in control” and “under control” are synonymous with “in specification.” Requirements have been met. Things are OK. No trouble.

“Out of control,” on the other hand, is synonymous with “out of specification.” Requirements have not been met. Things are not OK. Trouble.

Using this language, an obvious axiom would be: Take action when the process is out of control.

The everyday use of in and out of control is, however, unfortunate for control charts, the major tool of statistical process control (SPC). Why? Because in SPC these terms speak of processes as being stable or unstable. To characterize a process as stable or unstable, process limits, from process data, are needed. Specification limits are not needed.

Given the easy-to-understand basis for the action of meeting or not meeting requirements, coupled with the risk of confusion over the terms in control and out of control, why use control charts? If you are curious to see some of the benefits in doing so, read on. Two case studies are used.

Case one: Part thickness

During a regular review meeting in Plant 17, in- and out-of-specification data on the thickness of part 64 were reviewed.

Thickness of part 64
Number of measurements	In specification	Out of specification	Status
108	107	1	Not OK

The measure was red because of an out-of-specification outcome during production run 9; in everyday language, it was out of control. The agreed action was to find the root cause for this problem, followed by the appropriate corrective action.

Production records indicated a problem with a machine setup before run 9 commenced, and this explanation was given during the next meeting as the root cause for the out-of-specification result. Because this setup problem was not expected to recur, the case was closed.

Case one assumes that the machine setup problem—i.e., something different in the process—caused the out-of-specification point. Did this understanding lead to the best course of action? Before we explore this question, let’s look at case two.

Case two: Time to process

During the biweekly production review meeting, in- and out-of-specification data on the time to process part 76 were presented.

Time to process part 76
Number of measurements	In specification	Out of specification	Status
200	200	0	OK

The measure was green because everything was in specification: In everyday language, it was in control. No questions were asked, and production continued without further use of the data obtained during 10 productions. Did this in/out binary view of the world lead to the best course of action? Before we explore this question, we must revisit case one.

Case one revisited

Figure 1 plots the 108 thickness measurements in a histogram against the specifications. The problematic point, located above the upper specification limit, was sample 100 from production run 9.

Figure 1: Histogram of part thickness data during nine production runs. The blue lines, LSL and USL, are the lower and upper specification limits.

A control chart of individual values, or process behavior chart, of the data is shown in figure 2.

 
Figure 2: Control chart of individual values for the thickness data

Interpretation of figure 2’s control chart allows us to characterize the process as stable. This means there are no unnatural patterns in the data that would signal the occurrence of process changes, i.e., instability. (Postscript 1 below gives an overview of how to interpret a control chart.)

The two red lines at 78.4 and 84.1 in figure 2 are natural process limits, or control limits, which define the “voice of the process.” This voice tells us to expect process outcomes between 78.4 and 84.1:
• During the past nine productions
• In future productions so long as the process continues without evidence of change, i.e., stable process behavior

If we listen to the voice of the process, we learn that the out-of-specification value—in this case, sample 100’s value of 83.7—is not, on its own, a signal of change in the process. Why? Because this single measurement falls within the natural process limits. Consequently, the control chart analysis does not support the team’s conclusion that the out-of-specification value is accounted for by the problematic machine setup before commencing run 9.

Note: This understanding does not mean that a problematic setup should be ignored and left uncorrected; simply that the problem with the machine setup is not, on its own, a valid explanation of sample 100 being out of specification.

Out of specification is also synonymous with trouble. To plan how to get out of trouble, we start by comparing the voice of the process with the voice of the customer, i.e., the specifications (see figure 3).

 
Figure 3: Representation of the voice of the process and the voice of the customer. (LNPL and UNPL are the lower and upper natural process limits.)

With an upper specification limit of 83.5, and with process outcomes as high as 84.1 expected to occur in routine production, figure 3 shows graphically that the current process is not capable of meeting specifications.

Figure 3 also provides the insight to define the options to make the process capable:

Option 1: Lower the process average to ensure the control chart’s upper natural process limit is below the upper specification of 83.5.

Option 2: Reduce the level of variation in the process by changing the process in some fundamental way (e.g., use new materials, operating procedures, or equipment, or measure samples in duplicate or triplicate rather than just once).

Option 3: Do both, i.e., a more optimal average and a reduced level of process variation. (See Postscript 2 for a discussion on both these improvement strategies.)

In concluding case one, how has the control chart shown itself to be useful?
• By defining the voice of the process, it told us what to expect of the part thickness process.
• By listening to the voice of the process, we learned to not invest time looking for a root cause for the single out-of-specification point.
• By comparing the voice of the process with the voice of the customer, the options to effectively and permanently eliminate out-of-specification trouble from the process were made clear.

Case two revisited

A histogram of the 200 measurements in relation to the lower specification is shown in figure 4. (There is no upper specification.) The histogram suggests all is OK because the measurements are located at a safe-looking distance above the lower specification.

Figure 4: Histogram of the time to process data, including the lower specification limit of 700 seconds

Is all OK, meaning no need to ask further questions? To answer this question, we start with an average and range control chart (see figure 5.). Each point on the x-axis uses data from one batch. Five measurements are routinely taken across each batch, and the variation within batches is judged appropriate to study the variation between batches.

Figure 5: Average and range chart for the time to process part 76

With several signals of process change in figure 5, this process must be characterized as unstable over time. (Again, refer to Postscript 1 for some guidance on control chart interpretation.)

Because the process in figure 5 is unstable, we learn that the current process has the potential to operate with a narrower level of variation. (If all the points on the upper average chart were within the process limits, the process would operate with a lower level of variation.)

Reducing variation results in process improvement. How does the control chart help us to 1) realize this improvement; and 2) express this improvement opportunity as a cost-saving figure?

1. Improvement
We start by making sense of the signals of instability in figure 5: When are the changes in the process—the instability—thought to have occurred?

Batches 2 to 12 on figure 5’s average (upper) chart are all below the central line (which is the average of all 200 data). Batch 13’s average jumps up above the central line, and for the rest of the record, the average time to process part 76 looks to have increased. This interpretation is illustrated in figure 6 and tested in figure 7’s average and range chart, with the process limits based on the data from batches 1 to 12 only.

Figure 6: Figure 5’s average chart with annotations

 
Figure 7: Average and range chart of the time to process part 76, with the process limits based on data from batches 1 to 12 only

Figure 7 supports the theory that a reasonable degree of stability was present during the production of batches 1 to 12 because there are no signals in the data. Stronger still, the postulated increase in processing time from batch 13 onward is absolutely clear because 27 of the last 28 points are above the central line on figure 7’s average chart.

This understanding tells us to ask what happened around the time batches 12 and 13 were produced. The team investigated:
• Friday, April 18: Last production of the week
• Monday, April 21 to Wednesday, April 23: Periodic maintenance of the line
• Thursday, April 24: Restart production

The investigation identified an error from the periodic maintenance. A bias error in a temperature-sensor loop calibration meant the actual temperature in a heating step was several degrees below the target temperature because of the error in the sensor measurement. This error explained the sustained increase in processing time between April 24–April 30. The loop was recalibrated and the error eliminated.

Using the control chart, the steps involved are shown in figure 8.

Figure 8: Detecting and responding to instability in a process

Success with figure 8 leads to an improved process with leverage for optimization. As discussed below, this leverage can be translated into cost savings.

2. Cost-saving opportunity
For a baseline figure, the plant manager equated a 10-second reduction in time to process part 76 with savings of approximately $14,500 per month. To turn this into an estimated cost-saving figure, two averages are needed:
• Historical average: The best guess of what would happen if nothing in the process changed
• New average: The optimal average to be achieved through improvement

Using the year-to-date data, the historical average was 789.8 seconds.

To get to an estimate of a new, optimal average, we start by estimating the process’s stable standard deviation. Figure 7’s range control chart—the lower chart—contains this information:
• The average range for batches 1 to 12 is 44.58 (the green line in figure 7’s range chart).
• To convert this average range value into a standard deviation, we need a bias correction factor, d2, which is 2.326 for subgroups of size five.

Next, the plant manager would accept a process capability Cpk of 1.33 in the optimization of this operation. For a stable process, this level of capability provides one unit of standard deviation of “safety space” vs. the nearest specification limit, as shown in figure 9.

Figure 9: Visual representation of Cpk = 1.33 with only a lower specification limit in place; the histogram is the data from batches 1 to 12.

As per figure 9, the optimal process average is estimated as follows:

The estimated time saved by operating the process at the optimal average is:

               

A time saving of 13.84 seconds results in an annual cost saving in the ballpark of $250,000:

 

This cost-saving opportunity represents the estimated payback for getting the most from this process, which is a stable and capable process, running on-target at its optimal average.

To fully seize this opportunity, control charts are needed because they:
• Provide the insight and clues that are needed to turn an unstable process into a stable one (done by integrating figure 8 into the routine work of production)
• Are the only way to sustain a stable process over time 

The initial question raised in case two was, “Did this in/out binary view of the world lead to the best course of action?” The answer is no. The control chart bettered the situation:
• It identified the potential for the process to do better because the process was unstable, as revealed in figure 5.
• It provided a method to realize this potential, meaning how to make the process stable, as shown in figure 8.
• It facilitated a repackaging of this potential into a near $250,000 cost-saving opportunity by moving the process to a new, optimal average and comparing this with the historical average.

Control chart usage: Four fundamental questions

With regard to control charts:
Question 1: Did a change in the process occur?

Questions two, three, and four follow if question one is answered with yes:
Question 2: When did the change in the process occur?
Question 3: What caused the change in the process?
Question 4: How can the cause be economically controlled in production to eliminate (or at least reduce) its effect?

Without a signal of change on a control chart, it is premature to seek a “root cause” for one or more values that are undesired (e.g., out of specification). Why? Because the data themselves find no evidence that a root cause is there to be found. The control chart can therefore put the brakes on the loss coming from this course of action. In case one, the team’s belief that the cause of the out-of-specification occurrence had been identified and fixed was not supported by the data.

With a signal of change on a control chart—an unstable process—the green light is given to further interpret the chart. Figure 6 shows an example. Only when a process displays unstable behavior do questions two, three, and four come into play. As shown in case two, the expected payback from the invested effort in tackling questions two, three, and four can often be packaged into a sound dollar figure for effective communication and decision making.

Trouble comes in two flavors

Donald J. Wheeler’s “Two Definitions of Trouble” is based on the combination of 1) being in specification or out of specification; along with 2) being stable or unstable, as per a control chart analysis. This results in four possible states for any process, as shown visually in figure 10. (A predictable process is a stable process, and an unpredictable process is an unstable process.)

 
Figure 10: The four possibilities for any process. (Reproduced from Donald J. Wheeler’s article, “Two Definitions of Trouble.”)

Product trouble
Figure 10’s horizontal axis is well-known: Nonconforming means some product is out of specification, which means trouble. This trouble provides a well-established basis for action.

Yet, knowing how to get out of trouble is key because different paths can be taken:

No. 4—State of Chaos: If the process is unstable with some of it nonconforming, then responding to process changes detected on the control chart (as per figure 8) is often the path to success and the Ideal State.

No. 2—Threshold State: If the process is stable with some of it nonconforming—like case one—taking a different path toward the Ideal State is recommended; this requires a fuller study of the process to learn how to shrink variation and/or to relocate the average to a more optimal level.

Process trouble
Figure 10’s vertical axis, which could be called the stability axis, is somewhat unknown.

A stable process is performing up to its potential, i.e., doing the best it currently can. Moreover, with a stable process, the voice of the process defines what the process is expected to deliver today, tomorrow, next week....

An unstable process, on the other hand, is performing below its potential, i.e., the process could do better. Case two’s time-to-process data were used to estimate the payback from getting this process to perform up to its potential.

The most effective path to improvement is guided by the stability axis. As per the two case studies:
• A control chart of case one’s thickness data showed the futility of seeking a root cause for the out-of-specification point; improvement would come from a fuller study of the process.
• A control chart of case two’s time-to-process data showed the benefit in seeking a root cause for the detected process change (between batch’s 12 and 13); taking action on the identified root cause was the catalyst to improvement.

Wrap-up: Why use control charts?

We started by asking, “Why use control charts?” Control charts are the “voice” of the process. They can be central to process management by helping to ask the right questions. They can be used to give maximal assurance that specifications will be met. They can play a key role in process improvement. And, they can be used to put a sound dollar figure to improvement opportunities.

Might you get more out of your processes with the use of control charts?

Finally, to add value to this article, it would be great if you, the readers, post in the comments section why you use control charts.

Postscript 1: Control chart interpretation—stable or unstable?

Interpreting a control chart starts with the characterization of process behavior: stable or unstable? In traditional control chart terminology, this refers to the process being in- or out of control, meaning statistical control.

As per the Statistical Quality Control Handbook by the Western Electric Co. (second edition, 1958), a stable process possesses the following three characteristics (defined as a natural pattern on page 24):
• Most of the points are near the solid centerline
• A few of the points spread out and approach the control limits
• None of the points (or at least only a very rare and occasional point) exceeds the control limits 

These three characteristics are shown visually in figure 32 of the SQC Handbook (reproduced below as figure 11).

Figure 11: The three characteristics of a natural pattern—a stable process—as per Western Electric

Control chart interpretation starts out by assuming the process is stable. Evidence of instability is looked for, with instability detected by unnatural patterns on the control chart. From page 24 of the SQC Handbook, “...unnatural patterns tend to fluctuate too widely, or else they fail to balance themselves around the centerline.” And, “unnatural patterns always involve the absence of one or more of the three characteristics of a natural pattern.”

The use of detection rules results in the control chart becoming an operational definition of a stable process. Herein, two detection rules are applied to find the unnatural patterns, which are the signals of instability in the process:
• Detection rule 1: A point that falls beyond a process limit (control limit)
• Detection rule 2: Nine or more consecutive points on either side of the central line

Rule 1 is the first, original detection rule. Many other detection rules have been proposed over the years. For a detailed discussion, see “When Should We Use Extra Detection Rules?” The two rules given above combine simplicity with effectiveness in the author’s opinion.

Figure 2 is an example of a process characterized as stable; there is no unnatural pattern in the data.

Figure 5 is an example of a process characterized as unstable. In figure 5 and figure 7, the points signaled with a 1 and a 2 are those corresponding to detection rules 1 and 2 given above.

Postscript 2: Improvements to the part-thickness process

As seen in figure 1, the specification limits are 74.5 and 83.5, and the histogram is located closer to the upper specification. A standard, and important, practice is to also define a process target value and check if the process is on target or not. (The keen observer will have noticed the absence of a target value in figure 1.)

With regard to defining an effective improvement strategy to improve process capability, two situations are discussed. As above, a target minimum process capability is Cpk 1.33. (Figure 9 illustrates a Cpk of 1.33.)

Situation 1: Process target is the center of the specifications
As discussed above, the part thickness process was not capable because process outcomes higher than the upper specification limit were expected. This was illustrated in figure 3 and is shown in the upper histogram in figure 12.

The center of the specifications is 79.
Calculation: .
To hit the target of 79.0, the process average must be reduced by 2.26 units (81.26 – 79.0 = 2.26).

Operating the process in the center of specifications would deliver a capable process, as illustrated in figure 12 .

Figure 12: How to center the process in the middle of the specifications and deliver a capable process

Situation 2: Process target is the current average
The only way to achieve a capable process at the current average of 81.26 is to reduce process variation. As shown in figure 9, for a Cpk of 1.33, the distance from the process average to the nearest specification is four standard deviations. An improved process of Cpk 1.33 at the current average is illustrated in figure 13.

 
Figure 13: Illustration of the improvement needed to reduce variation at the current average and achieve a Cpk of 1.33

The formula for Cpk is:

Because the process has been operating closer to the upper specification limit, the formula becomes:

In relation to the upper specification limit, a Cpk of 1.33 is as shown in figure 13’s lower histogram. The improvement envisaged in figure 13 would not be trivial. It would require a near twofold decrease in the process’s standard deviation, from 0.94 to 0.56. As a general rule, it is often easier, even much easier, to relocate the process average than to reduce process standard deviation.

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