Ian Rooney
PQ Systems Pty Ltd

If your goal is to produce high quality, reasonably priced goods and services that successfully meet your customers’ needs, then the answer must be a resounding “Yes!”

Statistical process control (SPC), a set of techniques used to assist with improving processes and systems, dates back to the early 1920s when Dr. Walter Shewhart developed control charts. The methodologies pioneered by Shewhart and popularised by management guru and statistician Dr. W. Edwards Deming are more relevant in today’s volatile marketplace than ever before.

Traditionally, process managers collected data from processes, analysed it in some way, and often made changes to the process in an attempt to keep output within specification. Typically, organisations have a great deal of data but have not grasped the opportunity to gain the meaningful information and knowledge it provides. Too often, the decision to change processes is a knee-jerk reaction based on incomplete data--or worse, none. Making changes to processes or systems without understanding the nature and extent of the variation being exhibited by them is fraught with danger. SPC techniques can clearly define the cause of a problem or issue and drive good, data-driven decision making, replacing speculation and ‘gut’ feelings. Understanding process variation and its causes is the first issue that SPC addresses.

The successful implementation of a continuous improvement program requires a change in approach and philosophy—a move from simply detecting errors to preventing defects, and from there to continuous improvement. To be effective, continuous improvement requires a disciplined application of statistical process control. The major benefit to be derived from this approach is increased profits brought about by better products, goods or services, produced by improved processes and systems. Improved productivity and efficiency, reduced waste, rework, and costs will ensure increased profits.

The basic statistical tools employed by SPC are statistical graphs called control charts and histograms, and a set of calculations to determine capability. These techniques rely on collections of data that are accurate and reliable. It is therefore important that good data-gathering practices are followed. A robust sampling program supported by well-designed operational definitions, unambiguous data gathering, and reliable measurement techniques are among these practices. After collecting data from a process or system, the first step is to construct a control chart.

A control chart is a statistical tool that shows how data from a process changes over time. It is used to assess the statistical stability of the process and helps the user to better understand its behaviour and the variation occurring. Perhaps a simple example will help in understanding the usefulness of control charts. Figure 1 shows a chart that tracks the weekly sales for a successful seafood restaurant. Imagine for a moment that you are the manager of this establishment. What might your reaction be when, for the first time in the history of the restaurant, weekly sales exceed $120,000 on 24 October? Perhaps blinded by the euphoria of the moment, you might be tempted to expand your capacity to produce to meet this apparent new demand., After all, you and all your staff are exhausted at the end of this wonderful week! Perhaps you might consider employing extra staff, leasing additional furniture and equipment, and so on. How might you then feel when the low point of 16 January occurs? Now, in the depths of your despair, you may be tempted to undo all the expansionary measures you took just a few short weeks ago. The danger is that you may unwittingly ‘unwind’ your business to the extent that you no longer have the capacity to produce to the former high levels! Imagine how much easier the decision to expand or not would be if you had a crystal ball. SPC can provide a great deal of information that removes the guesswork from decision-making – a statistical crystal ball.

So, how can a control chart help? Replace your restaurant manager’s hat for a moment and let’s see how it works.

The control chart shown in figure 2 contains the same data displayed previously, but with the addition of a mean line and upper and lower control limits. These control limits are computed from the data and represent the boundaries within which the output from a process is expected to fall. In this case, they represent the extremes within which we can expect weekly sales to fall. Armed with this small piece of knowledge, would you take any action as a result of record weekly sales on 24 October? Of course not! You would understand that this was a data point within the bounds of expected variation. When the sales figures occur within the control limits, we say that they are a result of normal or expected variation. Statisticians call these the common causes of variation. If one of the weekly sales figures were to fall beyond one of the limits, this data point is considered unexpected, resulting from a special cause of variation. We describe such a data point as being statistically significant and, consequently, requiring investigation. We need to understand what has caused the unexpected event to occur so that better-than-expected results can be duplicated and less desirable results avoided. Not reacting to a ‘special cause’ event can be as catastrophic as over-reacting to a common cause event.

The simple restaurant scenario illustrates one of the important uses for control charts, namely, discriminating between the common (expected) and special (unexpected) causes of variation. Let’s explore this concept a little further. Suppose you kept a record of the time it takes to drive to work each day. The common causes of variation in travel time are traffic lights and weather conditions, while the special causes of variation might be a breakdown or accident. Special causes are a result of a specific change and are frequently associated with a chaotic problem, such as an accident. Since common causes create the normal everyday variation in the system, improving them will involve systemic changes. For example, improving the variation in travel time to work would require a major change: using different roads, departing at a different time, changing the mode of transportation to a motor bike, or a more drastic change, such as change of residence. However, if special causes are producing problems in the system, they will be specific events, such as an automobile breakdown. The short-term action to fix this problem is to get towed to a garage. The long-term action is to improve the maintenance of the car. Special causes are usually of this nature. An action must occur immediately to overcome the special cause, and long-term action must be taken to prevent the special cause from recurring.

If control charts are not used, two kinds of mistakes can be made: the assumption that a special cause is occurring when only normal variation is present, or the assumption that the process or system is operating normally when something special is occurring. These mistakes can also be thought of as “over-controlling” or “under-controlling” the process. To understand this, consider someone learning to drive. Every lane change is traumatic; a car turning ahead is a cause to hit the brakes. In fact, normal driving events seem unusual to a learner, who is therefore likely to “over-control.” The result is a jerky ride at best, a dangerous one at worst. At the other extreme, a new driver takes the car out in heavy rain and drives at the speed limit, applies the brakes as usual at a stop sign, and skids helplessly into the intersection. The driver fails to recognise unusual road conditions and, acting intuitively, “under-controls.” Control charts do for a process or system what experience does for a new driver. They graphically inform the user of the difference between ordinary and unusual events, common and special causes, so the best course of action can be taken. Understanding the sources of process variation is critical to improving a process. Actions to address and improve the common causes of variation are quite different from those used for special causes. If common causes are producing too much variation in the system, then improvement is required.

A process without special causes that exhibits only common causes of variation is considered to be “statistically stable.” When a process or system is statistically stable, the control chart becomes predictive. That is, if the system remains the same, data produced will vary “normally” between the control limits, and will have the same average as that shown on the control chart. This is a powerful aspect of control charts. The ability to assess process variation and system performance allows process managers to predict future performance. The widely fluctuating variation evident in the restaurant’s weekly sales makes the business difficult to manage week to week. The challenge here is to address the common causes of variation to reduce the width of the variation. In effect, we set out to narrow the distance between the control limits.

Once a control chart has been completed, it is usual to examine the data in a different way using a histogram. Histograms are used to gain further knowledge about a process, information about the shape of the distribution, the central location of the data and the width of the variation. Statisticians look for a histogram that forms a ‘normal distribution (see figure 3). This normal shape or curve is the most commonly occurring data shape in nature, manufacturing processes, or service provision systems. Certainly there are processes that have a natural upper or lower limit that causes the data to form a non-normal shape; however, the vast majority of process data forms a normal distribution. The importance of this is that if process data is statistically stable and forms a normal distribution, accurate predictions can be made about the future performance of the process. Histograms and control charts are closely related. They display the same process data in different ways. While control charts are used to assess system stability, histograms are used to assess normality and together they are used to predict future performance.

An important point needs to be made here. A statistically stable, normally distributed process does not necessarily produce desirable output. An extreme case could see such a process produce one hundred percent junk! By inscribing specification limits onto a histogram, an immediate picture of how well the process is performing in relation to these requirements can be seen. It is immediately obvious whether the process needs adjustment and what type of change is required.

Capability analysis is a statistical tool that examines and quantifies the relationship between numerical goals and process output. Statistical capability is expressed using a variety of indices, the best known of which are Cp and Cpk. The indices are easy to interpret and have universal meaning regardless of the process or system being studied. Capability indices are reliable only when they are based on a statistically stable process. Capability analysis and histograms work together to display and quantify two things about the relationship between process performance and process specifications. First, can the width of the process fit between the specifications, and second, how close is the process to the nearer specification limit. These relationships give an indication of what kind of improvement may be required.

If it is not possible for the process to fit between the specifications, you can conclude that the common causes of variation present in the process are too wide to produce adequate output. It follows that a systemic change to the process is required. If on the other hand, the process width is narrower than the specifications, but the process overlaps a specification (see figure 4), it may be a simpler matter to remedy. Shifting the process average away from the critical specification is often a simple solution to implement.

One of the best examples of the successful application of statistical process control can be found in the Japanese automotive industry. Narrow process variation in relation to specifications is a hallmark of Japanese vehicle manufacture as shown by the build quality and reliability of Japanese-made vehicles. The origins of SPC methodologies may be dimmed by the mists of time, but they are as relevant today and as powerful as ever. The assiduous, disciplined application of SPC will reap rich rewards.

Pareto diagrams are deceptively simple in concept but they can be an invaluable management tool for analysis and decision making. Although simple to construct and to interpret, Paretos are able to analyse complex issues and clarify the way forward.

A Pareto diagram is a simple bar chart that ranks items in decreasing order of occurrence. The purpose of a Pareto diagram is to separate the significant aspects of a problem or issue from those that are trivial. The Pareto diagram is a graphical representation of data and is similar to a histogramexcept that it monitors items rather than numbers. The diagram is based on the principle that there is an unequal distribution of items in the universe. It is the law of “the significant few versus the trivial many.” For example, there are often many causes of a problem or issue; however only some of them are significant. This is known as the 80:20 rule: the significant few items make up 80 percent of the problem or issue, while the trivial many make up about 20 percent. A Pareto diagram is used to identify the significant few items. Vilfredo Pareto, an Italian economist and sociologist, who conducted a study in Europe in the early 1900s on wealth and poverty, first developed this principle. Pareto found that wealth was concentrated in the hands of the few and poverty in the hands of the many. Pareto’s principle was named and popularised by Joseph M. Juran in the late 1940s. It was Juran who made the principle a universal concept.

A Pareto diagram, one of the most useful analytic tools, can easily be applied in any industry or setting. It can be used to analyse the causes of a problem or issue, to study the results of a change in a process or system, and to plan for continuous improvement. A Pareto diagram can be used to stratify or divide the data to identify the most significant aspects of a problem or issue. Theories for improvement can then be generated to reduce the significant aspects. After trying the improvement theories, new Pareto diagrams can be used to see if the theories have worked. At this point, the larger bars in the first Pareto diagram should be smaller. For continuous improvement, use the new diagram to make plans to reduce the “new” largest bars.

In some circumstances, the number of categories examined is small; that is, fewer than four. In these cases, a Pareto diagram has a strange appearance and may not seem to be useful. An alternative in this situation is to use a pie chart. A pie chart is a way of displaying data pictorially in a circle. The various portions of the data being examined are represented by segments of the circle (like pieces of a pie).

Cautionis required when using Pareto diagrams if the system being analysed has not been examined for statistical stability using a control chart. If the system being examined is statistically unstable, output may not be consistent. A wildly fluctuating system will produce inconsistent Pareto diagrams that can lead to misjudgments. Suppose a retail manager failed to note that customer returns varied greatly from month to month. By choosing a month in which returns were unusually high for the analysis, the

ranking of categories could be entirely different from those for a month in which returns were unusually low or at normal levels. Repeating the Pareto diagrams can help to confirm the order of the categories. However, the most effective protection against being misled is to first use a control chart to tell if the system is stable and predictable.

To interpret a Pareto diagram, start by looking at the chart to identify the categories that are significant compared to those that are trivial. Expect the significant few categories to represent approximately 80 percent of the data in the Pareto diagram. This can be tested by looking at the cumulative percentage line for the first few categories.

The example Pareto shows the number of complaints received by a hotel categorised by type of complaint. In the example, (reminiscent of an establishment run by Mr Faulty?) “Dining room service” and “Dining room food” are the two largest bars. Reading from the cumulative line to the right axis, they represent approximately 80 percent of the data. There is a substantial difference between the first two categories and the remaining bars. So, tackling the first two bars offers substantial advantage.

No matter how data is categorised, it can be ranked and made into a Pareto diagram. Be careful to limit the number of categories to 10 or fewer. Using too many categories may have the effect of flattening the Pareto so that no single bar is dramatically different from the others. In this situation, no significant advantage is gained by working on the tallest bar. If possible, try to re-categorise the data to see if a clear difference in the bars can be found.

As always, I look forward to your comments and questions. I’m at support@pqsystems.com

Like to know more about statistical process control? Please view our seminar schedule for a location near you.