12.1 Statistical Process Control

The goal of statistical process control is to make a process stable over time and then keep it stable unless planned changes are made. You might want, for example, to keep your weight constant over time. A manufacturer of machine parts wants the critical dimensions to be the same for all parts. “Constant over time” and “the same for all” are not realistic requirements. They ignore the fact that all processes have variation. Your weight fluctuates from day to day; the critical dimension of a machined part varies a bit from item to item; the time to process a college admission application is not the same for all applications. Variation occurs in even the most precisely made product due to small changes in the raw material, the adjustment of the machine, the behavior of the operator, and even the temperature in the plant. Because variation is always present, we can't expect to hold a variable exactly constant over time. The statistical description of stability over time requires that the pattern of variation remain stable, not that there be no variation in the variable measured.

Statistical Control

A process that continues to be described by the same distribution when observed over time is said to be in statistical control, or simply in control.

Control charts are statistical tools that monitor a process and alert us when the process has been changed so that it is now out of control. This is a signal to find and respond to the cause of the change.

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In the language of statistical quality control, a process that is in control has only common cause variation. Common cause variation is the inherent variability of the system due to many small causes that are always present. Because it is assumed that these many underlying small causes result in small, random perturbations to which all process outcomes are exposed, their cumulative effect is, by definition, assumed to be random by nature. Thus, an in-control process is a random process that generates random or independent process outcomes over time.

common cause variation

When the normal functioning of the process has changed, we say that special cause variation is added to the common cause variation. A special cause can be viewed as any factor impinging on the process and resulting in variation not consistent with common cause variation. In contrast to common causes, special causes can often be traced to some clear and identifiable event. Given that a special cause is ultimately associated with an identifiable event, some practitioners often refer to a special cause as an assignable cause. Examples might include an operator error, a jammed machine, or a bad batch of raw material. These are classic manufacturing examples in which the special cause variation has negative implications on the process. In particular, when dealing with manufacturing processes in which the goal is to produce parts as close to targets or specifications as possible, any added variation is undesirable. In such situations, we hope to be able to discover what lies behind special cause variation and eliminate that cause to restore the stable functioning of the process.

special cause variation

assignable cause

Historically, statistical process control (SPC) methods were devised to monitor manufactured parts with the intention of detecting unwanted special cause variation. However, one of the great contributions of the quality revolution is the recognition that any process, not just classical manufacturing processes, has the potential to be improved. In the business arena, SPC methods are routinely used for monitoring services processes—for example, patient waiting time in a hospital clinic. These same methods, however, can be used to monitor the ratings of a television show, daily stock returns, the level of ozone in the atmosphere, or even golf scores. With this broader perspective, process change due to a special cause might be viewed favorably—for example, a decrease in waiting times or an increase in monthly customer satisfaction ratings. In such situations, our intention should not be to eliminate the special cause but, rather, to learn about the special cause and promote its effects.

EXAMPLE 12.1 Common Cause, Special Cause

Imagine yourself doing the same task repeatedly, say, folding an advertising flyer, stuffing it into an envelope, and sealing the envelope. The time to complete the task will vary a bit, and it is hard to point to any one reason for the variation. Your completion time shows only common cause variation.

Now you receive a text. You engage in a text conversation, and though you continue folding and stuffing while texting, your completion time rises beyond the level expected from common causes alone. Texting adds special cause variation to the common cause variation that is always present. The process has been disturbed and is no longer in its normal and stable state.

If you are paying temporary employees to fold and stuff advertising flyers, you avoid this special cause by requiring your employees to turn off their cell phones while they are working.

The idea underlying control charts is simple but ingenious.3 By setting limits on the natural variability of a process, control charts work by distinguishing the always-present common cause variation in a process from the additional variation that suggests that the process has been changed by a special cause. When a control chart indicates process change, it is a signal to respond, which often entails taking corrective action. On the flip side, when a control chart indicates that there has been no process change, the chart still serves a purpose: it restrains the user from taking unnecessary actions. All too often, time and resources are wasted by misinterpreting common cause variation as special cause variation. When a control chart is not signaling, the best management practice is one of no action.4

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A wide variety of control charts are available to quality practitioners. Control charts can be broadly classified based on the type of data collection.

Types of Control Charts

Variable control charts are control charts devised for monitoring quantitative measurements, such as weights, time, temperature, or dimensions. Variable control charts include charts for monitoring the mean of the process and charts for monitoring the variability of the process.

Attribute control charts are control charts for monitoring counting data. Examples of counting data are number (or proportion) of defective items in a production run, number of invoice errors, or number of complaining customers per month. Section 12.3 discusses two of the most common attribute charts: the chart and the chart.

Apply Your Knowledge

Question 12.4

12.4 Special causes.

Rachel participates in bicycle road races. She regularly rides 25 kilometers over the same course in training. Her time varies a bit from day to day but is generally stable. Give several examples of special causes that might raise or lower Rachel's time on a particular day.

Question 12.5

12.5 Common causes and special causes.

In Exercise 12.1 (page 597), you described the process of getting on an airplane. What are some sources of common cause variation in this process? What are some special causes that can result in out-of-control variation?

12.5

An example of common cause variation would include long lines, etc. An example of a special cause might be a delayed flight, etc.