The Internal-Business-Process Perspective: Analyzing Quality Problems and Improving Quality

We present three techniques for identifying and analyzing quality problems: control charts, Pareto diagrams, and cause-and-effect diagrams.

Control Charts

Statistical quality control (SQC), also called statistical process control, is a formal means of distinguishing between random and nonrandom variations in an operating process. Random variations occur, for example, when chance fluctuations in the speed of equipment cause defective products to be produced, such as 3D printers that produce objects that have small holes in them or objects with uneven color. Nonrandom variations occur when defective products are produced as a result of a systematic problem such as an incorrect speed setting, a flawed part design, or the mishandling of a component part. A control chart, an important SQC tool, is a graph of a series of successive observations of a particular step, procedure, or operation taken at regular intervals of time. Each observation is plotted relative to specified ranges that represent the limits within which observations are expected to fall when caused by random events. Observations that fall outside the ranges are regarded as nonrandom and worth investigating.

Exhibit 20-3 presents control charts for the daily defect rates (defective 3D printers divided by the total number of 3D printers produced) at Formrob’s three 3D printer production lines. The defect rates in the prior 60 days for each production line provide a basis upon which to calculate the distribution of daily defect rates. The arithmetic mean ($\mu$, read as “mu”) and standard deviation ($\sigma$, read as “sigma,” how much an observation deviates from the mean) are the two parameters of the distribution that are used in the control charts in Exhibit 20-3. On the basis of experience, the company decides that managers should investigate any observation outside the $\mu \pm 2\sigma$ range. For example, if the average defect rate is $\mu =10\%$ or 0.1, and the standard deviation is $\sigma =2\%$ or 0.02, the company will investigate all observations when the defect rate is greater than $14\%\hspace{0.17em}[10\%+(2\times 2\%)]$ or less than $6\%\hspace{0.17em}[10\%-(2\times 2\%)].$ ^*

For production line A, all observations are within the range of $\mu \pm 2\sigma$, so managers believe no investigation is necessary. For production line B, the last two observations signal that a higher-than-expected percentage of 3D printers are not performing as they should, indicating that the problem is probably because of a nonrandom, out-of-control occurrence such as an incorrect speed setting or mishandling of a component part. Given the $\pm 2\sigma$ rule, both observations would be investigated. Production line C illustrates a process that would not prompt an investigation under the $\pm 2\sigma$ rule but that may well be out of control. Why? Because the last eight observations show a clear pattern: Over the last 7 days, the percentage of defective 3D printers increased and got further and further away from the mean. The pattern could be due to, for example, the tooling on a machine wearing out, resulting in poorly machined parts. As the tooling deteriorates further, the trend in producing defective 3D printers is likely to persist; the defect rate is expected to move beyond the random range. Statistical procedures have been developed using the trend as well as the variation to evaluate whether a process is out of control.

Pareto Diagrams

Observations outside control limits serve as inputs for Pareto diagrams. A Pareto diagram is a chart that indicates how frequently each type of defect occurs, ordered from the most frequent to the least frequent. Exhibit 20-4 presents a Pareto diagram of quality problems for all observations outside the control limits at the final inspection point in 2019. 3D printers that produce printed objects that have small holes in them are the most frequently recurring problem. They result in high rework costs, high warranty and repair costs, and low customer satisfaction.

Cause-and-Effect Diagrams

The most frequently recurring and costly problems identified by the Pareto diagram are analyzed using cause-and-effect diagrams. A cause-and-effect diagram identifies potential causes of defects using a diagram that resembles the bone structure of a fish (which is why the diagrams are also called fishbone diagrams).^* Exhibit 20-5 presents the cause-and-effect diagram describing potential reasons for printed objects that have small holes in them. The “backbone” of the diagram represents the problem being examined. The large “bones” coming off the backbone represent the main categories of potential causes of failure. The exhibit identifies four main causes for printed objects having small holes in them: human factors, methods and design factors, machine-related factors, and materials and components factors. Additional arrows, or bones, are added to provide more detailed reasons for each higher-level cause. Formrob’s engineers determine that the materials and components factor is a plausible reason for the printed objects to have small holes in them and that two potential causes of the material and component problems are incorrect component specifications and variations of the purchased components from the specifications. The engineers quickly determine that Formrob’s component specifications are correct. They then begin to explore reasons for variations in the purchased components. They discover that the aluminum frame (which holds in place various components of the 3D printer such as the printing bed, extruders, and motor) is mishandled and fractionally bent while being transported from the manufacturer to the shop floor. The resulting misalignment of components causes printed objects to have small holes in them.

Manufacturers use automated equipment and computers to record the number and types of defects and the operating parameters when defects occur. Using these inputs, computer programs simultaneously and iteratively prepare control charts, Pareto diagrams, and cause-and-effect diagrams with the goal of continuously reducing the mean defect rate, $\mu$, and the standard deviation, $\sigma$.

Nonfinancial Measures of Internal-Business-Process Quality

Companies routinely use nonfinancial measures to track the quality improvements they are making. Formrob’s managers use the following nonfinancial measures of internal-business-process quality:

• Percentage of defective products manufactured
• Percentage of reworked products
• Number of different types of defects analyzed using control charts, Pareto diagrams, and cause-and-effect diagrams
• Number of design and process changes made to improve design quality or reduce the costs of quality

Formrob’s managers believe that improving these measures will lead to greater customer satisfaction, lower costs of quality, and better financial performance.