3.2The seven QC tools and control charts

When a PM confronts quality data, the task is not to "just make some chart," but to choose the QC tool that fits the nature of the data at hand and the question being asked. Whether the goal is narrowing down the cause of defects, brainstorming candidate causes, or continuously monitoring whether a process remains stable calls for entirely different tools. This section covers the intended purpose of each tool against real data situations.

3.2.1Choosing among the seven QC tools

• A Pareto chart bar-charts defect counts by category in descending order, with a line overlay of cumulative percentage. Use it when you need to prioritize which defect category to focus limited response resources on—it visualizes the tendency for a small number of vital causes to account for most of the defects (the "80/20" pattern).
• A cause-and-effect diagram (fishbone diagram) systematically brainstorms candidate causes for a result (characteristic), organized under branches such as people/machine/method/material. Use it at the stage where the cause has not yet been narrowed down and you need to exhaustively surface candidate hypotheses—it does not measure the magnitude or count of causes, only organizes candidates.
• A histogram bins data into class intervals and bar-charts the frequency distribution. Use it when you want to grasp the shape of a process's variation—its center, spread, skew, or bimodality.
• A scatter diagram plots two variables (e.g., processing temperature and defect rate) as points to visually check whether and how strongly they correlate. Use it when you suspect one characteristic is related to another and want to verify it. Note that correlation does not necessarily imply causation.
• A control chart plots measurements over time with a center line (CL) and upper/lower control limits (UCL/LCL), used when you want to continuously monitor whether a process remains in a statistically stable (in-control) state. Its decisive difference from a histogram is that its primary purpose is detecting change over time, not a one-off snapshot of a distribution.
• A check sheet is a simple form for recording and tallying the count, type, or timing of defects. Used at the entry stage, when the priority is efficiently and comprehensively collecting the raw data itself—it is a collection tool more than an analysis tool.
• Stratification groups data by attribute—by machine, by operator, by lot, by time of day—for comparison. Used when you want to isolate whether a bias invisible in the aggregate is concentrated in a specific stratum (e.g., a particular operator or lot). It is less a standalone chart than an analytical lens combined with the other tools.

3.2.2Control-chart abnormality detection and response

• Representative abnormality rules: the process is judged to have departed from a statistically in-control state ("out of control") if any of the following is detected: (1) a point falls outside the control limits (UCL/LCL); (2) a run of several consecutive points (roughly 7 or more) falls on one side of the center line; or (3) points show a sustained upward/downward trend toward or away from the center line.
• Note that a point falling within the control limits (i.e., no abnormality flagged) does not by itself guarantee that the individual measurement meets the specification. Control limits are a statistical indicator of whether the process is stable within the range of chance variation, a distinct concept from the specification limits (customer requirements).
• What the PM should do upon detecting an abnormality: first investigate to identify the special cause (assignable cause—a sudden, identifiable cause rather than chance variation), then take corrective action to remove it. Conversely, repeatedly adjusting the process in response to ordinary chance-cause variation within the control limits (over-correction) actually increases variation and is a classic mistake to avoid.

Suppose a PM is assigned to analyze defect data from a manufacturing line's inspection process. First, a check sheet is used to comprehensively record one month's worth of defect counts, types, and occurrence times. Next, to decide which defect type to prioritize, a Pareto chart is built, revealing that "solder-joint defects" account for 65% of all defects—so resources should be concentrated on this one category first. But at this stage, why solder-joint defects occur is still unknown. A cause-and-effect diagram is used to brainstorm candidate causes across four perspectives—operator, machine (soldering-iron temperature setting), method (work procedure), and material (solder quality)—and "variation in soldering-iron temperature setting" emerges as the leading hypothesis. To verify this hypothesis, a scatter diagram plots soldering-iron temperature against defect rate, confirming a clear positive correlation. At this point the cause has been narrowed to temperature variation, but to continuously monitor whether the process remains stable, a control chart is introduced, plotting daily average temperature over time. After it goes live, one week shows an abnormal pattern: seven consecutive days with points biased above the center line. This is not chance variation but a situation that suggests a special cause (for instance, degradation of a particular machine's temperature sensor), and the action the PM should take is to investigate that specific machine and take corrective action such as replacing the sensor. If, conversely, an operator had been fine-tuning the temperature setting every day in response to ordinary within-limits daily variation, that would have been over-correction for chance variation—a mistaken response that actually widens the process's variation. Choosing the right tool for the question currently being asked, across the flow of data collection -> prioritization -> candidate-cause brainstorming -> correlation verification -> ongoing monitoring, is the judgment a PM is expected to exercise.

3.2.3Section summary

• Choose among the seven QC tools by the question you are asking: prioritization -> Pareto chart, candidate causes -> cause-and-effect diagram, correlation -> scatter diagram, ongoing monitoring -> control chart
• Control-chart abnormalities are points outside the control limits, a run biased to one side, or a trend. Being within the limits is not a guarantee of meeting specification
• Upon detecting an abnormality, identify and remove the special cause through corrective action. Over-correcting for chance variation increases variation