(i) The core logic of control charts for analysis and control charts for control
1. From "Non-steady State" to "Steady State": The Initial Mission of the Control Chart
When any process is initiated, it is almost certain to be in a non - statistically controlled state (abbreviated as "non - stable state"), that is, there are uneliminated systematic special causes in the process (such as uncalibrated machines, fluctuations in raw material batches, and differences in operators' techniques), resulting in the fluctuations of quality characteristics including both random errors (inevitable) and systematic errors (eliminable). At this time, if the control limits (such as mean ± 3σ) are directly calculated using non - stable state data, the limits will be too wide due to the instability of the mean and variance of the data: the abnormal points originally caused by systematic special causes will be misjudged as "normal fluctuations", and the control chart will lose its monitoring value.
Therefore, the first step in using a control chart must be to adjust the non - stable state to a stable state, that is, to identify and eliminate special causes of variation in the system through an analysis control chart, so that only random fluctuations remain in the process. The core of this stage is to "find problems and set a baseline", rather than "monitor production".
2. Control charts for analysis: Solve two key problems
The goal of the control chart for analysis is to answer two mutually prerequisite questions and ultimately achieve the "dual compliance" of the process.
(1) Is the process in a state of statistical control?
The essence of the state of statistical control (stable state) is "predictable fluctuations" - the distribution (mean, variance) of quality characteristics is stable, without trends, cycles, or sudden changes. The control chart for analysis determines the stable state by the positions and arrangements of data points:
- If a point falls outside the control limits (3σ), it indicates the existence of strong systematic special causes (such as machine failures).
- If the points are within the limits but are arranged abnormally (e.g., 7 consecutive points are rising, or 10 out of 11 points are on the same side), it indicates the existence of weak system special causes (e.g., the raw materials are gradually deteriorating).
The process can reach a stable state only after repeatedly performing the steps of "drawing a control chart → finding special causes → eliminating special causes → recollecting data" until there are no abnormal signals in the process.
(2) Does the process capability meet the technical requirements?
Process capability indices (such as Cp, Cpk) measure "the ability of a process to meet specification requirements", but their calculation must be based on a stable state - only when the fluctuations under the stable state are "inherent fluctuations" can we accurately determine whether the process can continuously produce qualified products. For example:
- If the process is not in a steady state (e.g., the temperature fluctuates), even if qualified products are occasionally produced, the calculated Cp will be artificially high (because the data contains random and systematic fluctuations and cannot reflect the true capability).
- Only under a steady state can Cp truly reflect "the relationship between process fluctuations and specification limits" (for example, if the specification limit is ±0.1 mm and the process fluctuation is ±0.05 mm, then Cp = 1.33, meeting the requirements).
Therefore, it is necessary to first achieve a steady state through analysis using control charts and then calculate the process capability index. Otherwise, the result is meaningless.
3. Four states of the process and improvement paths
According to "whether it is in a stable state" (statistical control state) and "whether it meets the technical requirements" (technical control state), processes can be divided into four categories, corresponding to different improvement strategies:
State I: Double satisfaction (steady state + meeting the capacity requirement)
The most ideal target state - the process fluctuation is stable (predictable), and the fluctuation range is completely within the specification limits (for example, the specification is ±0.1mm, and the process fluctuation is ±0.05mm). At this time, the product quality is consistent, and the customer satisfaction is high. It is the preferred state for the last process of the production line.
State II: Technology meets the requirements but not in a steady state
Although qualified products can be produced temporarily, the process is unstable (e.g., the machine is not calibrated and its performance is inconsistent). For example, the specification of a certain injection-molded part is 50±0.2mm. The machine can occasionally produce qualified parts with a size of 50.1mm, but often produces out-of-tolerance parts with a size of 50.3mm due to pressure fluctuations. This state poses a very high risk - long-term operation will lead to batch scrap due to the accumulation of special causes. It is necessary to immediately find and eliminate the special causes in the system (e.g., calibrate the machine) to achieve a stable state first.
State III: Steady state but insufficient capacity
The process is stable (the fluctuations are predictable), but the fluctuation range exceeds the specification limits (for example, the specification is ±0.1mm, and the process fluctuation is ±0.15mm). For example, the specification of a certain resistor is 100±1Ω, and the stable output of the process is 100±1.5Ω. Although the fluctuations are consistent, it often exceeds the tolerance. At this time, the process capability needs to be improved (such as replacing with a precision resistor and optimizing the welding process) to make the fluctuations meet the specifications.
Status IV: Double non - satisfaction (the worst)
It is neither stable (with irregular fluctuations) nor meets the specifications (often out of tolerance). For example, the sterilization temperature in a food factory fluctuates (unsteady state), resulting in excessive bacteria in some products (insufficient capability). At this time, immediate rectification is required, and the path selection depends on the technical and economic costs:
- If the cost of eliminating special causes (e.g., repairing the thermostat) is low, first reach State II (technically satisfied), and then reach State I.
- If the cost of improving capabilities (such as replacing sterilization equipment) is low, first reach state III (steady state) and then reach state I.
The adjustment process of the control chart for analysis is essentially a cycle of quality improvement - gradually approaching State I through "identifying special causes → eliminating special causes → verifying the effects".
4. Control charts for control: The "daily regulations" for maintaining a stable state
After the analysis control chart confirms that the process has reached the target state (usually State I), the control limits need to be fixed (i.e., the mean and 3σ limits of the analysis control chart are used as permanent standards), and the chart is converted into a control chart for control purposes. This transformation is equivalent to "quality legislation":
- In daily production, simply plot new data points on the control chart. If the points are within the limits and randomly arranged, it indicates that the process remains in a stable state.
- If the points are out of bounds or in an abnormal arrangement (such as 9 consecutive points on the same side), immediately trigger the process of "investigate the assignable cause → eliminate the assignable cause → restore the steady state".
The core of the control chart for control is "maintenance" - it is not responsible for process improvement, but only for monitoring whether the process deviates from the existing stable state. For example: In the size control of automobile engine pistons, after the stable state is confirmed by the control chart for analysis, the control chart for control monitors the sizes of 10 pistons every day. If a point goes out of the control limits, immediately check whether the lathe tool is worn. After replacement, re - verify to ensure that the process returns to the stable state.
(Ⅱ) The underlying logic of the criteria for judging abnormality
The "judgment of non - randomness" in the control chart refers to identifying the systematic special causes in the process. Its core logic is based on the principle of small - probability events: under the steady state, the data follow a normal distribution, and the probabilities of certain events (such as points going beyond the 3σ limits, nine consecutive points on the same side) are extremely low (usually...)(<0.5%), if it occurs, the process can be determined to be abnormal.
1. Two types of core criteria for detecting abnormalities
The criteria for detecting out - of - control situations are divided into two categories, covering all possible abnormal patterns.
(1) Judge as abnormal when a point is out of bounds (Criterion 1)
The limits of the control chart are ±3σ (corresponding to a 99.73% confidence interval). Under the stable state, the probability of a point going out of the bounds is only 0.27% (about 1 occurrence per 370 points). If a point goes out of the bounds, it indicates the existence of strong systematic special causes (such as raw material batch mixing, machine breakdown), and immediate treatment is required.
(2) Judge as abnormal if the in - boundary points are not randomly arranged (Criterion 2 - 8)
Under steady - state conditions, the arrangement of points within the limits should be completely random (e.g., uniformly distributed on both sides of the center line, without trends/cycles). If a non - random arrangement occurs (e.g., 9 consecutive points on the same side, 6 consecutive points rising), it indicates the presence of weak special causes in the system (e.g., operator fatigue, gradual deterioration of raw materials). For example:
- Nine consecutive points on the same side: The probability under steady state is approximately 0.39%, indicating that the process mean has shifted (e.g., the machine temperature rises slowly).
- Six consecutive points rising: The probability is about 0.16%, indicating that the process has a trend of continuous improvement or deterioration (e.g., the tool gradually wears out and the size gets larger).
2. Partitioning of the control chart: Enhance the sensitivity of detecting abnormal situations
To more accurately identify abnormalities, the control chart is equally divided into 6 zones (A, B, and C are symmetrical, with each zone having a width of 1σ):
- Zone A (2σ - 3σ): It is the farthest from the centerline. The probability of a point falling in Zone A is only 2.14% (once every 47 points).
- Area B (1σ - 2σ): Probability 13.59%;
- Area C (0 - 1σ): Probability 34.13%.
The function of partitioning is to refine the abnormal patterns. For example:
- Criterion 3 (Two out of three consecutive points fall on the same side of Zone A): Under steady - state conditions, the probability is approximately 0.5%, indicating a slight shift in the process mean.
- Criterion 4 (alternating up and down for 14 consecutive points): The probability is about 0.4%, indicating the existence of periodic special causes (e.g., different operating techniques when operators take turns).
3. Eight common rules for detecting special causes (GB/T 4091-2001)
All eight rules of the conventional control chart are based on "low - probability events" and cover all common abnormal patterns.
1. The point falls outside Area A;
2. Nine consecutive points fall on the same side of the center line.
3. Six consecutive points increasing or decreasing;
4. Alternate up and down for 14 consecutive points;
5. Two out of three consecutive points fall on the same side of Area A.
6. Four out of five consecutive points fall on the same side of Zone B or Zone A.
7. 15 consecutive points fall in Zone C (on both sides of the center line);
8. Eight consecutive points fall on both sides of the center line and none of them is in Zone C.
The common goal of these guidelines is to achieve early detection and early handling. That is, before batch scrap is caused by special causes in the system, trigger rectification through the signals on the control chart to ensure that the process always remains in a stable state.