6.3 Out-of-Control Rules & Process Analysis

6.3 Out-of-Control Rules & Process Analysis

Statistical Zone Division Architecture

In classical statistical process control developed by Dr. Walter Shewhart, a process is in a state of statistical control when its variation is driven solely by common causes (inherent, stable, random noise). When an assignable cause (special cause) enters the system—such as a cracked cutting insert, a contaminated chemical bath, a worn collet, or an untrained operator—it introduces unnatural instability.

While a single point falling outside the three-sigma control limits ($> UCL$ or $< LCL$) is the most obvious signal of an out-of-control condition, unnatural non-random patterns can occur entirely inside the control limits. To detect these subtle shifts, trends, and systematic disturbances rapidly, the space between the Centerline ($CL$) and each three-sigma control limit is partitioned into three equal statistical zones, each spanning one standard deviation ($1\sigma$):

+3 sigma ------------------------------------------------ UCL (Upper Control Limit)
              ZONE A  (Upper)  [Between +2 sigma and +3 sigma]
+2 sigma ------------------------------------------------
              ZONE B  (Upper)  [Between +1 sigma and +2 sigma]
+1 sigma ------------------------------------------------
              ZONE C  (Upper)  [Between Centerline and +1 sigma]
 CENTER  ================================================ CL (Centerline: Mean)
              ZONE C  (Lower)  [Between Centerline and -1 sigma]
-1 sigma ------------------------------------------------
              ZONE B  (Lower)  [Between -1 sigma and -2 sigma]
-2 sigma ------------------------------------------------
              ZONE A  (Lower)  [Between -2 sigma and -3 sigma]
-3 sigma ------------------------------------------------ LCL (Lower Control Limit)

Theoretical Normal Probabilities for Each Zone

Assuming an underlying normal distribution of subgroup statistics under common cause variation:

• Zone C ($CL \pm 1\sigma$): Spans from the centerline to $\pm 1\sigma$. Approximately $68.27%$ of all subgroup points will fall in Zone C ($34.135%$ on each side).
• Zone B ($1\sigma$ to $2\sigma$): Spans between $1\sigma$ and $2\sigma$ on either side. Approximately $27.18%$ of all points will fall in Zone B ($13.59%$ on each side).
• Zone A ($2\sigma$ to $3\sigma$): Spans between $2\sigma$ and $3\sigma$ on either side. Approximately $4.28%$ of all points will fall in Zone A ($2.14%$ on each side).
• Beyond Control Limits ($> 3\sigma$): The probability of a point plotting beyond either control limit purely by random chance is only $0.27%$ (approximately 3 in 1,000, or a probability $p = 0.0027$).

Because the expected probabilities in each zone are known, observing unlikely clustering, runs, or trends across these zones indicates an assignable cause with an extremely high degree of statistical confidence.

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The Western Electric and Nelson Run Rules

In 1956, the Western Electric Company published its landmark Statistical Quality Control Handbook, formalizing the original four run rules. In 1984, Dr. Lloyd S. Nelson expanded these into an exhaustive set of Eight Rules for Detecting Special Causes of Variation, which are now standard across modern automated SPC software and ASQ body of knowledge exams.

Master Reference Table: Nelson Rules for Process Instability

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In-Depth Analysis of Critical Out-of-Control Patterns

1. The Freak / Single Point Beyond Limits (Rule 1)

Rule 1 is the classical Shewhart alarm. It indicates a sudden, dramatic disruption. Because the chance of a false alarm is only 0.27%, a technician must never ignore a single point outside the limits. Immediate action is required to verify the measurement, inspect the tooling, and quarantine product produced since the prior subgroup.

2. Level Shifts and Runs (Rule 2)

A run of 9 consecutive points on one side of the centerline indicates that the process mean has shifted. Even though none of the points have breached the three-sigma limit, the probability of 9 heads in a row on a fair coin toss is $(0.5)^9 = 1/512$. When this occurs, the process baseline is no longer operating at the calculated centerline. On attribute charts, a run of 9 points below the centerline on a $p$ chart indicates a statistically verified quality improvement; the technician should investigate the cause to make the improvement permanent and recalculate new baseline limits.

3. Trends and Machine Drift (Rule 3)

A trend of 6 consecutively increasing (or decreasing) points reveals a steady, progressive physical change. On machining operations, cutting tool flank wear causes part dimensions to grow (for outer diameters) or shrink (for internal bores) predictably over time. Identifying a trend enables predictive tool offsetting before out-of-specification scrap is produced.

4. Systematic Fluctuations and Sawtooth Patterns (Rule 4)

A sawtooth pattern where 14 consecutive points bounce strictly up-down-up-down indicates systematic negative autocorrelation. In precision inspection, this almost always traces back to:

• Two distinct entities: Sampling from Spindle A then Spindle B, or Operator 1 then Operator 2.
• Process Tampering (Deming's Funnel Rule 2): An operator measuring a part, seeing it slightly above the centerline, dialing the CNC offset downward; measuring the next part, seeing it below centerline, dialing the offset upward. This unnecessary adjustment doubles process variance!

5. Stratification vs. Mixture: The Subtle Pathology Pair

Two of the most frequently missed questions on the ASQ CQT exam involve distinguishing Stratification (Rule 7) from Mixture (Rule 8):

• Stratification (Rule 7): Points hug the centerline unnaturally. Novice inspectors mistake this for 'outstanding quality.' In reality, it represents a statistical defect: the subgroup standard error was calculated incorrectly, or the technician is committing a rational subgrouping violation by combining parts from two vastly different machines into a single subgroup, causing subgroup averages to artificially cluster near the center.
• Mixture (Rule 8): Points hug the upper and lower control limits with an unnatural void in Zone C. This occurs when two distinct populations are being sampled sequentially without being blended. For instance, Subgroup 1 is drawn from Machine 1 (mean = 10.05 mm) and Subgroup 2 is drawn from Machine 2 (mean = 9.95 mm). The points alternate near the limits, leaving Zone C empty.

   STRATIFICATION (Rule 7: Hugging Centerline)     MIXTURE (Rule 8: Hugging Limits)
 UCL +-------------------------------------+    UCL +---*-------*-------*-------*-------+
     |                                     |        |     *       *       *       *     |
     |                                     |        |                                   |
  CL |--------*--*-**-*-**-*-**------------|     CL |-----------------------------------|
     |                                     |        |                                   |
     |                                     |        |     *       *       *       *     |
 LCL +-------------------------------------+    LCL +---*-------*-------*-------*-------+
       15 consecutive points in Zone C                 8 consecutive points outside Zone C

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The Quality Technician Troubleshooting Protocol

When an out-of-control condition is identified on a production control chart, the quality technician must execute a rigorous, standardized five-step containment and corrective action protocol:

  [Step 1: Verification] ---> [Step 2: Immediate Containment] ---> [Step 3: Root Cause Analysis]
            |                                                                   |
  Verify gage calibration,                                             Investigate 6Ms
  part identity & math                                                 (Fishbone / 5 Whys)
                                                                                |
                                                                                v
  [Step 5: Chart Annotation] <--- [Step 4: Corrective Action Implementation] <--+
  Record date, time, rule,        Replace tool, adjust feed,
  NCR #, action & initials        re-zero fixture, verify yield

Step 1: Verification & Data Integrity

Before sounding an emergency alarm or shutting down a production line, verify the data:

• Confirm that the calculation (e.g., $p_i = np_i / n_i$) was performed correctly.
• Verify that the correct part number, revision level, and blueprint specifications were referenced.
• Check the measuring instrument: Is the micrometer, drop indicator, or vision system zeroed and within its calibration interval? Has thermal expansion affected the gage?
• Repeat the measurement on the suspect subgroup to confirm reproducibility.

Step 2: Immediate Containment and Quarantine

If the out-of-control signal is verified:

• Halt suspect production: Immediately alert the machine operator and cell supervisor.
• Establish containment boundaries: Trace back to the last known in-control subgroup. All product manufactured between the last verified in-control point and the current subgroup is suspect.
• Apply physical hold tags: Attach red Nonconforming Material / Hold tags to all suspect totes, bins, or pallets.
• Move to quarantine: Physically transfer suspect product to the secure quality quarantine holding area to prevent inadvertent shipment or downstream assembly.

Step 3: Root Cause & Assignable Cause Investigation

Apply structured problem-solving to isolate the assignable cause using the 6Ms:

• Machine: Check for spindle runout, loose collet chucks, damaged cutting inserts, broken drive belts, or thermal drift.
• Material: Verify incoming raw material lot number, hardness certification, bar stock diameter, or alloy heat treatment.
• Method: Check feed rates, spindle RPM, coolant flow, depth of cut, and adherence to standard operating procedures (SOP).
• Measurement: Audit gage repeatability, fixture seating, and inspector technique.
• Man (Personnel): Evaluate shift changeovers, operator training, fatigue, or deviations from work instructions.
• Mother Nature (Environment): Investigate ambient shop temperature spikes, humidity shifts affecting composite curing, or nearby press vibrations.

Step 4: Corrective Action & Verification

Implement an engineering or operational correction to permanently eliminate the assignable cause:

• Replace worn tooling, repair hydraulic lines, clean contaminated wash tanks, or update CNC program offsets.
• Produce and inspect a First Article Inspection (FAI) part to verify that the process has returned to statistical control within baseline limits.
• Disposition quarantined material through the Material Review Board (MRB): rework, scrap, sort, or return to vendor.

Step 5: Control Chart Documentation and Annotation

A control chart is an official legal and quality record. Every out-of-control event must be permanently annotated directly on the chart log:

• Draw a prominent circle around the out-of-control point(s).
• Note the date, exact time, and production shift.
• Reference the specific out-of-control rule violated (e.g., "Rule 1: Point above UCL" or "Rule 3: 6 consecutive increasing points").
• Record the identified assignable cause (e.g., "Chipped carbide insert on tool #4").
• Reference the Nonconformance Report (NCR) tracking number.
• Detail the immediate corrective action taken (e.g., "Replaced insert, offset adjusted -0.0015 in., FAI pin verified").
• Affix the technician's official signature or quality stamp.

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Deming's Funnel Experiment: The Danger of Tampering

A classic question on quality technician certification exams addresses tampering—the operational mistake of treating common cause variation as if it were a special cause. Dr. W. Edwards Deming demonstrated the mathematical consequences of tampering through the Funnel Experiment, where drops of a marble through a funnel aimed at a tabletop target are adjusted under four distinct rules:

• Rule 1 (No Adjustment): The funnel remains fixed directly over the target. Variation in drops represents stable, inherent common cause variation (process variance $= \sigma^2$).
• Rule 2 (Compensate from Last Error): After each drop, the funnel is moved from its current position by an amount equal and opposite to the last error. Result: Process variance doubles ($2\sigma^2$), increasing standard deviation by $41%$.
• Rule 3 (Compensate from Target): The funnel is reset relative to the original target by an amount equal and opposite to the last drop's distance from target. Result: The system experiences violent, unbounded oscillation, walking further and further away.
• Rule 4 (Aim at Last Drop): The funnel is set directly over the spot where the last marble landed. Result: The process drifts aimlessly in a random walk, with variance exploding toward infinity.

Core Lesson for Technicians: If a process is in statistical control, DO NOT ADJUST THE MACHINE based on individual part measurements! Machine adjustments made when only common causes exist will artificially increase product variability and generate scrap.

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Common Exam Traps for CQT Candidates

• Exam Trap 1: Misidentifying Stratification as "Good Precision": Any exam question describing 15 points clustered in Zone C represents Rule 7 (Stratification). It is an out-of-control signal requiring investigation into rational subgrouping and formula limits, never an indicator of superior capability.
• Exam Trap 2: Confusing Shift (Rule 2) with Trend (Rule 3): A shift is a step change where 8 or 9 points sit on one side of the centerline; a trend is a progressive progression of 6 points constantly rising or falling.
• Exam Trap 3: Applying All 8 Nelson Rules to Every Chart: While automated software can evaluate all 8 rules, applying all rules simultaneously to attribute charts with small sample sizes dramatically inflates the Type I error rate (false alarm rate). In manual shop-floor SPC, technicians typically apply Rules 1 through 4.
• Exam Trap 4: Erasing or Removing Out-of-Control Points: Never delete or erase an out-of-control point from a control chart. Out-of-control points are excluded from the mathematical calculation of future baseline limits only after an assignable cause has been identified, documented, and permanently eliminated.