Manufacturing Process Capability Improvement Project

This project prepares a capability-improvement package for a manufacturing process that is drifting toward a specification limit. The goal is to decide whether the line can be released for production, which controls must be changed, and what evidence proves that the improvement is real.

The project is not only a C_{pk} calculation. A credible process capability review must connect requirements, measurement-system adequacy, process centering, variation reduction, containment, defect risk, root-cause evidence, control-plan updates, and validation after the change.

Project Objective

Improve a turning process that produces a critical shaft diameter. The final engineering deliverable should answer:

1. Is the measurement system good enough to support release decisions?
2. What are the current C_p and C_{pk} values?
3. Which side of the tolerance is limiting the process?
4. What is the approximate nonconformance risk under the current distribution?
5. Which containment action protects the customer while the process is corrected?
6. Which process changes improve centering and variation?
7. What validation evidence is required before normal release?

The deliverable should be a process-capability improvement report with calculations, assumptions, containment records, root-cause analysis, updated control plan, validation run results, and a release decision.

Baseline Scenario

A CNC turning cell produces a precision shaft for a bearing assembly. The customer drawing specifies:

The process must meet:

• C_{pk}\geq1.33 for production release;
• Gage R&R no greater than 20\% of tolerance width for the release measurement;
• documented containment for any lot produced after the drift signal;
• validation run after corrective action using normal material, operators, tooling, coolant, and inspection method.

Use the following baseline data.

Parameter	Value
lower specification limit, LSL	19.950\ \text{mm}
upper specification limit, USL	20.050\ \text{mm}
baseline process mean, \mu_0	20.018\ \text{mm}
baseline process standard deviation, s_0	0.014\ \text{mm}
measurement-system standard deviation, s_{GRR}	0.0040\ \text{mm}
weekly production demand	18000\ \text{shafts}
rework cost per shaft	\18$
scrap cost per shaft	\42$
customer escape severity	high

These values are simplified. A real improvement project must also check part family, material lots, tool wear, machine thermal growth, fixture condition, coolant temperature, operator method, calibration status, sample independence, autocorrelation, non-normality, and whether the distribution is stable enough for capability claims.

Step 1: Confirm Tolerance Width

The tolerance width is:

Substitute:

Engineering Comment

The tolerance width is only 0.100\ \text{mm}. A small measurement or centering error can consume a large part of the available margin. This is why the measurement system must be reviewed before treating capability values as release evidence.

Step 2: Screen the Measurement System

Use the usual six-standard-deviation spread for the measurement-system study:

Percent of tolerance consumed by measurement variation:

Engineering Comment

The measurement system consumes about 24\% of tolerance, which fails the 20\% release criterion. The process may still be physically capable or incapable, but the current measurement method is too weak for confident release. The project should improve the fixture, method, resolution, operator training, or environmental control before final validation.

Step 3: Calculate Baseline Capability

Potential capability:

Substitute:

Upper-side capability:

Lower-side capability:

Therefore:

Engineering Comment

The process fails the release criterion. The spread is already marginal because C_p=1.19<1.33, and the mean is shifted toward the upper specification limit, which makes C_{pk} much worse. The first corrective action should not be only tighter inspection. The process needs centering and variation reduction.

Step 4: Estimate Nonconformance Risk

For a normal screening estimate, compute the z-score to the upper specification limit:

The lower-side z-score is:

The upper tail dominates. A standard normal tail at z=2.29 is approximately:

For weekly demand:

If all nonconforming shafts were detected internally and reworked:

If they were scrapped:

Engineering Comment

This is only a screening estimate because it assumes normality, independence, and stable variation. It is still enough to justify containment. A high-severity customer escape should not wait for a perfect statistical model when the process is already off-center and measurement capability is marginal.

Step 5: Define Containment

Containment should protect the customer without pretending that sorting is the permanent solution. A practical containment package includes:

• hold all unshipped shafts produced after the first drift signal;
• identify affected lots by machine, fixture, tool offset, operator shift, material lot, and inspection record;
• remeasure suspect inventory using the best available calibrated method;
• use a guarded release rule if measurement uncertainty remains material;
• segregate oversize or uncertain parts from releasable material;
• notify production planning that capacity is reduced until the control plan is restored;
• record disposition: release, rework, scrap, or engineering-use-only.

Engineering Comment

Containment buys time. It does not close the corrective action. If the process remains off-center, inspection will only convert a capability problem into a queueing, rework, and delivery problem.

Step 6: Rank Root Causes

The first review identifies three credible contributors.

Candidate cause	Evidence to collect	Likely effect
tool wear compensation too slow	diameter trend versus parts since tool change	mean drifts upward
thermal growth after restart	first-piece and warm-machine comparison	mean shifts during warm-up
weak inspection fixture location	repeated measurements by operator and fixture	apparent variation increases

Use a simple risk-priority screen for the dominant failure mode: oversize shaft creates bearing assembly interference.

State	Severity	Occurrence	Detection	RPN
before improvement	8	6	4	192
after planned controls	8	2	2	32

Engineering Comment

RPN is not a physical risk measure and should not override severity. Its value here is prioritization: tool compensation, thermal stabilization, and measurement-fixture control are more useful than adding final inspection alone.

Step 7: Implement the Improvement

The corrective package is:

1. reset the tool-offset target from 20.018\ \text{mm} toward 20.000\ \text{mm};
2. add warm-up and first-piece confirmation after machine restart;
3. replace the worn inspection locator and standardize part seating force;
4. reduce the sampling interval during the first two hours after tool change;
5. add a reaction rule if two consecutive subgroup means move toward the upper limit;
6. require engineering review before releasing any held lot.

After fixture and method improvement, the new measurement-system estimate is:

Measurement spread:

Percent tolerance:

Engineering Comment

The measurement system now satisfies the 20\% criterion. It is still not perfect, but it is adequate for this release decision if calibration, fixture condition, and operator method are controlled.

Step 8: Validate the Improved Process

A validation run with normal production conditions gives:

Parameter	Value
validation sample size	125 shafts
validation mean, \mu_1	20.004\ \text{mm}
validation standard deviation, s_1	0.0098\ \text{mm}

Compute:

Upper-side capability:

Lower-side capability:

Therefore:

Engineering Comment

The improved process meets the C_{pk}\geq1.33 requirement with margin. The result is credible only if the validation run represents normal production: ordinary operators, material, coolant, tool life, restart conditions, inspection method, and data recording. A special demonstration run under ideal conditions would not be enough.

Step 9: Update the Control Plan

The updated control plan should include:

Control element	Updated requirement
critical characteristic	shaft diameter, 20.000\pm0.050\ \text{mm}
measurement method	calibrated fixture with standardized seating and operator instruction
measurement-system criterion	6s_{GRR}\leq20\% of tolerance
startup control	warm-up plus first-piece confirmation after restart
tool-change control	offset verification and increased sampling after replacement
routine sampling	subgroup checks at defined production intervals
reaction rule	stop, segregate, and call engineering on drift toward upper limit
lot release	release only after capability and containment evidence are reviewed
recurrence check	review first three production weeks after change

Engineering Comment

Capability improvement is fragile if the reaction rule is vague. The control plan must say who stops production, what is segregated, which evidence is reviewed, and who can release the line again.

Final Deliverable

The project deliverable should include:

• drawing requirement and release criterion;
• baseline measurement-system review;
• baseline C_p, C_{pk}, and nonconformance-risk estimate;
• affected-lot containment record;
• root-cause evidence and prioritized corrective actions;
• updated measurement method and Gage R&R evidence;
• validation-run data and capability calculations;
• updated control plan and reaction rules;
• release decision with owner, date, and residual risk.

Acceptance Criteria

Criterion	Acceptance evidence
measurement system adequate	Gage R&R spread no greater than 20\% of tolerance
process capable	validation C_{pk}\geq1.33 under normal production conditions
customer protected	affected lots held, measured, segregated, and dispositioned
root cause addressed	tool, thermal, and fixture controls updated with evidence
recurrence controlled	reaction rules and sampling plan added to the control plan
release traceable	engineering signoff links calculations, lots, and validation record

Final Decision

The engineering recommendation is:

Do not release the baseline process. Release the improved process only after the measurement system is acceptable, affected inventory is contained, validation shows C_{pk}=1.56, and the updated control plan is active.

The project should close only after normal production data confirms that the corrected process remains centered and stable. A one-time capability calculation is not a process-control system.