Check stability before capability

Check stability before capability

Capability compares a process distribution with stated specification limits. First establish that measurement is fit for the decision and that the process behaviour supports the chosen analysis. Cp compares specification width with six estimated standard deviations; Cpk also reflects how far the mean lies from the nearer specification. An attractive number does not cure instability, establish an applicable customer threshold or remove sampling uncertainty. State the estimator, distribution assumptions and study conditions when reporting results. This example supplies stable-normal parameters solely to demonstrate arithmetic. It is not evidence that a real process is qualified, approved or certain to produce no nonconforming output.

Follow the method

1. Supplied stable normal model / mean 10.01, sigma 0.02
2. Normal probability density (1/mm)
3. Width (mm)
4. Spec lower: 9.9
5. Spec upper: 10.1

Separate the capability calculation from the approval decision

Fictional case: a width process is supplied as stable and approximately normal with mean 10.01 mm and sigma .02 mm. Specifications are 9.90–10.10 mm. These parameters and the existing native distribution remain unchanged. Engineer Asha must explain why Cp and Cpk differ and whether either number authorizes production acceptance.

Follow the method

1. Specification width
2. Cp
3. Nearer mean-to-limit distance
4. Cpk
5. Acceptance

A good-looking index is not a qualification record

Calculate and interpret Cp and Cpk from explicitly supplied stable-normal parameters while keeping evidence prerequisites and acceptance authority separate.

Fictional case: a width process is supplied as stable and approximately normal with mean 10.01 mm and sigma .02 mm. Specifications are 9.90–10.10 mm. These parameters and the existing native distribution remain unchanged. Engineer Asha must explain why Cp and Cpk differ and whether either number authorizes production acceptance.

Role: Quality engineer with the customer-requirements owner

Normal condition

Distribution, stability, measurement fitness, sampling and specification authority are established for the intended use before a capability conclusion is applied.

The gap

A slide presents 1.667 as a universal passing score and treats the six-point SPC illustration from another lesson as proof of this process’s stability.

• The parameters are supplied synthetic assumptions, not estimates from customer production.
• No universal acceptance threshold, confidence bound or customer approval is supplied.

1. Separate requirements from process estimates

   Asha identifies specification width 10.10−9.90=.20 mm and records where the actual product requirements would come from. Mean and sigma describe the supplied process, not allowable product limits.

   Why: The process distribution and customer tolerance are different authorities. Substituting control limits for specifications would make capability self-referential.

   Evidence: The record names LSL, USL, mean and sigma separately.

2. Check the interpretation prerequisites

   She labels stable/normal/measurement-suitable as supplied exercise assumptions and lists the actual evidence needed before a real claim. She does not invent a baseline study.

   Why: A calculated ratio remains arithmetic even when prerequisites are absent; its predictive capability interpretation would then be unsupported.

   Evidence: A prerequisite checklist distinguishes given assumptions from verified workplace records.

3. Calculate potential width ratio

   Cp=.20/(6×.02)=1.6667, approximately 1.667. This compares specification width with the supplied six-sigma process spread.

   Why: Cp alone does not locate the mean within the tolerance. A narrow distribution could still be shifted toward or beyond a specification.

   Evidence: The formula retains millimetres in numerator and denominator before cancellation.

4. Calculate the nearer-side ratio

   Upper distance is 10.10−10.01=.09 mm; lower distance is 10.01−9.90=.11 mm. Cpk=min(.09,.11)/(3×.02)=1.50.

   Why: The upper side is closer. The smaller Cpk reflects this off-center mean without changing the supplied spread.

   Evidence: The worked record identifies the limiting side and preserves both distances.

5. Write a bounded decision

   Asha reports the two indices under the stated assumptions and requests applicable acceptance requirements and appropriate uncertainty/evidence before a production decision.

   Why: Neither number is a universal pass threshold. A capability calculation does not replace process control, customer conditions or the authorized release record.

   Evidence: The report states synthetic calculation only and separates interpretation from acceptance.

The same spread drifts toward the upper limit

In a hypothetical comparison the mean becomes 10.07 mm while sigma remains .02 mm and specifications stay unchanged.

Cp remains 1.667; Cpk becomes .03/.06=.50. Treat any real drift through process investigation rather than celebrating the unchanged Cp.

The spread-only ratio cannot reveal loss of centering. A changing real process also challenges the stable-distribution premise.

The comparison identifies changed mean, unchanged spread and reduced nearer-side margin.

Run a practice session

Materials

• Parameter cards
• Calculator
• Prerequisite/decision record

1. Identify the two authorities · 5 minutes

   Which numbers come from requirements and which from the process?

2. Calculate both indices · 8 minutes

   Why is the upper side limiting?

3. Work the changed case · 10 minutes

   What does the calculation still not prove?

4. Debrief drift · 5 minutes

   Why can Cp stay constant while risk changes?

Debrief

• Require the learner to name the supplied assumptions.
• Do not award a pass/fail verdict without stated applicable criteria.

Draw the two mean-to-limit distances before calculating Cpk.

Transfer into the work

Owner: Capability-study owner with customer quality

Record: Study scope, measurement/baseline evidence, indices and applicable decision

Review: Before qualification and after material process changes

Evidence: Traceable data, suitable assumptions and authorized acceptance basis

Resolve instability or measurement gaps before using a capability index as decision evidence.