Capability Index on a Process That Drifts
A machining cell produces a hub bore with specification 25.400 ± 0.050 mm; the bore diameter is a safety-related characteristic. The analyst has 40 subgroups of n = 5 collected over two weeks and plots X̄-R. The R chart is in control. The X̄ chart shows a gradual upward drift across each shift, with two points above the upper control limit in the last 12 subgroups. Operators reset the tool offset at the start of each shift. Calculated from all 40 subgroups, Cp = 1.38 and Cpk = 1.05. The customer's PPAP requirement is Ppk ≥ 1.67 with evidence that the process is in statistical control. The program manager wants to submit Cp = 1.38 and note that Cpk 'will improve,' because the launch review is Friday. The analyst is also told that the last five parts measured were all within specification.
1. Why are the reported indices not valid evidence as presented? Distinguish Cp, Cpk, Pp, and Ppk and the effect of the drift.
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The process is not stable, so none of the indices describes a predictable process.
- Cp compares tolerance width to within-subgroup variation only; it measures potential and assumes a centered, stable process. It ignores the drift entirely.
- Cpk adds the mean offset but is still computed from short-term (within-subgroup) sigma. With tool wear present, within-subgroup sigma understates the variation the customer will actually experience over time.
- Pp/Ppk use the overall standard deviation and describe actual performance, but only if the data represent a stable process; here they would average across a moving mean and understate the worst-case periods.
The upward drift and two out-of-limit points are special-cause variation (tool wear or thermal growth). The process mean is a moving target, so a single Cpk is a snapshot of one moment in the wear cycle - likely the favorable one. Five conforming parts are anecdotal and cannot offset a control chart signal. The customer requires stability precisely because an unstable process cannot be predicted.
2. What investigation is needed before any capability index is reported?
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Establish stability first.
- Stratify the data by shift, tool, and operator; plot diameter against time and against pieces-since-tool-change to quantify the wear slope.
- Determine whether the drift is inherent tool wear (predictable, treatable by planned offset changes) or a special cause such as thermal growth, a fixture problem, or inconsistent offset resets.
- Test whether the current reset frequency is adequate: if the mean crosses the limit within a shift, the offset strategy is not controlling the process.
- Remove or control the cause - more frequent compensated offsets, tool-life management, coolant/temperature control - and verify with a control chart.
- Recompute capability only from a new, stable data set using rational subgroups that reflect the way the process really runs. Report the index for the controlled process, not an average over an unstable one.
3. What should be submitted to the customer by Friday, and how should the deadline pressure be handled?
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Submit the truth plus a plan; do not submit Cp alone.
Submitting Cp = 1.38 while concealing the unstable Cpk and the out-of-control points misrepresents capability on a safety characteristic - an integrity and regulatory issue, not a presentation choice. Instead:
- Report the actual status: process not yet demonstrated stable or capable to Ppk ≥ 1.67.
- Show the control charts, the identified drift mechanism, and the containment in place (100% inspection using a gauge with known %GRR, plus traceability).
- Submit the action plan with dates: offset strategy revision, requalification run, new capability study, updated PFMEA and control plan.
- Request a conditional/interim PPAP approval or deviation with the customer's written agreement.
Customers routinely accept an honest interim plan; they rarely forgive a capability claim that collapses after launch. Delay the submission rather than alter the story.