This is a ready-to-use worksheet for calculating process capability indices. Replace every <<FILL: ...>> placeholder with your own values, and do not skip the prerequisite checks in section 1; a capability index calculated on data that fails them is a number without a defensible meaning. A worked filled specimen follows the template. Confirm the statistical approach with a qualified statistician for your data, and see statistics in quality: Cpk and control charts for the reasoning behind each step.
Worksheet header
| Field | Entry |
|---|---|
| Worksheet number | <<FILL: WS-ID>> |
| Product / characteristic | <<FILL: product, characteristic, units>> |
| Specification limits (LSL / USL) | <<FILL>> |
| Target (if defined) | <<FILL: or "center of spec">> |
| Data set used | <<FILL: batch IDs or date range, number of subgroups, subgroup size>> |
| Prepared by / date | <<FILL>> |
| Reviewed by (statistician / QA) / date | <<FILL>> |
1. Prerequisite checks (complete before calculating anything)
| Check | Method | Result | Action if failed |
|---|---|---|---|
| Statistical control confirmed | <<FILL: reference the control chart and period reviewed>> | <<FILL: in control / not in control>> | If not in control, stop. Capability has no defensible meaning until the process is stable; resolve the special cause and re-chart first. |
| Normality checked | <<FILL: e.g. Anderson-Darling or Shapiro-Wilk, plus a probability plot>> | <<FILL: pass/fail, statistic/p-value>> | If failed, go to section 4 (non-normal data) before proceeding to section 2. |
| Measurement system adequacy (Gauge R&R) | <<FILL: % of tolerance or % contribution consumed by the measurement system>> | <<FILL>> | If the measurement system consumes more than roughly 10 percent of tolerance, resolve or account for it before trusting the index; sigma is partly the gauge, not the process. |
| Data set size | <<FILL: number of subgroups or individual values>> | Established (commonly 25+ subgroups) / Provisional (fewer) | If provisional, complete section 5 (short-run and low-volume) and label every reported index accordingly. |
| Data spans the real sources of variation | <<FILL: shifts, operators, lots, raw material sources represented? Yes/No>> | <<FILL>> | A data set confined to one shift or one operator understates real variation; broaden the sampling window before relying on the result. |
2. Inputs
| Input | Value |
|---|---|
| Lower specification limit (LSL) | <<FILL>> |
| Upper specification limit (USL) | <<FILL>> |
| Number of subgroups (k) | <<FILL>> |
| Subgroup size (n) | <<FILL: 1 for I-MR, 2+ for X-bar/R or X-bar/S>> |
| Overall mean (mu, grand average of all individual values) | <<FILL>> |
| Within-subgroup sigma (short-term; from R-bar/d2 or pooled subgroup standard deviation, or MR-bar/1.128 for individuals) | <<FILL: value and method>> |
| Overall sigma (long-term; standard deviation of all individual values) | <<FILL>> |
3. Calculate the indices
Show the arithmetic, not just the result.
3a. Cp (potential capability, within-subgroup sigma)
Cp = (USL - LSL) / (6 x within-subgroup sigma)
Calculation: <<FILL: substitute values>> = <<FILL: result>>
3b. Cpk (actual capability, within-subgroup sigma)
Cpk = min[ (USL - mu) / (3 x within-subgroup sigma), (mu - LSL) / (3 x within-subgroup sigma) ]
Calculation: <<FILL: substitute values, show both halves>> = <<FILL: result>>
Which side governs (upper or lower)? <<FILL>> (this tells you which direction to move the mean if you want to improve Cpk by recentering rather than by reducing spread)
3c. Pp (potential performance, overall sigma)
Pp = (USL - LSL) / (6 x overall sigma)
Calculation: <<FILL>> = <<FILL: result>>
3d. Ppk (actual performance, overall sigma)
Ppk = min[ (USL - mu) / (3 x overall sigma), (mu - LSL) / (3 x overall sigma) ]
Calculation: <<FILL>> = <<FILL: result>>
3e. One-sided characteristics
If only one specification limit applies (for example an upper limit on an impurity or a microbial count), compute only the relevant half of the Cpk/Ppk formula (commonly written Cpu/Ppu or Cpl/Ppl) and record Cp/Pp as not applicable, since there is no two-sided window to compare.
| Field | Entry |
|---|---|
| One-sided characteristic? | <<FILL: Yes/No>> |
| Relevant limit and index used | <<FILL: e.g. Cpu, upper limit only>> |
| Result | <<FILL>> |
4. Non-normal data path (complete only if section 1’s normality check failed)
| Step | Entry |
|---|---|
| Transformation attempted | <<FILL: none / log / Box-Cox, lambda = ...>> |
| Normality of transformed data | <<FILL: pass/fail>> |
| If transformation did not achieve normality, distribution fitted instead | <<FILL: e.g. Weibull, lognormal>> |
| Goodness-of-fit result for the fitted distribution | <<FILL>> |
| 0.135 and 99.865 percentiles read from the fitted curve | <<FILL: values>> |
| Percentile-based index calculated using those percentiles in place of the +/- 3 sigma points | <<FILL: result>> |
5. Short-run and low-volume path (complete only if the data set is provisional)
| Step | Entry |
|---|---|
| Batch or subgroup count actually available | <<FILL>> |
| Minimum your procedure calls established | <<FILL: e.g. 25>> |
| Index reported as provisional and labeled as such everywhere it is used | <<FILL: Yes, confirmed>> |
| Pooling across similar characteristics considered? | <<FILL: Yes/No, and the rationale for why the pooled characteristics share a variation mechanism, or why pooling was rejected>> |
| Cpm calculated (if hitting target matters as much as staying inside limits) | <<FILL: Cpm = (USL-LSL) / (6 x sqrt(sigma^2 + (mu-target)^2)); result>> |
| Re-baseline trigger (when this provisional index will be replaced with an established one) | <<FILL: e.g. at N additional batches>> |
6. Interpretation
| Question | Answer |
|---|---|
| Does Cpk meet the internal or contractual minimum (commonly 1.33)? | <<FILL: Yes/No>> |
| Gap between Cp and Cpk (centering problem)? | <<FILL: value; large gap means recentering would help>> |
| Gap between Cpk and Ppk (between-subgroup drift)? | <<FILL: value; large gap means the process wanders between subgroups even though each subgroup is tight>> |
| Recommended action | <<FILL: recenter, reduce variation, investigate between-subgroup source, accept and monitor, escalate>> |
7. Acceptance criteria
This worksheet is complete and its result defensible when all of the following are true:
- Statistical control was confirmed with a control chart before capability was calculated.
- Normality was checked, and a transformation or a fitted-distribution method was used and documented if the check failed.
- The measurement system’s contribution to observed variation was assessed and is not confounding the result.
- The data set size is stated, and any index below the established minimum is labeled provisional.
- Both the within-subgroup pair (Cp, Cpk) and the overall pair (Pp, Ppk) are calculated and compared, not just one flattering number.
- The arithmetic is shown, not just the final index.
References
ASQ / ANSI Z1.9 background statistics for process capability concepts. ISO 22514-2, Statistical methods in process management, Capability and performance, Part 2: Process capability and performance of time-dependent process models (replaced the withdrawn ISO 21747:2006). FDA, Process Validation: General Principles and Practices (2011), Stage 2/3 capability expectations. See statistics in quality: Cpk and control charts for the underlying reasoning, the Box-Cox and percentile-based non-normal methods, and the Cpm short-run alternative.
Confirm the current version of each reference before issue, and confirm the statistical method with a qualified statistician for your specific data.
Filled specimen
A fill operation, target 10.00 mL, LSL 9.80 mL, USL 10.20 mL, 25 subgroups of 5 vials each.
Section 1, prerequisites: Control chart (X-bar/R) reviewed for the 25-subgroup period, no special-cause signals, confirmed in control. Anderson-Darling normality test on the pooled individual values, p = 0.41, fails to reject normality. Gauge R&R on the fill-volume balance, measurement system consumes 6 percent of tolerance, acceptable. Data set is 25 subgroups (established). Subgroups span two shifts and three raw-material lots of stopper components.
Section 2, inputs: LSL 9.80 mL, USL 10.20 mL, k = 25, n = 5, overall mean 10.04 mL, within-subgroup sigma 0.040 mL (from R-bar/d2), overall sigma 0.060 mL.
Section 3, calculations:
- Cp = (10.20 - 9.80) / (6 x 0.040) = 0.40 / 0.24 = 1.67
- Cpk = min[ (10.20 - 10.04)/(3 x 0.040), (10.04 - 9.80)/(3 x 0.040) ] = min[1.33, 2.00] = 1.33 (upper side governs)
- Pp = (10.20 - 9.80) / (6 x 0.060) = 0.40 / 0.36 = 1.11
- Ppk = min[ (10.20 - 10.04)/(3 x 0.060), (10.04 - 9.80)/(3 x 0.060) ] = min[0.89, 1.33] = 0.89 (upper side governs)
Section 6, interpretation: Cp minus Cpk gap of 0.34 shows real centering cost; the fill is running high relative to target and recentering the setpoint toward 10.00 mL would raise Cpk without touching the process spread. The Cpk-to-Ppk gap of 0.44 is larger still and points to between-subgroup drift, consistent with the two-shift, three-lot span of the data; the action is to investigate whether shift or raw-material lot explains the wandering mean before trusting the short-term Cpk as representative of ongoing performance. Recommended action: recenter the setpoint and open a trend investigation into shift-to-shift and lot-to-lot variation, then re-run this worksheet after the change to confirm both Cpk and Ppk improved.
Common inspection findings this worksheet prevents
- A Cpk reported with no evidence the process was in control when the data was collected.
- Capability calculated on visibly skewed data with no normality check, transformation, or distribution fit.
- Only Cpk reported, with no Ppk, on a process that is actually drifting between subgroups.
- A capability claim with no visible arithmetic, so nobody can verify the number against the underlying data.
- A Cpk from four or five batches presented as an established capability with no provisional label.
How to adapt this worksheet
- Set the worksheet number, characteristic, and specification limits in the header.
- Do not skip section 1. A capability number calculated before confirming control, normality, and measurement-system adequacy is the single most common finding in this area.
- If the chart type is not I-MR or X-bar/R, substitute the correct within-subgroup sigma estimator for your chart type and state it.
- For a low-frequency product, complete section 5 in full rather than forcing a 25-subgroup study that will not exist for years.
- Attach this worksheet to the capability study protocol, the CPV monitoring plan, or the PPQ report it supports.
- Confirm every reference against the current published version before issue.