Enter your specification limits and the process mean and standard deviation to compute Cp, Cpk (and Pp/Ppk), the estimated sigma level, and the expected parts-per-million defective. The distribution is shown against the spec limits so you can see centering and spread at a glance.
Process capability indices measure whether a process's natural variation fits within the engineering specification limits. Cp and Cpk describe potential and actual capability; Pp and Ppk are their long-term performance counterparts. This calculator computes all four (using the σ you provide), plus Cpu, Cpl, the sigma level, and the estimated parts-per-million defective from a normal model — and draws the distribution against your spec limits so you can see centering and spread at a glance.
Cp = (USL − LSL) / 6σ compares the width of the specification (the tolerance) to the natural spread of the process (±3σ). It tells you whether the process is precise enough — but it assumes the process is perfectly centered, so a high Cp with the mean off to one side can still produce lots of defects.
Cpk fixes that by accounting for where the mean actually sits. It is the smaller of Cpu = (USL − μ)/3σ and Cpl = (μ − LSL)/3σ — the distance from the mean to the nearest spec limit, in units of 3σ. Cpk ≤ Cp always; they are equal only when the process is exactly centered. A large gap between Cp and Cpk signals an off-center process that you can improve simply by re-centering the mean.
Cp and Cpk traditionally use the short-term (within-subgroup) standard deviation, often estimated from control-chart ranges as R-bar/d2. They describe the capability the process could achieve when it is stable and in control — its potential. Pp and Ppk use the overall (long-term) standard deviation computed from all the individual data points, which also captures drift, shift, and between-subgroup variation. They describe how the process actually performed over time.
Because this tool takes a single σ value, it reports Cp/Cpk and Pp/Ppk as identical. In real analysis you would feed the within-subgroup σ for Cp/Cpk and the overall σ for Pp/Ppk; a Ppk noticeably lower than Cpk means the process is not stable — special causes are inflating the long-term spread.
Common acceptance thresholds: Cpk ≥ 1.00 means the ±3σ spread just fits inside the spec (about 2,700 ppm defective if centered) — generally not acceptable. Cpk ≥ 1.33 (a 4σ process) is the traditional minimum for an established process. Cpk ≥ 1.67 (5σ) is expected for critical or safety characteristics. Cpk ≥ 2.00 corresponds to the classic Six Sigma goal. This calculator color-codes Cpk red below 1.00, amber from 1.00 to 1.33, and green at 1.33 and above.
The sigma level reported here is the short-term Z to the nearest spec limit, equal to 3 × Cpk — it is the number of standard deviations between the mean and the closest limit. The estimated ppm defective comes from a normal distribution: the area in the tails beyond each spec limit, converted to parts per million. Note the famous Six Sigma figure of 3.4 ppm assumes a 1.5σ long-term mean shift; a truly centered 6σ process has only about 0.002 ppm. This tool uses the σ and mean you enter with no shift applied, so its ppm reflects exactly the distribution you specify. Real ppm also depends on the data actually being normal — heavy tails or skew can make the normal estimate optimistic.
Cp measures only whether the process spread fits within the tolerance, assuming the process is perfectly centered: Cp = (USL − LSL)/6σ. Cpk also accounts for how far off-center the mean is, taking the minimum of (USL − μ)/3σ and (μ − LSL)/3σ. Cpk is always less than or equal to Cp; they are equal only when the process is centered between the limits.
Cpk ≥ 1.33 is the common minimum for an established process (a 4σ process). Critical or safety-related characteristics usually require Cpk ≥ 1.67, and the Six Sigma goal is Cpk ≥ 2.00. A Cpk below 1.00 means the process spread does not fit inside the spec limits and will produce significant scrap.
The formulas are identical, but the standard deviation differs. Cp/Cpk use the short-term within-subgroup sigma (the process potential when stable). Pp/Ppk use the overall long-term sigma computed from all the data, capturing drift and shifts (actual performance). If Ppk is much lower than Cpk, the process is not in statistical control. With a single sigma value, the two pairs are equal.
Assuming the measurements follow a normal distribution, the tool computes the probability of falling above the USL and below the LSL using the standard normal CDF (via an erf approximation), adds those two tail areas, and multiplies by 1,000,000. This is the expected long-run defect rate for the mean and sigma you entered, with no 1.5σ shift.
A perfectly centered six-sigma process has only about 0.002 ppm defective. The 3.4 ppm figure builds in a 1.5σ long-term shift in the mean, reflecting the empirical observation that real process means drift over time. So 3.4 ppm is the conservative, real-world expectation for a 6σ short-term capability. This calculator does not apply that shift — it uses exactly the mean and sigma you provide.
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