# Six Sigma Quality API
> Six Sigma and quality-engineering maths as an API, computed locally and deterministically — the process-capability and defect maths behind a quality programme. The capability endpoint takes a process mean, standard deviation and the upper and/or lower specification limits and returns Cp = (USL−LSL)/6σ and Cpk = min((USL−μ)/3σ, (μ−LSL)/3σ) together with Cpu, Cpl and the expected DPMO and yield from the normal tails — a centred Cpk of 1.33 is the classic capable-process target. The dpmo endpoint turns defects, units and opportunities (or a yield) into defects per million opportunities, the yield and the process sigma level using the conventional 1.5σ long-term shift — the famous six-sigma 3.4 DPMO, and 3000 DPMO landing at about 4.25 sigma. The yield endpoint rolls per-step yields into the rolled throughput yield Π(yieldᵢ) — the chance a unit passes every step defect-free — with the normalized yield and the total defects per unit, and can start from DPU instead. The normal tails come from an accurate erfc and the sigma level from an exact inverse-normal. Everything is computed locally and deterministically, so it is instant and private. Ideal for quality-engineering, manufacturing, Lean Six Sigma and process-improvement app developers, SPC and capability-study tools, and green/black-belt training. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 compute endpoints. This is the capability and DPMO maths; for general descriptive statistics use a statistics API.

## Authentication
All requests require your oanor API key in the `x-oanor-key` header. Get one at https://www.oanor.com/developer/keys.

```bash
curl -H "x-oanor-key: oanor_live_…" "https://api.oanor.com/sixsigma-api/..."
```

## Pricing
- **Free** (Free) — 3,550 calls/Mo, 2 req/s
- **Starter** ($6/Mo) — 39,500 calls/Mo, 6 req/s
- **Pro** ($16/Mo) — 192,000 calls/Mo, 15 req/s
- **Mega** ($49/Mo) — 1,090,000 calls/Mo, 40 req/s

## Endpoints

### SixSigma

#### `GET /v1/capability` — Process capability Cp/Cpk

**Parameters:**
- `mean` (query, required, string) — Process mean μ Example: `6`
- `sigma` (query, required, string) — Standard deviation σ Example: `1`
- `usl` (query, optional, string) — Upper spec limit Example: `10`
- `lsl` (query, optional, string) — Lower spec limit Example: `2`

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/sixsigma-api/v1/capability?mean=6&sigma=1&usl=10&lsl=2"
```

**Response:**
```json
{
    "data": {
        "cp": 1.3333,
        "cpk": 1.3333,
        "cpl": 1.3333,
        "cpu": 1.3333,
        "note": "Cp = (USL−LSL)/6σ; Cpk = min((USL−μ)/3σ, (μ−LSL)/3σ). A centred Cpk of 1.33 is the classic capable-process target. DPMO uses the normal tails; sigma level adds the 1.5σ shift.",
        "inputs": {
            "lsl": 2,
            "usl": 10,
            "mean": 6,
            "sigma": 1
        },
        "expected_dpmo": 63.342,
        "expected_yield": 0.999936658,
        "process_sigma_level": 5.3328
    },
    "meta": {
        "timestamp": "2026-06-05T21:48:48.860Z",
        "request_id": "483f95da-6e41-451c-9fc1-2f3669e6fe78"
    },
    "status": "ok",
    "message": "Process capability",
    "success": true
}
```

#### `GET /v1/dpmo` — DPMO & sigma level

**Parameters:**
- `defects` (query, optional, string) — Defect count Example: `3`
- `units` (query, optional, string) — Units inspected Example: `1000`
- `opportunities` (query, optional, string) — Opportunities/unit (default 1) Example: `1`
- `yield` (query, optional, string) — Yield (% or 0–1) instead
- `dpmo` (query, optional, string) — DPMO directly instead
- `shift` (query, optional, string) — Sigma shift (default 1.5)

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/sixsigma-api/v1/dpmo?defects=3&units=1000&opportunities=1"
```

**Response:**
```json
{
    "data": {
        "dpmo": 3000,
        "note": "DPMO = defects/(units·opportunities)·1e6. Sigma level = Φ⁻¹(yield) + shift (1.5σ by convention) — 6σ ≈ 3.4 DPMO, 3000 DPMO ≈ 4.25σ.",
        "inputs": {
            "shift": 1.5,
            "units": 1000,
            "defects": 3,
            "opportunities": 1
        },
        "sigma_level": 4.2478,
        "yield_percent": 99.7,
        "defects_per_opportunity": 0.003
    },
    "meta": {
        "timestamp": "2026-06-05T21:48:48.967Z",
        "request_id": "1c6f3b83-919e-483b-8ff9-b0677d7e2cab"
    },
    "status": "ok",
    "message": "DPMO and sigma level",
    "success": true
}
```

#### `GET /v1/yield` — Rolled throughput yield

**Parameters:**
- `yields` (query, optional, string) — Comma list of step yields Example: `0.99,0.98,0.97`
- `dpu` (query, optional, string) — Comma list of DPU instead

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/sixsigma-api/v1/yield?yields=0.99%2C0.98%2C0.97"
```

**Response:**
```json
{
    "data": {
        "note": "RTY = Π(step yields) — the chance a unit passes every step defect-free. Normalized yield = RTY^(1/n); total DPU = −ln(RTY).",
        "inputs": {
            "steps": 3,
            "yields": [
                0.99,
                0.98,
                0.97
            ]
        },
        "total_dpu": 0.060712,
        "normalized_yield": 0.979965985,
        "rolled_throughput_yield": 0.941094,
        "rolled_throughput_yield_percent": 94.1094
    },
    "meta": {
        "timestamp": "2026-06-05T21:48:49.062Z",
        "request_id": "4a6d85ec-b4f7-4438-a25a-b8c388f611b1"
    },
    "status": "ok",
    "message": "Rolled throughput yield",
    "success": true
}
```

### Meta

#### `GET /v1/meta` — Spec

**Example:**
```bash
curl -H "x-oanor-key: $KEY" \
  "https://api.oanor.com/sixsigma-api/v1/meta"
```

**Response:**
```json
{
    "data": {
        "notes": "Sigma level uses the conventional 1.5σ long-term shift (override with 'shift'). Capability DPMO is the long-term normal tail without the shift. For general statistics use a statistics API.",
        "service": "sixsigma-api",
        "endpoints": {
            "GET /v1/dpmo": "DPMO, yield and sigma level from defects/units/opportunities or a yield.",
            "GET /v1/meta": "This document.",
            "GET /v1/yield": "Rolled throughput yield, normalized yield and total DPU from step yields or DPU.",
            "GET /v1/capability": "Cp, Cpk, Cpu, Cpl and expected DPMO/yield from mean, sigma and spec limits."
        },
        "description": "Six Sigma quality maths: process capability (Cp, Cpk, Pp, Ppk), DPMO & sigma level, and rolled throughput yield."
    },
    "meta": {
        "timestamp": "2026-06-05T21:48:49.163Z",
        "request_id": "9291c475-f771-4ff9-aad2-7636f64b1feb"
    },
    "status": "ok",
    "message": "Meta",
    "success": true
}
```


---
Marketplace page: https://www.oanor.com/api/sixsigma-api
OpenAPI spec: https://www.oanor.com/api/sixsigma-api/openapi.json