# Shop-floor formulas

> Standard shop-floor formulas, each with a worked example and a calculator: takt time, first pass yield, DPMO, Cp and Cpk, MTBF, MTTR and TEEP.

Source: https://deda.systems/handbook/shop-floor-formulas
Last updated: 2026-11-13

The calculations a production head, a quality engineer and a maintenance in-charge reach for most often. **Each one has the formula in full, an example you can check by hand, and a calculator.** For OEE itself, see the [OEE calculator and guide](https://deda.systems/handbook/oee-calculator).

## Takt time

Takt time is the pace at which you must finish one unit to meet customer demand. It is set by the customer, not by the machine. *Takt* is a German word for a precise interval of time, like the beat in music.

    Takt time = Available production time ÷ Customer demand

**Example.** A line has 450 minutes of available time in a shift and the customer needs 300 units per shift. Takt time = 450 ÷ 300 = 1.50 minutes per unit, or 90 seconds per unit.

**Takt time, cycle time and lead time are three different things.** Takt time is the target pace that demand requires. Cycle time is how long one part or one operation actually takes, measured on the floor. Production lead time is how long a product takes to move through the whole process from start to finish, including the time it spends waiting. If cycle time is longer than takt time, the line cannot meet demand without overtime.

*Takt time calculator: an interactive calculator on the web page. Inputs: Available production time per shift (minutes) (example 450); Units the customer needs per shift (example 300). Outputs: Takt time, In minutes.*

## First pass yield and rolled throughput yield

First pass yield (FPY) is the share of units that go through a process step correctly the first time, with no scrap and no rework. Rolled throughput yield (RTY) is the chance that a unit passes every step in a row without a defect.

    FPY = (Units entering − Defective units) ÷ Units entering
    RTY = FPY of step 1 × FPY of step 2 × … × FPY of the last step

**Example.** 500 parts enter an operation and 35 are scrapped or reworked. FPY = (500 − 35) ÷ 500 = 93.0%. A part then passes through four operations with first pass yields of 98%, 95%, 99% and 97%. RTY = 0.98 × 0.95 × 0.99 × 0.97 = 89.4%.

RTY can never be higher than the weakest step, and is usually lower. A plant whose final inspection passes 99% of parts can still have a low RTY if rework is happening quietly at every stage.

*Yield calculator: an interactive calculator on the web page. Inputs: Units entering the step (example 500); Units scrapped or reworked (example 35); FPY of each step in %, separated by commas (example 98, 95, 99, 97). Outputs: First pass yield, Rolled throughput yield.*

## DPMO (Defects per million opportunities)

DPMO lets you compare the defect rate of a simple part with that of a complex one, by counting how many chances for a defect each unit has.

    DPMO = Defects ÷ (Units × Opportunities per unit) × 1,000,000

**Example.** An inspector finds 18 defects in 1200 assemblies. Each assembly has 5 characteristics that are checked. DPMO = 18 ÷ (1200 × 5) × 1,000,000 = 3000.

**A caveat on “six sigma = 3.4 DPMO”.** The 3.4 figure assumes the process mean drifts by 1.5 standard deviations over the long term. That shift is a convention from the Six Sigma method, not a law of statistics. Without it, limits at six standard deviations correspond to about 0.002 defects per million.

*DPMO calculator: an interactive calculator on the web page. Inputs: Defects found (example 18); Units inspected (example 1200); Defect opportunities per unit (example 5). Outputs: DPMO.*

## Process capability: Cp and Cpk

Cp compares the width of the tolerance with the natural spread of the process. Cpk does the same but also accounts for how far the process is off-centre, so Cpk is never larger than Cp.

    Cp = (USL − LSL) ÷ 6σ
    Cpk = the smaller of (USL − mean) ÷ 3σ and (mean − LSL) ÷ 3σ
    USL and LSL are the upper and lower specification limits. σ is the process standard deviation.

**Example.** A shaft diameter is specified as 25.00 ± 0.05 mm, so USL = 25.05 and LSL = 24.95. A study gives a mean of 25.01 mm and a standard deviation of 0.012 mm. Cp = 0.10 ÷ (6 × 0.012) = 1.39. Cpk = the smaller of 1.11 and 1.67 = 1.11.

**What number is required?** That is set by your customer. A Cpk of at least 1.33 is a very common requirement, and 1.67 is commonly asked for on critical characteristics. The automotive PPAP manual published by AIAG uses 1.33 and 1.67 as the bands for judging initial process studies. Always check the customer-specific requirement.

**Two conditions.** Capability indices only mean something when the process is stable (in statistical control) and the data are roughly normally distributed. Pp and Ppk use the same formulas with the overall standard deviation of all the data, while Cp and Cpk use the short-term variation within subgroups.

*Cp and Cpk calculator: an interactive calculator on the web page. Inputs: Upper specification limit (USL) (example 25.05); Lower specification limit (LSL) (example 24.95); Process mean (example 25.01); Standard deviation (example 0.012). Outputs: Cp, Cpk, Upper side, Lower side.*

## MTBF, MTTR and availability

MTBF (mean time between failures) says how long a machine runs between breakdowns. MTTR (mean time to repair) says how long a breakdown takes to fix. Together they give the machine’s inherent availability.

    MTBF = Total operating time ÷ Number of failures
    MTTR = Total repair time ÷ Number of repairs
    Inherent availability = MTBF ÷ (MTBF + MTTR)

**Example.** In a month a press runs for 400 hours and breaks down 5 times. The repairs take 10 hours in total. MTBF = 400 ÷ 5 = 80.0 hours. MTTR = 10 ÷ 5 = 2.00 hours. Inherent availability = 97.6%.

**This is not the availability in OEE.** Inherent availability counts only breakdowns and repairs. OEE availability also counts changeovers and waiting for material. MTBF is also not a prediction of machine life: it describes failures during normal operation. For parts that are replaced and not repaired, the equivalent measure is MTTF (mean time to failure).

*MTBF and MTTR calculator: an interactive calculator on the web page. Inputs: Total operating time (hours) (example 400); Number of failures (example 5); Total repair time (hours) (example 10). Outputs: MTBF, MTTR, Inherent availability.*

## TEEP (Total effective equipment performance)

TEEP measures a machine against every minute of the calendar, where OEE measures it only against the time it was planned to run. It shows how much capacity is still unused before you invest in another machine.

    Utilisation = Planned production time ÷ All calendar time
    TEEP = OEE × Utilisation

**Example.** A machine runs one shift with 420 minutes of planned production time in a 1440-minute day, at 76.4% OEE. Utilisation = 420 ÷ 1440 = 29.2%. TEEP = 76.4% × 29.2% = 22.3%.

*TEEP calculator: an interactive calculator on the web page. Inputs: OEE (%) (example 76.4); Planned production time per day (minutes) (example 420); Calendar time per day (minutes) (example 1440). Outputs: Utilisation, TEEP.*

## All the formulas in one table

| Measure | Formula | Answers the question |
| --- | --- | --- |
| OEE | Availability × Performance × Quality | How much of planned time made good parts at full speed? |
| Availability (OEE) | Run time ÷ Planned production time | How much of planned time was the machine running? |
| Performance (OEE) | (Ideal cycle time × Total count) ÷ Run time | Was it running at full speed? |
| Quality (OEE) | Good count ÷ Total count | Were the parts right the first time? |
| TEEP | OEE × (Planned production time ÷ Calendar time) | How much total capacity is used? |
| Takt time | Available production time ÷ Customer demand | How fast must we finish each unit? |
| First pass yield | (Units in − Defective units) ÷ Units in | How many were right with no rework? |
| Rolled throughput yield | Product of the FPY of every step | What is the chance of passing every step cleanly? |
| DPMO | Defects ÷ (Units × Opportunities) × 1,000,000 | How does the defect rate compare across products? |
| Cp | (USL − LSL) ÷ 6σ | Is the process spread narrow enough for the tolerance? |
| Cpk | min[(USL − mean) ÷ 3σ, (mean − LSL) ÷ 3σ] | Is it narrow enough and centred? |
| MTBF | Operating time ÷ Number of failures | How long between breakdowns? |
| MTTR | Repair time ÷ Number of repairs | How long does a breakdown take to fix? |
| Inherent availability | MTBF ÷ (MTBF + MTTR) | What uptime do breakdowns alone allow? |

## Where this comes from

> The formulas and definitions on this page are the standard published ones. These are the references we checked them against. If you find an error, write to [deep@deda.systems](mailto:deep@deda.systems) and we will correct it.

- [Lean Enterprise Institute, Lean Lexicon: takt time](https://www.lean.org/lexicon-terms/takt-time/) and [cycle time](https://www.lean.org/lexicon-terms/cycle-time/).
- [ASQ Quality Glossary](https://asq.org/quality-resources/quality-glossary). First pass yield and related quality terms.
- [NIST/SEMATECH e-Handbook of Statistical Methods, section 6.1.6](https://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm). Process capability indices Cp and Cpk.
- AIAG, *Production Part Approval Process (PPAP)*, 4th edition. Acceptance bands for initial process studies.
- Seiichi Nakajima, *Introduction to TPM: Total Productive Maintenance*, Productivity Press, 1988. OEE and its factors.

## Frequently asked questions

### How do you calculate takt time?

Divide the available production time by customer demand for the same period. With 450 minutes available and a demand of 300 units, takt time is 1.5 minutes, or 90 seconds, per unit.

### What is the difference between takt time and cycle time?

Takt time is the pace customer demand requires. Cycle time is the time an operation actually takes, measured on the floor. When cycle time is longer than takt time, the process cannot meet demand in the available time.

### What is the difference between Cp and Cpk?

Cp compares the tolerance width with the process spread and ignores where the process is centred. Cpk also accounts for centring, by taking the distance from the mean to the nearer specification limit. Cpk equals Cp only when the process is exactly centred.

### What Cpk value is acceptable?

Your customer sets the requirement. A minimum Cpk of 1.33 is common, with 1.67 often required for critical characteristics. The AIAG PPAP manual uses 1.33 and 1.67 as the bands for judging initial process studies.

### Is MTBF the same as machine life?

No. MTBF is operating time divided by the number of failures for equipment that is repaired and returned to service. It describes how often failures occur, not how long the machine will last.

### What is the difference between FPY and RTY?

First pass yield measures one process step. Rolled throughput yield multiplies the first pass yields of every step, giving the probability that a unit passes the entire process with no defect and no rework.