Shop-floor formulas

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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%.

• Lean Enterprise Institute, Lean Lexicon: takt time and cycle time.
• ASQ Quality Glossary. First pass yield and related quality terms.
• NIST/SEMATECH e-Handbook of Statistical Methods, section 6.1.6. 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.