Quality Control

Quality control calculators and formulas for process capability and equipment effectiveness. Includes Cp, Cpk, and overall equipment effectiveness (OEE) calculations.

12Formulas

All levels Difficulty

Updated Jul 2026

← All Industrial Engineering (30) Quality Control (12)

Fundamental

Failure Rate

λ = 1 / MTBF

Fundamental

System Availability (Reliability Engineering)

Availability (%) = (MTBF / (MTBF + MTTR)) * 100

Fundamental

Mean Time To Repair (MTTR)

MTTR = Total Repair Time / Number of Repairs

Fundamental

Mean Time Between Failures (MTBF)

MTBF = Total Operating Time / Number of Failures

Fundamental

Rolled Throughput Yield

RTY = Y1 * Y2 * Y3 * ... * Yn

Fundamental

First Pass Yield

FPY (%) = (Units Passing Without Rework / Total Units Started) * 100

Fundamental

Process Capability Index (Cpk, Accounting for Centering)

Cpk = min[(USL - μ)/(3σ), (μ - LSL)/(3σ)]

Fundamental

X-bar Control Chart Limits

UCL/LCL = X̄̄ ± A2 * R̄

Fundamental

Defects Per Million Opportunities (DPMO)

DPMO = (Number of Defects / (Units * Opportunities per Unit)) * 1,000,000

Fundamental

Six Sigma Process Sigma Level

Sigma Level ≈ 0.8406 + sqrt(29.37 - 2.221*ln(DPMO))

Fundamental

Overall Equipment Effectiveness

OEE = Availability × Performance × Quality

Fundamental

Process Capability Index

C_p = (USL − LSL) / (6σ)