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Reliability

Reference data and engineering information about reliability for miscellaneous applications.

reliability

Overview

Engineering reference data for Reliability in miscellaneous.

Key Formulas

Unit Conversion

y=x⋅ky = x \cdot k

Multiply by conversion factor.

Linear Interpolation

y=y1+(x−x1)(y2−y1)x2−x1y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}

Estimate between two known points.

Percentage

p=partwhole×100%p = \frac{\text{part}}{\text{whole}} \times 100\%

Part as fraction of whole.

Variables

Symbol Description Unit
xx Input value —
yy Output value —
kk Conversion factor —

System Reliability Configurations

Reliability for systems can be evaluated based on the arrangement of their components.

Series Systems

In a series system, all components must function for the entire system to be operational. The overall system reliability is the product of the reliabilities of each individual component.

Rs=R1⋅R2⋅R3…RnR_s = R_1 \cdot R_2 \cdot R_3 \dots R_n

Where:

  • RsR_s is the reliability of the series system.
  • R1,R2,…,RnR_1, R_2, \dots, R_n are the reliabilities of the individual components.

Parallel Systems

In a parallel (redundant) system, the system functions if at least one component is operational. This configuration significantly increases overall reliability.

For a simple parallel system with two components, the reliability is:

Rs=R1⋅(1−R2)+R2⋅(1−R1)+R1⋅R2R_s = R_1 \cdot (1 - R_2) + R_2 \cdot (1 - R_1) + R_1 \cdot R_2

This can be generalized for nn parallel components as:

Rs=1−∏i=1n(1−Ri)R_s = 1 - \prod_{i=1}^{n} (1 - R_i)

Where:

  • RsR_s is the reliability of the parallel system.
  • RiR_i is the reliability of the iith component.

MTBF, MTTF, and MTTR Distinctions

While often used interchangeably in casual context, these metrics have specific applications:

  • MTBF (Mean Time Between Failures): Primarily used for repairable systems. It is the average time between successive failures.
  • MTTF (Mean Time To Failure): Primarily used for non-repairable items or components that are replaced upon failure. It is the average expected time to the first failure.
  • MTTR (Mean Time To Repair): Measures the average time required to repair a failed component and restore the system to operational status.

All three are key parameters in calculating system Availability, where:

Availability=MTBFMTBF+MTTR\text{Availability} = \frac{\text{MTBF}}{\text{MTBF} + \text{MTTR}}

References