Mining Economics

Reliability of Systems

Series and parallel reliability — why a chain is only as strong as its weakest link, and why redundancy multiplies dependability.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Mine equipment forms reliability networks. In a series arrangement every component must work for the system to function, so reliabilities multiply — the system is always less reliable than its weakest part. In a parallel (redundant) arrangement the system fails only if *all* paths fail, so we multiply the failure probabilities and subtract from one — redundancy dramatically raises dependability.

The Core Formula Matrix

Series system:

R_{s} = R_{1} \times R_{2} \times \dots \times R_{n} = \prod R_{i}

Parallel (redundant) system:

R_{p} = 1 - \prod (1 - R_{i})

R_{i}

= reliability of component

i

(probability it works).

The ‘IIT Traps’

⚠
Series multiplies reliabilities, not failure rates. $R_{s} = \prod R_{i}$ ; adding them is wrong and can exceed 1.
⚠
**Parallel multiplies the *failures* $(1 - R_{i})$ .** Multiplying the reliabilities themselves gives a lower (incorrect) answer.
⚠
Decompose mixed systems block by block. Reduce each parallel sub-block first, then combine in series.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

Two components, each of reliability

0.9

, are connected in series. The system reliability is:

Q2MEDIUM2 Marks · NAT

The same two components (

R = 0.9

each) are connected in parallel. The system reliability is ______. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

Two components of reliability

0.8

each are in parallel, and that block is in series with a third component of reliability

0.9

. The overall system reliability is ______. (Round off to three decimal places.)