VIPSolutionsIf MTBF is 2 0 0 hours and MTTR is 5 hours, what is the availability?, explain in very detail
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If MTBF is 2 0 0 hours and MTTR is 5 hours, what is the availability?, explain in very detail
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Asked by: manish kumar
Created at: 2026-01-15 12:11:14
Asked by: manish kumar
Created at: 2026-01-15 12:11:14
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# Availability Calculation: Detailed Explanation
Given:
- **MTBF (Mean Time Between Failures):** 200 hours
- **MTTR (Mean Time To Repair):** 5 hours
## 1. Key Concepts
### MTBF
- The **average time** a system operates **before it fails**.
- Includes **operating time** only, **not** repair time.
### MTTR
- The **average time** taken to **repair** the system and restore it to operation **after a failure**.
### Availability Formula
Availability quantifies the **proportion of time** a system is operational.
The standard formula is:
\[
\text{Availability (A)} = \frac{\text{MTBF}}{\text{MTBF} + \text{MTTR}}
\]
---
## 2. Step-by-Step Calculation
### Step 1: Substitute Values
\[
A = \frac{200}{200 + 5}
\]
### Step 2: Simplify Denominator
\[
A = \frac{200}{205}
\]
### Step 3: Calculate Decimal Value
\[
A = .9756
\]
### Step 4: Convert to Percentage
\[
A = .9756 \times 100 = 97.56\%
\]
---
## 3. Explanation of the Formula
- **Numerator (MTBF):** Total time the system works without failing.
- **Denominator (MTBF + MTTR):** **One complete cycle** of operation and repair — the time between one failure and the next, including both uptime and downtime.
- **The ratio** tells you the **percentage of time** the system is available for use.
---
## 4. Interpretation
- **Availability = 97.56%**
- This means, **on average**, the system will be up and running **97.56% of the time**.
- In **every 205 hours** (200 hours of operation + 5 hours of repair), the system is **down for 5 hours**.
---
## 5. Visual Representation
```plaintext
|<-------- 200h (uptime) -------->|<-- 5h (downtime) -->|
|========= Available =============|==== Not Available ==|
|<----------------- 205 hours total cycle ------------->|
```
---
## 6. Summary Table
| Parameter | Value |
|-----------|-------------|
| MTBF | 200 hours |
| MTTR | 5 hours |
| Availability | 97.56% |
---
## 7. Key Points
- Higher MTBF (less frequent failures) **increases** availability.
- Lower MTTR (faster repairs) **increases** availability.
- The closer Availability is to **100%**, the more reliable the system.
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