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RAID Reliability

The Mathematics of Not Losing Data

RAID's primary purpose is to protect data against disk failures. But how well does it actually protect? When we say "RAID 5 can survive one disk failure," what does that really mean in terms of probability? How much more reliable is RAID 6 than RAID 5? These questions require rigorous mathematical analysis.

Reliability analysis is not academic exercise—it drives real decisions worth millions of dollars. Data centers choose RAID levels based on calculated failure probabilities. The rise of multi-terabyte drives has fundamentally changed the reliability calculus, making configurations that were once safe now dangerously inadequate.

What You Will Learn

By the end of this page, you will understand how to calculate Mean Time To Data Loss (MTTDL) for various RAID configurations, the critical role of rebuild time in array reliability, why large-capacity drives disproportionately increase risk, how to compare reliability across RAID levels quantitatively, and the practical factors that complicate theoretical reliability models.

Reliability Fundamentals

Before calculating RAID reliability, we need to establish fundamental reliability concepts:

Mean Time Between Failures (MTBF)

MTBF represents the average time between failures for a device running continuously. For a disk with MTBF of 1,000,000 hours, the failure rate λ (lambda) is:

$$\lambda = \frac{1}{MTBF} = \frac{1}{1,000,000} = 10^{-6} \text{ failures/hour}$$

The probability of a disk failing within time period t follows an exponential distribution:

$$P(failure\ within\ t) = 1 - e^{-\lambda t}$$

For small λt, this approximates to: $$P(failure\ within\ t) \approx \lambda t$$

Mean Time To Repair (MTTR)

MTTR is the average time to replace a failed disk and rebuild the array. This includes:

Detection time (monitoring notification)
Response time (human reaction, spare procurement)
Physical replacement time
Rebuild time (data reconstruction)

Typical MTTR values:

Enterprise with hot spares and monitoring: 4-8 hours
Enterprise without hot spares: 24-48 hours
Consumer/hobbyist: 48-168 hours (days to weeks)

Mean Time To Data Loss (MTTDL)

MTTDL is the average time until a RAID array experiences data loss due to disk failures. This is the key metric for comparing RAID reliability.

$$MTTDL = \frac{1}{\text{Rate of data-loss events}}$$

For RAID 0 (no redundancy): $$MTTDL_{RAID0} = \frac{MTBF}{n}$$

With n disks each having MTBF of 1,000,000 hours:

4-disk RAID 0: MTTDL = 250,000 hours ≈ 28.5 years
8-disk RAID 0: MTTDL = 125,000 hours ≈ 14.3 years

Availability

System availability is the fraction of time the system is operational:

$$Availability = \frac{MTTF}{MTTF + MTTR}$$

For very reliable systems, this is often expressed as "nines":

99% = "two nines" = 3.65 days downtime/year
99.9% = "three nines" = 8.76 hours downtime/year
99.99% = "four nines" = 52.6 minutes downtime/year
99.999% = "five nines" = 5.26 minutes downtime/year

MTBF Is Not Lifespan

A common misconception: MTBF of 1,000,000 hours doesn't mean the disk will last 114 years. MTBF describes the failure rate in a population of disks, assuming constant random failure rate. Real disks follow a 'bathtub curve' with higher failure rates early (infant mortality) and late (wear-out). Enterprise warranties (5 years) better reflect expected service life.

Mirror-Based RAID Reliability

RAID 1 (Two-Way Mirror) MTTDL:

In RAID 1, data loss occurs only if:

First disk fails (rate = 2λ, since either disk can fail first)
Second disk fails BEFORE the first is rebuilt

The probability of second failure during rebuild time T_rebuild: $$P(second\ failure) \approx \lambda \times T_{rebuild}$$

The MTTDL calculation: $$MTTDL_{RAID1} = \frac{(MTBF)^2}{2 \times MTTR}$$

Example Calculation:

MTBF = 1,000,000 hours per disk
MTTR = 24 hours (including rebuild)

$$MTTDL_{RAID1} = \frac{(1,000,000)^2}{2 \times 24} = \frac{10^{12}}{48} \approx 20.8 \times 10^9 \text{ hours}$$

This equals approximately 2.4 million years—effectively infinite for practical purposes.

RAID 10 MTTDL:

RAID 10 with n disks has n/2 mirror pairs. Data loss occurs when both disks in ANY mirror pair fail during the rebuild window.

For small failure probabilities, the MTTDL formula is: $$MTTDL_{RAID10} = \frac{(MTBF)^2}{(n-1) \times MTTR}$$

Note that (n-1) reflects that after one disk fails, there are n-1 remaining disks that could cause data loss (though only 1 of those n-1 would actually cause loss—this formula is an approximation that's accurate for small failure probabilities).

More precisely: $$MTTDL_{RAID10} = \frac{(MTBF)^2}{n \times MTTR} \times \frac{n-1}{n-1} = \frac{MTBF^2}{n \times MTTR}$$

Example: 8-disk RAID 10: $$MTTDL_{RAID10} = \frac{(10^6)^2}{8 \times 24} = \frac{10^{12}}{192} \approx 5.2 \times 10^9 \text{ hours}$$

This is approximately 600,000 years—still exceptionally reliable.

RAID 10 MTTDL vs. Array Size (MTBF=1M hours, MTTR=24 hours)
Disks	Mirror Pairs	MTTDL (hours)	MTTDL (years)
4	2	2.08 × 10¹⁰	2,377,000
8	4	5.21 × 10⁹	595,000
16	8	2.60 × 10⁹	297,000
32	16	1.30 × 10⁹	148,000
64	32	6.51 × 10⁸	74,000

Why RAID 10 Scales Well

Notice that even a 64-disk RAID 10 array maintains an MTTDL of 74,000 years. This is because data loss requires both disks in a SPECIFIC pair to fail during rebuild. Adding more pairs increases the probability of having A failure somewhere, but the critical failure (same pair) remains unlikely.

RAID 5 Reliability Analysis

RAID 5 reliability is critically dependent on rebuild time because data loss occurs if any second disk fails during rebuild, not just a specific partner disk.

RAID 5 MTTDL Formula:

$$MTTDL_{RAID5} = \frac{(MTBF)^2}{n \times (n-1) \times MTTR}$$

Compare this to RAID 1:

RAID 1: Denominator = 2 × MTTR
RAID 5 with 5 disks: Denominator = 5 × 4 × MTTR = 20 × MTTR

Example: 5-disk RAID 5: $$MTTDL_{RAID5} = \frac{(10^6)^2}{5 \times 4 \times 24} = \frac{10^{12}}{480} \approx 2.08 \times 10^9 \text{ hours}$$

This equals approximately 238,000 years—still impressive, but an order of magnitude less than RAID 1.

The Impact of Array Size:

Larger RAID 5 arrays have dramatically lower MTTDL:

$$MTTDL_{RAID5} \propto \frac{1}{n \times (n-1)}$$

For large n, this approximates n²:

Disks (n)	n × (n-1)	Relative MTTDL
3	6	100% (baseline)
5	20	30%
8	56	11%
10	90	7%
15	210	3%

A 15-disk RAID 5 array has only 3% the MTTDL of a 3-disk RAID 5 array. This is why RAID 5 recommendations cap array size at 5-8 disks.

RAID Reliability Calculator
Python
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def calculate_mttdl(
    raid_level: str,
    num_disks: int,
    mtbf_hours: float,
    mttr_hours: float
) -> dict:
    """
    Calculate Mean Time To Data Loss for various RAID levels.
    
    Args:
        raid_level: "0", "1", "5", "6", "10"
        num_disks: Total number of disks
        mtbf_hours: Mean Time Between Failures per disk (hours)
        mttr_hours: Mean Time To Repair including rebuild (hours)
    
    Returns:
        Dictionary with MTTDL and related metrics
    """
    if raid_level == "0":
        # Any failure = data loss
        mttdl = mtbf_hours / num_disks
        
    elif raid_level == "1":
        # Two-way mirror: both must fail during rebuild
        mttdl = (mtbf_hours ** 2) / (2 * mttr_hours)
        
    elif raid_level == "5":
        # n disks, any 2 failing during rebuild = loss
        n = num_disks
        mttdl = (mtbf_hours ** 2) / (n * (n - 1) * mttr_hours)
        
    elif raid_level == "6":
        # Need 3 failures during rebuild window(s) for data loss
        n = num_disks
        # Simplified formula for RAID 6
        mttdl = (mtbf_hours ** 3) / (n * (n - 1) * (n - 2) * mttr_hours ** 2)
        
    elif raid_level == "10":
        # n/2 mirror pairs, both in same pair must fail
        n = num_disks
        mttdl = (mtbf_hours ** 2) / (n * mttr_hours)
    
    else:
        raise ValueError(f"Unknown RAID level: {raid_level}")
    
    # Convert to years
    hours_per_year = 8760
    mttdl_years = mttdl / hours_per_year
    
    # Annual probability of data loss
    annual_failure_prob = hours_per_year / mttdl
    
    return {
        "raid_level": raid_level,
        "num_disks": num_disks,
        "mttdl_hours": mttdl,
        "mttdl_years": mttdl_years,
        "annual_failure_probability": annual_failure_prob,
        "nines_reliability": -1 * (1 if annual_failure_prob >= 1 else 
                                   0 - (1 - annual_failure_prob).__log10__() 
                                   if hasattr((1-annual_failure_prob), '__log10__') 
                                   else float('inf'))
    }
 
# Compare 8-disk arrays across RAID levels
# MTBF: 1,000,000 hours (typical enterprise disk)
# MTTR: 24 hours (with hot spare and monitoring)
 
print("Comparison of 8-disk arrays (MTBF=1M hours, MTTR=24 hours):\n")
print(f"{'RAID':^6} | {'MTTDL (years)':^15} | {'Annual Loss Prob':^16}")
print("-" * 45)
 
import math
 
for raid in ["0", "5", "6", "10"]:
    result = calculate_mttdl(raid, 8, 1_000_000, 24)
    years = result['mttdl_years']
    prob = result['annual_failure_probability']
    
    if years > 1000:
        years_str = f"{years/1000:.1f}K"
    else:
        years_str = f"{years:.1f}"
    
    print(f"RAID {raid:>2} | {years_str:>13}   | {prob:.2e}")
 
print("\nEffect of rebuild time on RAID 5 (8 disks, 8TB each):\n")
for mttr in [8, 24, 48, 96]:
    result = calculate_mttdl("5", 8, 1_000_000, mttr)
    print(f"MTTR {mttr:>2}h: MTTDL = {result['mttdl_years']/1000:.1f}K years")

The Hidden Danger

These calculations assume independent, random failures. Real-world correlations (batch defects, environmental events, stress during rebuild) mean actual failure rates are often higher than theoretical models suggest. Treat these numbers as best-case estimates.

RAID 6 Reliability Analysis

RAID 6 with its dual parity can survive two simultaneous failures, making it dramatically more reliable than RAID 5, especially for large arrays.

RAID 6 MTTDL Formula:

Data loss requires three failures during successive rebuild windows:

$$MTTDL_{RAID6} = \frac{(MTBF)^3}{n \times (n-1) \times (n-2) \times (MTTR)^2}$$

The key differences from RAID 5:

Numerator: MTBF cubed instead of squared
Denominator: MTTR squared (two rebuild windows)

Example: 8-disk RAID 6: $$MTTDL_{RAID6} = \frac{(10^6)^3}{8 \times 7 \times 6 \times 24^2}$$ $$= \frac{10^{18}}{336 \times 576} = \frac{10^{18}}{193,536}$$ $$\approx 5.17 \times 10^{12} \text{ hours} \approx 590 \text{ million years}$$

RAID 5 vs RAID 6 MTTDL Comparison (MTBF=1M hours, MTTR=24 hours)
Disks	RAID 5 MTTDL	RAID 6 MTTDL	RAID 6 Advantage
6	347K years	285M years	820×
8	148K years	590M years	3,980×
10	95K years	1.16B years	12,200×
12	67K years	2.2B years	33,000×
16	40K years	7.1B years	178,000×

Why RAID 6 Advantage Increases with Array Size:

As arrays grow, the probability of second failure during rebuild increases dramatically for RAID 5 (more disks that could fail). RAID 6 mitigates this by tolerating that second failure and only failing if a THIRD failure occurs during the second rebuild.

The ratio of RAID 6 to RAID 5 MTTDL:

$$\frac{MTTDL_{RAID6}}{MTTDL_{RAID5}} = \frac{MTBF}{(n-2) \times MTTR}$$

For 16 disks with MTBF=1M hours and MTTR=24 hours: $$\frac{10^6}{14 \times 24} = \frac{10^6}{336} \approx 2,976$$

RAID 6 is nearly 3,000× more reliable than RAID 5 for a 16-disk array.

When RAID 6 Becomes Mandatory

Industry best practice now recommends RAID 6 whenever: (1) Array has more than 6 disks, (2) Individual disks are 4TB or larger, (3) Rebuild time exceeds 12 hours, (4) The data is business-critical. The performance overhead of RAID 6 is minor compared to the reliability gain.

The Large Capacity Drive Problem

The dramatic increase in drive capacities—from 500GB in 2006 to 20TB+ in 2024—has fundamentally altered RAID reliability calculations. The problem is twofold: longer rebuild times and unrecoverable read errors (UREs).

Impact of Longer Rebuild Times:

Rebuild time is approximately proportional to drive capacity:

$$T_{rebuild} \approx \frac{Capacity}{Rebuild_Speed}$$

With a rebuild speed of ~100 MB/s:

1 TB drive: ~3 hours
4 TB drive: ~12 hours
10 TB drive: ~28 hours
20 TB drive: ~56 hours

Since MTTDL is inversely proportional to MTTR: $$MTTDL \propto \frac{1}{MTTR}$$

A 20 TB drive array has approximately 20× lower MTTDL than the same array with 1 TB drives, due to rebuild time alone.

The Unrecoverable Read Error (URE) Problem:

Enterprise HDDs specify a URE rate of approximately 1 in 10^15 bits read (10^14 for consumer drives). This means:

$$P(URE) = 1 - (1 - 10^{-15})^{bits_read}$$

During RAID 5 rebuild, we must read ALL surviving disks entirely. For an 8-disk RAID 5 with 10 TB drives, we read: $$7 \text{ disks} \times 10 \text{ TB} = 70 \text{ TB} = 560 \times 10^{12} \text{ bits}$$

Probability of at least one URE: $$P(URE) = 1 - (1 - 10^{-15})^{560 \times 10^{12}} \approx 1 - e^{-0.56} \approx 43%$$

A 43% chance of an unrecoverable error during rebuild!

If a URE occurs in a sector that needs to be XORed for reconstruction, that sector cannot be recovered. The result is partial data loss, or complete array failure if the file system cannot tolerate the corruption.

URE Probability During RAID 5 Rebuild (7 surviving disks)
Drive Size	Data Read	URE Probability (Enterprise)	URE Probability (Consumer)
1 TB	7 TB	5.6%	43%
4 TB	28 TB	20%	86%
8 TB	56 TB	36%	97%
10 TB	70 TB	43%	99%
16 TB	112 TB	59%	99.9%

Why RAID 6 Helps with UREs:

RAID 6 can tolerate ONE URE during rebuild:

If a URE occurs, the sector can be reconstructed using Q parity
Only a URE combined with a second disk failure causes data loss
The probability of URE + disk failure is much lower than URE alone

However, even RAID 6 struggles with very large drives:

Two UREs during rebuild = data loss
For 20TB drives, P(2+ UREs) during rebuild becomes non-negligible

Mitigations:

Use enterprise drives with 10^15 URE specification
Regular scrubbing to detect and repair UREs before failures
Keep array sizes smaller (split into multiple RAID groups)
Consider RAID alternatives like ZFS with checksums (can identify which block is corrupt)
For very large capacities, consider erasure coding with more than 2 parity chunks

The Death of RAID 5 for Large Drives

RAID 5 with drives 4TB or larger is no longer considered safe for any data you cannot afford to lose. The combination of long rebuild times and URE probability makes data loss during rebuild unacceptably likely. RAID 6 or RAID 10 is mandatory for large-capacity arrays.

Correlated Failures and Real-World Deviations

All MTTDL formulas assume independent disk failures. In reality, failures are often correlated, making actual reliability lower than mathematical predictions.

Sources of Correlated Failures:

Manufacturing batch defects: Drives from the same production run may share weaknesses
- Mitigation: Diversify drive purchases across batches, manufacturers
Environmental factors: Temperature, humidity, vibration affect all drives
- Mitigation: Proper cooling, vibration isolation, redundant cooling
Firmware bugs: A bug triggered by specific patterns affects all drives with that firmware
- Mitigation: Diverse firmware versions, careful firmware updates
Rebuild stress: Intense I/O during rebuild can trigger latent failures
- Study data: ~5% of rebuilds trigger second failure
- Mitigation: Reduce rebuild aggressiveness, hot spares
Infrastructure failures: Power supply, HBA, backplane failures affect multiple drives simultaneously
- Mitigation: Redundant power, cables if possible

Google and Backblaze Studies:

Large-scale studies of real disk failures reveal important patterns:

Google Study (2007, ~100K drives):

Annual failure rate: 1.7% (year 1), 8.6% (year 2), 8.6% (year 3)
Failures cluster in time (after one failure, more likely soon)
Temperature correlation was surprisingly weak
SMART attributes only weakly predictive

Backblaze Studies (ongoing, 200K+ drives):

Annual failure rates: 0.5% - 10%+ depending on model/age
Significant variation between manufacturers and models
Early failures (infant mortality) and wear-out failures both significant
Some models show "cliffs" where failure rates spike

Practical Reliability Improvements

•Distribute drives across enclosures: If one power supply fails, only half the array is affected
•Mix drive batches: Purchase drives over time or from different suppliers
•Monitor proactively: SMART monitoring, predictive analytics to replace before failure
•Test restores regularly: A RAID array is only reliable if you've verified recovery works
•Document everything: Record serial numbers, purchase dates, firmware versions for each drive
•Have spares ready: Hot spares for automated rebuild; cold spares for quick manual replacement
•Regular scrubbing: Catch latent errors before they matter during rebuild
•Backup independently: RAID protects against hardware failure, not data corruption or deletion

The 10× Rule

A practical engineering rule: assume real-world reliability is about 10× worse than theoretical MTTDL calculations suggest, due to correlated failures, UREs, and environmental factors. Design with this margin of safety.

RAID Reliability Comparison and Selection Guide

Let's synthesize our reliability analysis into practical guidance for RAID selection:

Reliability Ranking (best to worst):

RAID 6 — Survives 2 failures; robust against UREs; best for large arrays
RAID 10 — Survives 1 per pair; fast rebuild; consistent performance
RAID 1 — Same as RAID 10 but limited scale
RAID 5 — Survives 1 failure; increasingly risky with large drives
RAID 0 — No fault tolerance; suitable only for ephemeral data

RAID Selection Matrix by Requirements
Requirement	Recommended RAID	Rationale
Maximum reliability, any cost	RAID 6 or 3-way mirror	Survives 2 failures
High reliability, high write performance	RAID 10	No write penalty, survives failures
Balanced reliability and efficiency	RAID 6	Good efficiency with double parity
Maximum capacity efficiency	RAID 5 (small array, small drives)	Only if rebuild time <12h and drives <4TB
Temporary/replaceable data	RAID 0	Never for important data
Boot/OS drives	RAID 1	Simple, fast recovery
Large capacity, many drives	RAID 6 mandatory	15+ drives makes double failure likely
Database transaction logs	RAID 10 or RAID 1	Fast synchronous writes, high reliability

Decision Flowchart:

1. Is the data irreplaceable or critical?
   NO → RAID 0 acceptable (with backups)
   YES → Continue

2. Are drives 4TB or larger OR array 8+ drives?
   YES → RAID 6 or RAID 10 required
   NO → RAID 5 may be acceptable

3. Is write performance critical (>50% writes)?
   YES → RAID 10 preferred
   NO → RAID 6 acceptable

4. Is storage efficiency more important than performance?
   YES → RAID 6 (if requirements allow)
   NO → RAID 10

5. Is budget severely constrained?
   YES → RAID 5 with very careful monitoring
        (understand the risk)
   NO → RAID 6 or RAID 10 based on above

RAID Is Not Backup

Even the most reliable RAID configuration cannot protect against: accidental deletion, software bugs corrupting data, ransomware encryption, fire/flood/theft affecting the entire array, controller failure corrupting the array, silent data corruption (without scrubbing). Always maintain independent backups following the 3-2-1 rule: 3 copies, 2 media types, 1 off-site.

Summary: RAID Reliability Engineering

We've explored the mathematical foundations and practical considerations of RAID reliability. Here are the essential concepts:

Key Takeaways

•MTTDL (Mean Time To Data Loss) is the key metric for comparing RAID reliability, calculated from MTBF, MTTR, and array configuration
•RAID 5 reliability degrades quadratically with array size (n × (n-1) in the denominator), making large RAID 5 arrays dangerous
•RAID 6 provides orders of magnitude better reliability than RAID 5, especially for larger arrays, by tolerating two failures
•Rebuild time directly impacts reliability—longer rebuilds mean longer vulnerability windows. Large drives dramatically increase risk.
•Unrecoverable Read Errors (UREs) during rebuild can cause data loss even with surviving drives. Large drives make UREs nearly certain.
•Correlated failures in the real world mean actual reliability is significantly lower than theoretical calculations suggest
•RAID 5 should not be used with drives 4TB+ or arrays with 8+ drives. RAID 6 or RAID 10 is mandatory for critical data.
•RAID is not backup—it protects against hardware failure only, not data corruption, deletion, or catastrophic events

Module Conclusion:

You have now completed a comprehensive study of RAID technology, from fundamental concepts through advanced reliability engineering. You understand how striping and mirroring work, the mathematics of parity, performance characteristics under various workloads, and the probability calculations that determine whether your data survives disk failures.

This knowledge is foundational for anyone working with storage systems—whether designing enterprise data centers, configuring NAS devices, or simply making informed decisions about protecting important data.

Module Complete

Congratulations! You have mastered the principles of RAID: Redundant Array of Independent Disks. You now possess the knowledge to design storage systems that balance performance, capacity, and reliability according to specific requirements—a core competency for systems engineers and storage architects.