Distributed Storage & Reliability Engineering
RAID-5 MTTDL & Erasure-Coding Overhead Formula
Calculate Patterson-Gibson-Katz RAID-5 Mean Time To Data Loss MTTDL = (MTBF^2) / (N*(N - 1)*MTTR) and compare Reed-Solomon (k + m) erasure-coding storage overhead against 3-way replication.
Why 20 TB+ drives killed wide single-parity RAID-5 and drove cloud object stores to (k + m) erasure coding!
David Patterson, Garth Gibson, and Randy Katz’s (1988) Markov reliability model shows why single-parity RAID-5 suffers catastrophic rebuild vulnerability on wide arrays of high-capacity drives: any of the N drives fails at rate N / MTBF, and if ANY of the remaining (N - 1) drives fails during the long sequential rebuild window MTTR, the stripe suffers permanent data loss — yielding RAID-5 Mean Time To Data Loss MTTDL_hours = (MTBF^2) / (N * (N - 1) * MTTR)! Modern cloud object stores replace single parity and 3x replication (300% raw capacity for only 2-fault tolerance) with Reed-Solomon (k data + m parity) Erasure Coding, delivering m-concurrent-failure durability at Raw-to-Usable Storage Amplification (k + m) / k (Usable Storage Efficiency = k / (k + m))!
Verify on exact integers: Stripe_Width N = 10 drives (B2), Drive_MTBF = 900,000 hr (B3), Rebuild_Time MTTR = 18.0 hr (B4), and Reed-Solomon Erasure Stripe k = 8 data chunks (B5) + m = 4 coding chunks (B6): RAID-5 MTTDL in Million Hours is (900,000^2) / (10 * 9 * 18 * 1,000,000) = 810,000 / 1,620 = 500.00 Million Hours! Quadrupling drive capacity so rebuild time jumps 4x to MTTR = 72 hr slashes MTTDL 4x to 125.00 Million Hours! Meanwhile, (8 + 4) Erasure Coding achieves 4-drive simultaneous fault tolerance at Raw Amplification (8 + 4) / 8 = 1.5000x (Usable Efficiency = 0.6667 = 66.67%) — cutting raw petabytes in HALF versus 3.0000x replication!
| Storage Durability Metric (N=10, MTBF=900k hr, MTTR=18 hr, EC=8+4) | Formula | Verified Output |
|---|---|---|
| RAID-5 MTTDL (Million Hours) | (MTBF^2) / (N*(N - 1)*MTTR*10^6) | 500.00 Million hr |
| RAID-5 MTTDL if Rebuild Quadruples (72h) | 500.00 / 4 | 125.00 Million hr (-75%!) |
| Erasure Coding Amplification ((k+m)/k) | (8 + 4) / 8 | 1.5000x Raw/Usable (vs 3.0x Rep) |
| Erasure Coding Usable Efficiency | k / (k + m) = 8 / 12 | 0.6667 (66.67% Usable) |
Patterson-Gibson-Katz RAID-5 MTTDL (Million Hours) Formula
Validate integer array width N >= 3 (1 parity + >= 2 data drives), MTBF > 0, and rebuild duration MTTR > 0.
=LET(n_dr, B2, mt_bf, B3, mt_tr, B4, IF(OR(n_dr < 3, INT(n_dr) <> n_dr, mt_bf <= 0, mt_tr <= 0), "Invalid Storage Input", ROUND((mt_bf ^ 2) / (n_dr * (n_dr - 1) * mt_tr * 1000000), 2)))Reed-Solomon (k + m) Storage Amplification & Usable Efficiency Formula
Validate integer data chunks k >= 1 and parity chunks m >= 1.
=IF(OR(B5 < 1, INT(B5) <> B5, B6 < 1, INT(B6) <> B6), "Invalid EC Stripe", ROUND((B5 + B6) / B5, 4))Try the example
Use the original values or change them to test your understanding.