When dealing with redundant server clusters, we're essentially solving a probability problem where:

Total uptime = 1 - Probability(all nodes being down simultaneously)

For a system with independent nodes (no correlated failures), this becomes a straightforward probability multiplication.

Each server has two states:

P(up) = uptime_percentage (e.g., 0.95)
P(down) = 1 - P(up) (e.g., 0.05)

The probability of all N nodes failing simultaneously:

P(all_down) = (P(down))^N
System_availability = 1 - P(all_down)

Let's implement this in Python:

def calculate_uptime(node_uptime, node_count):
    """Calculate cluster uptime given individual node reliability"""
    node_downtime = 1 - node_uptime
    probability_all_down = node_downtime ** node_count
    return 1 - probability_all_down

# Example usage:
print(f"2 nodes @95%: {calculate_uptime(0.95, 2):.4f}")  # 0.9975 (99.75%)
print(f"3 nodes @95%: {calculate_uptime(0.95, 3):.4f}")  # 0.999875 (99.9875%)

Real-world systems often need more sophisticated models that account for:

• Correlated failures (network partitions, power outages)
• Degraded states (partial failures)
• Maintenance windows

For these scenarios, we might use Markov models or Monte Carlo simulations.

We can also compute this using logarithmic probabilities for numerical stability:

import math

def log_uptime(node_uptime, node_count):
    log_p_down = math.log10(1 - node_uptime)
    log_p_all_down = node_count * log_p_down
    return 1 - (10 ** log_p_all_down)

When dealing with server clusters, uptime calculation follows probability principles. For independent nodes with identical uptime percentages, we can model this using binomial probability.

For a cluster of 2 nodes with 95% uptime each (5% downtime):

P(both down) = 0.05 * 0.05 = 0.0025 (0.25%)
P(at least one up) = 1 - P(both down) = 99.75%

Extending to 3 nodes:

P(all three down) = 0.05^3 = 0.000125 (0.0125%)
P(at least one up) = 1 - 0.000125 = 99.9875%

The general formula for N nodes with individual uptime U:

ClusterUptime = 1 - (1 - U)^N

Here's a reusable function to calculate cluster uptime:

def calculate_cluster_uptime(node_uptime, node_count):
    """
    Calculate cluster uptime probability
    
    Args:
        node_uptime: float (0-1) representing individual node uptime
        node_count: integer number of nodes
        
    Returns:
        float probability of cluster availability
    """
    downtime = 1 - node_uptime
    total_downtime_prob = downtime ** node_count
    return 1 - total_downtime_prob

While the math provides the theoretical maximum:

• Real-world systems have dependencies
• Network connectivity affects actual availability
• Maintenance windows may create correlated downtime

For clusters with varying node reliability:

# Calculate for nodes with 95%, 90%, and 99% uptime
def mixed_uptime_calculation(uptime_list):
    downtime_product = 1
    for uptime in uptime_list:
        downtime_product *= (1 - uptime)
    return 1 - downtime_product