engineeringkit.reliability#

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Lifetime distributions, independent systems, availability and maintenance.

Reliability engineering: lifetime distributions, systems, availability and maintenance.

engineeringkit.reliability.availability(mtbf, mttr)[source]#

Availability.

Parameters:

  • mtbf (s) – Input in the units stated above.

  • mttr (s) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.bathtub_hazard(t, early_scale=1, early_rate=1, random_rate=0.01, wear_scale=1e-06, wear_power=2)[source]#

Bathtub hazard.

Parameters:

  • t (s) – Input in the units stated above.

  • early_scale (1/s) – Input in the units stated above.

  • early_rate (1/s) – Input in the units stated above.

  • random_rate (1/s) – Input in the units stated above.

  • wear_scale (1/s^(wear_power+1)) – Input in the units stated above.

  • wear_power (1) – Input in the units stated above.

Returns:

1/s.

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.birnbaum_importance_series(reliabilities, i)[source]#

Birnbaum importance series.

Parameters:

  • reliabilities (1) – Input in the units stated above.

  • i (1) – Input in the units stated above.

Returns:

dimensionless sensitivity.

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.expected_failures(lam, total_time)[source]#

Expected failures.

Parameters:

  • lam (1/s) – Input in the units stated above.

  • total_time (s) – Input in the units stated above.

Returns:

expected count.

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.exponential_failure_probability(t, lam)[source]#

Exponential failure probability.

Parameters:

  • t (s) – Input in the units stated above.

  • lam (1/s) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.exponential_hazard(lam)[source]#

Exponential hazard.

Parameters:

lam (1/s) – Input in the units stated above.

Returns:

1/s.

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.exponential_mttf(lam)[source]#

Exponential mttf.

Parameters:

lam (1/s) – Input in the units stated above.

Returns:

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.exponential_reliability(t, lam)[source]#

Exponential reliability.

Parameters:

  • t (s) – Input in the units stated above.

  • lam (1/s) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.failure_rate_from_mtbf(mtbf)[source]#

Failure rate from mtbf.

Parameters:

mtbf (s) – Input in the units stated above.

Returns:

1/s.

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.k_of_n_reliability(n, k, r)[source]#

K of n reliability.

Parameters:

  • n (1) – Input in the units stated above.

  • k (1) – Input in the units stated above.

  • r (1) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.maintainability(t, mu)[source]#

Maintainability.

Parameters:

  • t (s) – Input in the units stated above.

  • mu (1/s) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.parallel_reliability(*r)[source]#

Parallel reliability.

Parameters:

r (1) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.poisson_failures_probability(k, lam, total_time)[source]#

Evaluate a Poisson count probability stably in log space.

Parameters:

  • k (1) – Input in the units stated above.

  • lam (1/s) – Input in the units stated above.

  • total_time (s) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.reliability_growth_duane(t, K, alpha)[source]#

Reliability growth duane.

Parameters:

  • t (s) – Input in the units stated above.

  • K (s^(1-alpha)) – Input in the units stated above.

  • alpha (1) – Input in the units stated above.

Returns:

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.renewal_interval_cost_rate(preventive_cost, failure_cost, lam, T)[source]#

Compute a simple scheduled-maintenance cost-rate baseline, not a renewal solver.

Parameters:

  • preventive_cost (currency units) – Input in the units stated above.

  • failure_cost (currency units) – Input in the units stated above.

  • lam (1/s) – Input in the units stated above.

  • T (s) – Input in the units stated above.

Returns:

currency/s.

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.repair_rate(mttr)[source]#

Repair rate.

Parameters:

mttr (s) – Input in the units stated above.

Returns:

1/s.

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.safety_integrity_pfd(lam_du, test_interval)[source]#

Estimate average dangerous undetected failure probability for rare failures.

Parameters:

  • lam_du (1/s) – Input in the units stated above.

  • test_interval (s) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.series_reliability(*r)[source]#

Series reliability.

Parameters:

r (1) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.unavailability(mtbf, mttr)[source]#

Unavailability.

Parameters:

  • mtbf (s) – Input in the units stated above.

  • mttr (s) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.weibull_cdf(t, eta, beta)[source]#

Weibull cdf.

Parameters:

  • t (s) – Input in the units stated above.

  • eta (s) – Input in the units stated above.

  • beta (1) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.weibull_hazard(t, eta, beta)[source]#

Weibull hazard.

Parameters:

  • t (s) – Input in the units stated above.

  • eta (s) – Input in the units stated above.

  • beta (1) – Input in the units stated above.

Returns:

1/s.

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.weibull_mttf(eta, beta)[source]#

Weibull mttf.

Parameters:

  • eta (s) – Input in the units stated above.

  • beta (1) – Input in the units stated above.

Returns:

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.

engineeringkit.reliability.weibull_reliability(t, eta, beta)[source]#

Weibull reliability.

Parameters:

  • t (s) – Input in the units stated above.

  • eta (s) – Input in the units stated above.

  • beta (1) – Input in the units stated above.

Returns:

probability [0,1].

Return type:

result

Notes

Assumptions, governing equations and validity limits are discussed in Reliability: distributions, independence and rate units. SI inputs are required; raw numbers carry no dimensional metadata.