relife.replacement_policy.RunToFailure

relife.replacement_policy.RunToFailure

class relife.replacement_policy.RunToFailure(model: relife.model.AbsolutelyContinuousLifetimeModel, args: Tuple[numpy.ndarray, ...] = (), a0: Optional[numpy.ndarray] = None, cf: Optional[numpy.ndarray] = None, rate: numpy.ndarray = 0)[source]

Bases: object

Run-to-failure renewal policy.

Run-to-failure renwal policy.

Renewal reward process where assets are replaced on failure with costs cf.

Parameters

  • model (AbsolutelyContinuousLifetimeModel) – Absolutely continuous lifetime model of the asset.

  • args (Tuple[ndarray,...], optional) – Extra arguments required by the lifetime model, by default ().

  • a0 (float or 2D array, optional) – Current ages of the assets, by default 0 for each asset.

  • cf (float, 2D array or 3D array, optional) – Costs of failures, by default None.

  • rate (float, 2D array or 3D array, optional) – Discount rate, by default 0.

Notes

If cf is set to None, if should be defined when using methods to compute costs.

If cf and rate are 2D or 3D array, then:

  • axis=-2 represents the indices of each asset,

  • axis=-3 represents the indices of each component of the cost vector.

References

1

Van der Weide, J. A. M., & Van Noortwijk, J. M. (2008). Renewal theory with exponential and hyperbolic discounting. Probability in the Engineering and Informational Sciences, 22(1), 53-74.

Methods

asymptotic_expected_equivalent_annual_cost

The asymptotic expected equivalent annual cost.

asymptotic_expected_total_cost

The asymptotic expected total cost.

expected_equivalent_annual_cost

The expected equivalent annual cost.

expected_total_cost

The expected total discounted cost.

rrp_args

Arguments of the underlying renewal reward process.

sample

Run-to-failure renewal policy sampling.

Attributes

discount

Exponential discounting.

reward

The failure cost of the asset.
reward: relife.reward.FailureCost = <relife.reward.FailureCost object>

The failure cost of the asset.

discount: relife.discounting.ExponentialDiscounting = <relife.discounting.ExponentialDiscounting object>

Exponential discounting.

rrp_args(cf: Optional[numpy.ndarray] = None, rate: Optional[numpy.ndarray] = None) → Tuple[Tuple[numpy.ndarray, ...], ...][source]

Arguments of the underlying renewal reward process.

Parameters

  • cf (float, 2D array or 3D array, optional) – Costs of failures, by default None.

  • rate (float, 2D array or 3D array, optional) – Discount rate, by default None.

Returns

(model_args, reward_args, model1_args, reward1_args, discount_args)

Return type

Tuple[Tuple[ndarray,…],…]

Notes

If an argument is None, the value of the class attribute is taken.

expected_total_cost(t: numpy.ndarray, cf: Optional[numpy.ndarray] = None, rate: Optional[numpy.ndarray] = None) → numpy.ndarray[source]

The expected total discounted cost.

The expected total discounted cost is computed by solving the renewal equation.

Parameters

  • t (1D array) – Timeline.

  • cf (float, 2D array or 3D array, optional) – Costs of failures, by default None.

  • rate (float, 2D array or 3D array, optional) – Discount rate, by default None.

Returns

The cumulative expected total cost for each asset along the timeline.

Return type

ndarray

Notes

If an argument is None, the value of the class attribute is taken.

asymptotic_expected_total_cost(cf: Optional[numpy.ndarray] = None, rate: Optional[numpy.ndarray] = None) → numpy.ndarray[source]

The asymptotic expected total cost.

Parameters

  • cf (float, 2D array or 3D array, optional) – Costs of failures, by default None.

  • rate (float, 2D array or 3D array, optional) – Discount rate, by default None.

Returns

The asymptotic expected total cost for each asset.

Return type

ndarray

Notes

If an argument is None, the value of the class attribute is taken.

expected_equivalent_annual_cost(t: numpy.ndarray, cf: Optional[numpy.ndarray] = None, rate: Optional[numpy.ndarray] = None) → numpy.ndarray[source]

The expected equivalent annual cost.

where \(z\) is the expected total cost.

Parameters

  • t (1D array) – Timeline.

  • cf (float, 2D array or 3D array, optional) – Costs of failures, by default None.

  • rate (float, 2D array or 3D array, optional) – Discount rate, by default None.

Returns

The expected equivalent annual cost for each asset along the timeline.

Return type

ndarray

Notes

If an argument is None, the value of the class attribute is taken.

The expected equivalent annual cost at time \(t\) is:

\[EEAC(t) = \dfrac{\delta z(t)}{1 - e^{-\delta t}}\]
asymptotic_expected_equivalent_annual_cost(cf: Optional[numpy.ndarray] = None, rate: Optional[numpy.ndarray] = None) → numpy.ndarray[source]

The asymptotic expected equivalent annual cost.

Parameters

  • cf (float, 2D array or 3D array, optional) – Costs of failures, by default None.

  • rate (float, 2D array or 3D array, optional) – Discount rate, by default None.

Returns

The asymptotic expected equivalent annual cost for each asset.

Return type

ndarray

Notes

If an argument is None, the value of the class attribute is taken.

The asymptotic expected equivalent annual cost is:

\[EEAC_\infty = \lim_{t \to \infty} EEAC(t)\]
sample(T: float, cf: Optional[numpy.ndarray] = None, rate: Optional[numpy.ndarray] = None, n_samples: int = 1, random_state: Optional[int] = None) → relife.data.ReplacementPolicyData[source]

Run-to-failure renewal policy sampling.

Parameters

  • T (float) – End of the observation period.

  • cf (float, 2D array or 3D array, optional) – Costs of failures, by default None.

  • rate (float, 2D array or 3D array, optional) – Discount rate, by default None.

  • n_samples (int, optional) – Number of samples, by default 1.

  • random_state (int, optional) – Random seed, by default None.

Returns

Samples of replacement times, durations, costs and events for each asset.

Return type

ReplacementPolicyData

Notes

If an argument is None, the value of the class attribute is taken.

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