RunToFailurePolicy

class relife.policy.RunToFailurePolicy(lifetime_model, cf, discounting_rate=0.0, a0=None)

Run-to-failure renewal policy.

Asset is replaced upon failure with cost \(c_f\).

Parameters:

lifetime_modelany lifetime distribution or frozen lifetime model

A lifetime model representing the durations between events.

cffloat or 1darray

Costs of failures

discounting_ratefloat, default is 0.

The discounting rate value used in the exponential discounting function

a0float or 1darray, optional

Current ages of the assets, by default 0 for each asset. If it is given, left truncations of a0 will be take into account for the first cycle.

Attributes:

cf

Cost of failure.

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 asymtotic expected equivalent annual cost.
asymptotic_expected_net_present_value	The asymtotic expected net present value.
expected_equivalent_annual_cost	The expected equivalent annual cost.
expected_net_present_value	The expected net present value.
sample	Renewal data sampling.

property a0

Current ages of the assets.

Returns:

np.ndarray

asymptotic_expected_equivalent_annual_cost(total_sum=False)

The asymtotic expected equivalent annual cost.

\[\lim_{t\to\infty} q(t)\]

Parameters:

total_sumbool, default False

If True, returns the total sum over the first axis of the result. If the policy data encodes several assets, this option allows to return the sum result on the flit rather than calling np.sum afterwards.

Returns:

ndarray

The asymptotic expected values.

asymptotic_expected_net_present_value(total_sum=False)

The asymtotic expected net present value.

\[\lim_{t\to\infty} z(t)\]

Parameters:

total_sumbool, default False

If True, returns the total sum over the first axis of the result. If the policy data encodes several assets, this option allows to return the sum result on the flit rather than calling np.sum afterwards.

Returns:

ndarray

The asymptotic expected values.

property cf

Cost of failure.

Returns:

np.ndarray

expected_equivalent_annual_cost(tf, nb_steps, total_sum=False)

The expected equivalent annual cost.

\[q(t) = \dfrac{\delta z(t)}{1 - e^{-\delta t}}\]

where :

• \(t\) is the time.

• \(z(t)\) is the expected net present value at time \(t\).

• \(\delta\) is the discounting rate.

Parameters:

tffloat

The final time.

nb_stepsint

The number of steps used to discretized the time.

total_sumbool, default False

If True, returns the total sum over the first axis of the result. If the policy data encodes several assets, this option allows to return the sum result on the flit rather than calling np.sum afterwards.

Returns:

tuple of two ndarrays

A tuple containing the timeline and the computed values.

expected_net_present_value(tf, nb_steps, total_sum=False)

The expected net present value.

\[z(t) = \mathbb{E}(Z_t) = \int_{0}^{\infty}\mathbb{E}(Z_t~|~X_1 = x)dF(x)\]

where :

• \(t\) is the time

• \(X_1 \sim F\) is the random lifetime of the first asset

• \(Z_t\) are the random costs at each time \(t\)

• \(\delta\) is the discounting rate

It is computed by solving the renewal equation.

Parameters:

tffloat

The final time.

nb_stepsint

The number of steps used to discretized the time.

total_sumbool, default False

If True, returns the total sum over the first axis of the result. If the policy data encodes several assets, this option allows to return the sum result on the flit rather than calling np.sum afterwards.

Returns:

tuple of two ndarrays

A tuple containing the timeline and the computed values.

sample(size, time_window, seed=None)

Renewal data sampling.

This function will sample data and encapsulate them in an object.

Parameters:

sizeint

The size of the desired sample.

time_windowtuple of two floats

Time window in which data are sampled

sizeint or tuple of 2 int

Size of the sample

seedint, optional

Random seed, by default None.