OneCycleRunToFailurePolicy

class relife.policies.OneCycleRunToFailurePolicy(lifetime_model, cf, discounting_rate=0.0, period_before_discounting=1.0)

One cyle run-to-failure policy.

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

Note

OneCycleRunToFailurePolicy differs from RunToFailurePolicy because only one cycle of replacement is considered.

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

Attributes:

cf

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.
get_cf	Cost of failure.
set_cf

asymptotic_expected_equivalent_annual_cost(a0=None)

The asymtotic expected equivalent annual cost.

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

Parameters:

a0float or np.ndarray, optional

Initial ages of the assets.

Returns:

ndarray

The asymptotic expected values.

asymptotic_expected_net_present_value(a0=None)

The asymtotic expected net present value.

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

Parameters:

a0float or np.ndarray, optional

Initial ages of the assets.

Returns:

ndarray

The asymptotic expected values.

expected_equivalent_annual_cost(tf, nb_steps, a0=None)

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.

a0float or np.ndarray, optional

Initial ages of the assets.

Returns:

tuple of two ndarrays

A tuple containing the timeline and the computed values.

expected_net_present_value(tf, nb_steps, a0=None)

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.

a0float or np.ndarray, optional

Initial ages of the assets.

Returns:

tuple of two ndarrays

A tuple containing the timeline and the computed values.

get_cf()

Cost of failure.

Returns:

np.ndarray