BaseOneCycleAgeReplacementPolicy

class relife.policy.BaseOneCycleAgeReplacementPolicy(lifetime_model, reward, discounting_rate=0.0, period_before_discounting=1.0)

Methods

asymptotic_expected_equivalent_annual_cost	Calculate the asymptotic expected equivalent annual cost.
asymptotic_expected_total_cost	Calculate the asymptotic expected total cost.
expected_equivalent_annual_cost	Calculate the expected equivalent annual cost over a given timeline.
expected_total_cost	Calculate the expected total cost over a given timeline.
sample_count_data
sample_lifetime_data

asymptotic_expected_equivalent_annual_cost()

Calculate the asymptotic expected equivalent annual cost.

It takes into account discounting_rate attribute value.

The asymptotic expected total cost is:

\[\lim_{t\to\infty} \text{EEAC}(t)\]

where \(\text{EEAC}(t)\) is the expected equivalent annual cost at \(t\). See expected_equivalent_annual_cost() for more details.

Returns:

np.ndarray

The asymptotic expected equivalent annual cost.

asymptotic_expected_total_cost()

Calculate the asymptotic expected total cost.

It takes into account discounting_rate attribute value.

The asymptotic expected total cost is:

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

where \(z(t)\) is the expected total cost at \(t\). See expected_total_cost() for more details.

Returns:

np.ndarray

The asymptotic expected total cost.

expected_equivalent_annual_cost(tf, nb_steps)

Calculate the expected equivalent annual cost over a given timeline.

It takes into account discounting_rate attribute value.

The expected equivalent annual cost \(\text{EEAC}(t)\) is given by:

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

where :

• \(t\) is the time

• \(z(t)\) is the expected_total_cost at \(t\). See expected_total_cost() for more details.`.

• \(\delta\) is the discounting rate.

Parameters:

timeline: np.ndarray

Values of the timeline over which the expected equivalent annual cost is to be calculated.

Returns:

np.ndarray

The expected equivalent annual cost.

expected_total_cost(tf, nb_steps)

Calculate the expected total cost over a given timeline.

It takes into account discounting_rate attribute value.

The expected total cost \(z(t)\) is computed by solving the renewal equation and is given by:

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

where :

• \(t\) is the time

• \(X_i \sim F\) are \(n\) random variable lifetimes, i.i.d., of cumulative distribution \(F\).

• \(Z_t\) is the random variable reward at each time \(t\).

• \(\delta\) is the discounting rate.

Parameters:

timeline: np.ndarray

Values of the timeline over which the expected total cost is to be calculated.

Returns:

np.ndarray

The expected total cost.