AgeReplacementPolicy

class relife.policies.AgeReplacementPolicy(baseline)

Age replacement renewal policy.

Asset is replaced at age \(a_r\) with cost \(c_p\), or upon failure with cost \(c_f\).

Parameters:

lifetime_modelParametricLifetimeModel

Lifetime model representing durations between events.

References

[1]

Mazzuchi, T. A., Van Noortwijk, J. M., & Kallen, M. J. (2007). Maintenance optimization. Encyclopedia of Statistics in Quality and Reliability, 1000-1008.

Methods

annual_number_of_failures	The expected annual number of replacements upon failure.
annual_number_of_replacements	The expected annual number of replacements.
asymptotic_expected_equivalent_annual_cost	The asymptotic expected equivalent annual cost.
asymptotic_expected_net_present_value	The asymptotic expected net present value.
compute_optimal_ar	Compute the optimal ages of replacement.
expected_equivalent_annual_cost	The expected equivalent annual cost.
expected_net_present_value	The expected net present value.

annual_number_of_failures(nb_years, *, ar, a0=None)

The expected annual number of replacements upon failure.

Parameters:

nb_yearsint

Number of years used to project annual replacements.

arfloat or np.ndarray

Ages of replacement.

a0float or np.ndarray, optional

Initial ages.

Returns:

outtuple of np.ndarray

Timeline and corresponding values.

annual_number_of_replacements(nb_years, *, ar, a0=None)

The expected annual number of replacements.

Parameters:

nb_yearsint

Number of years used to project annual replacements.

arfloat or np.ndarray

Ages of replacement.

a0float or np.ndarray, optional

Initial ages.

Returns:

outtuple of np.ndarray

Timeline and corresponding values.

asymptotic_expected_equivalent_annual_cost(*, ar, a0=None, discounting_rate=0.0, **costs)

The asymptotic expected equivalent annual cost.

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

Parameters:

arfloat or 1d array

Preventive ages of replacement.

a0float or 1d array, optional

Initial ages of the assets.

discounting_ratefloat, default is 0.

The discounting rate used for cost computations.

**costsfloats or 1d arrays

Required costs, such as cp, cf and/or cr.

Returns:

ndarray

The asymptotic expected values.

asymptotic_expected_net_present_value(*, ar, a0=None, discounting_rate=0.0, **costs)

The asymptotic expected net present value.

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

Parameters:

arfloat or 1d array

Preventive ages of replacement.

a0float or 1d array, optional

Initial ages of the assets.

discounting_ratefloat, default is 0.

The discounting rate used for cost computations.

**costsfloats or 1d arrays

Required costs, such as cp, cf and/or cr.

Returns:

ndarray

The asymptotic expected values.

compute_optimal_ar(discounting_rate=0.0, **costs)

Compute the optimal ages of replacement.

Parameters:

discounting_ratefloat, default is 0.

The discounting rate used for cost computations.

**costsfloats or 1d arrays

Required costs, such as cp, cf and/or cr.

Returns:

outfloat or 1d array

Optimal ages of replacement.

expected_equivalent_annual_cost(tf, nb_steps, *, ar, a0=None, discounting_rate=0.0, **costs)

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 discretize the time.

arfloat or 1d array

Preventive ages of replacement.

a0float or 1d array, optional

Initial ages of the assets.

discounting_ratefloat, default is 0.

The discounting rate used for cost computations.

**costsfloats or 1d arrays

Required costs, such as cp, cf and/or cr.

Returns:

outtuple of np.ndarray

Timeline and corresponding values.

expected_net_present_value(tf, nb_steps, *, ar, a0=None, discounting_rate=0.0, **costs)

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 discretize the time.

arfloat or 1d array

Preventive ages of replacement.

a0float or 1d array, optional

Initial ages of the assets.

discounting_ratefloat, default is 0.

The discounting rate used for cost computations.

**costsfloats or 1d arrays

Required costs, such as cp, cf and/or cr.

Returns:

outtuple of np.ndarray

Timeline and corresponding values.