CN104766162A - Opportunistic maintenance method considering different fixed maintenance costs - Google Patents

Abstract

The invention discloses an opportunistic maintenance method considering different fixed maintenance costs. The opportunistic maintenance method comprises the following steps that the replacement probability of a component i is calculated; the maintenance cost expectation value of the component i is calculated according to the failure replacement probability, the opportunistic maintenance probability, the preventive replacement probability, fixed failure costs, failure maintenance costs, preventive maintenance costs and the fixed maintenance costs of a failure component providing opportunities; the expectation service life of the component i is calculated; the average maintenance cost ratio of the component is calculated through the expectation costs and expectation service life of the component i; the average cost ratio of a system is calculated according to the average maintenance cost ratio of all components, a model is optimized, and the average cost ratio of the system is minimized. The different fixed maintenance costs are considered in the opportunistic maintenance model, and therefore the opportunistic maintenance model has the wider use range.

Description

A kind ofly consider the opportunity maintenance method that fixing maintenance cost is different

Technical field

The present invention relates to opportunity maintenance strategy, particularly relate to a kind of fixing no opportunity maintenance method of maintenance cost of consideration.

Background technology

Maintenance problem is a key factor of the field development such as impact industry, military affairs, aviation, closely bound up with the problem such as reliability level, resource consumption, sustainable development of industrial productivity, product quality, commercial unit or military equipment.Formulate rationally effective maintenance control strategy most important to raising maintenance efficiency, and in real work, the needs more tallied with the actual situation to make Maintenance Decision Models, the maintenance decision research tool carrying out the multiple component system considering mutual relationship between parts is of great significance.

In general, if the interaction between the parts in system can be divided three classes: economy dependence, structure dependence and random dependence.Current multi-part is repaiied decision model and is mainly launched around three class strategies: grouping maintenance, batch maintenance and opportunity maintenance.Opportunity maintenance is exactly mainly do together with preventative maintenance combines with corrective maintenance by consideration, thus saves the dismounting cost of corrective maintenance.Combination has two kinds, and one is that fault can retain, and is generally used for parallel redundant system, and one is that fault cannot retain, and is generally used for cascade system.

First opportunity maintenance strategy is proposed by foreign scholar Berg, the system of two same parts compositions for life-span obeys index distribution at first, when one of them component failure, if exceed control limit L given in advance another service time, then will both carry out changing or keeping in repair.Zheng with Fard discusses the system comprising the different parts of k class, and they are using the standard of failure rate as judge.Pham and Wang studies the opportunity maintenance strategy of a class for k/n system.In the strategy that Dagpunar proposes, Poisson distribution is obeyed in the generation of postulated mechanism meeting.The condition maintenarnce of single part is introduced this strategy by Bruno, Christophe, Antoine.Wijnlnalen and Hontelez brings the condition maintenarnce of different parts into opportunity maintenance strategy.AlfredT. then look for another way with JoelA., discussing with availability is that the System Computer of optimization aim can maintenance policy.Opportunity maintenance is more paid attention to decide maintenance opportunity according to the operation conditions of parts reality, thus more can save maintenance cost and improve maintenance efficiency.

In opportunity maintenance strategy, carry out certain research both at home and abroad at present; but the fixing maintenance cost of acquiescence is consistent in current opportunity maintenance model, do not consider the inconsistent problem of inconsistent caused fixing maintenance cost stop time that different faults causes.

Summary of the invention

For overcoming the deficiency that above-mentioned prior art exists; one of the present invention object is that providing a kind of considers the fixing no opportunity maintenance method of maintenance cost; it takes into account opportunity maintenance model by difference being fixed maintenance cost; thus make opportunity maintenance model have usable range widely, be specially adapted to the complication system of the different stop times that different faults causes.

For reaching above-mentioned and other object, the present invention proposes a kind of opportunity maintenance method that fixing maintenance cost is different of considering, comprises the steps:

Step one, the replacement probability of calculating unit i, comprises failure replacement probability, chance replacement probability, preventive replacement probability;

Step 2, the maintenance cost expectation value of the fixing maintenance cost calculating unit i of trouble unit utilizing described failure replacement probability, chance replacement probability, preventive replacement probability and dead loss expense, breakdown maintenance cost, preventative maintenance expense and offer an opportunity;

Step 3, the life expectancy of calculating unit i;

Step 4, utilizes the expect cost of parts i and the average maintenance scale of charges of life expectancy calculating unit;

Step 5, according to the average maintenance scale of charges computing system average cost rate of each parts, Optimized model, makes system average cost rate minimize.

Further, described failure replacement probability is:

$P_i\left\{f\right\}={\∫}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}+[1-{\∫}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\∫}_{W_i}^{T_i}{f}_i\left(t\right)\right[1-{\∫}_{W_i}^t{g}_i\left(u\right)\mathrm{du}\left]\mathrm{dt}\right\}$

Wherein, f _it () represents the fault probability function of parts, W is maintenance threshold values, and T is preventative threshold values,

Further, described chance replacement probability comprises two classes: the first kind is the fixing maintenance cost that the trouble unit fixed expense offered an opportunity is greater than parts i, and its chance replacement probability is $P_i\left\{o1\right\}=[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{g}_{1i}\left(t\right)\right[1-{\&Integral;}_{W_i}^t{f}_i\left(u\right)\mathrm{du}\left]\mathrm{dt}\right\};$ Equations of The Second Kind is the fixing maintenance cost that the trouble unit fixed expense offered an opportunity is less than in parts i, and its chance replacement probability is $P_i\left\{o2\right\}=[1-$ ${\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}\left]\right\{{\&Integral;}_{W_i}^{T_i}{g}_{2i}\left(t\right)[1-{\&Integral;}_{W_i}^t{f}_i\left(u\right)\mathrm{du}]\mathrm{dt}\},$ Wherein, g _1i(t)=δ _iexp [-δ _i(t-W _i)], ${\mathrm{\&delta;}}_i={\mathrm{\&Sigma;}}_{j<i}^N({\mathrm{\&lambda;}}_{\mathrm{fj}}+{\mathrm{\&lambda;}}_{\mathrm{pj}});$ g _2i(t)＝δ _iexp[-δ _i(t-W _i)]， ${\mathrm{\&delta;}}_i={\mathrm{\&Sigma;}}_{j<i}^N({\mathrm{\&lambda;}}_{\mathrm{fj}}+{\mathrm{\&lambda;}}_{\mathrm{pj}}),$ λ _fifor failure replacement rate, λ _pifor preventive replacement rate.

Further, described preventive replacement probability is:

$P_i\left\{p\right\}=[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}][1-{\&Integral;}_{W_i}^{T_i}{f}_i\left(t\right)\mathrm{dt}][1-{\&Integral;}_{W_i}^{T_i}{g}_i\left(t\right)dt]$

Further, described maintenance cost expectation value is:

E _i[C]＝P _i{f}*(C _fi+C _oi)+P _i{o1}*C _pi+P _i{o2}*(C _pi+C _oi-C _oj)

+P _i(p}*(C _pi+C _oi)

Wherein, C _oifor dead loss expense, C _fifor breakdown maintenance cost, C _pifor preventative maintenance expense, C _ojfor the fixing maintenance cost of trouble unit offered an opportunity, P _i{ f} represents that parts i carries out the probability of failure replacement; P _i{ o1} represents that parts i obtains the probability of opportunity maintenance, and this chance is greater than the fixing maintenance cost of parts i by the trouble unit fixed expense offered an opportunity; P _i{ o2} represents that parts i obtains the probability of opportunity maintenance, and this chance is less than the fixing maintenance cost in parts i by the trouble unit fixed expense offered an opportunity.

Further, in step 3, the life expectancy in the replacement cycle of parts i is:

$\begin{array}{c}{E}_i\left[T\right]={\&Integral;}_0^{W_i}{\mathrm{tf}}_i\left(t\right)\mathrm{dt}+T_i{P}_i\left\{p\right\}+[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{\mathrm{tf}}_i\left(t\right)\right[1-\\ {\&Integral;}_{W_i}^t{g}_i\left(u\right)\mathrm{du}\left]\mathrm{dt}\right\}+[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{\mathrm{tg}}_i\left(t\right)\right[1-{\&Integral;}_{W_i}^t{f}_i\left(u\right)\mathrm{du}\left]\mathrm{dt}\right\}\end{array}.$

Further, in step 4, the average maintenance scale of charges of parts i is:

$Z_i(W_i,T_i)=\frac{E_i\left[C\right]}{E_i\left[T\right]}$

Further, in step 5, Optimized model is:

$\left\{\begin{array}{cc}\mathrm{Min}& Z(W,T)={\mathrm{\&Sigma;}}_{i=1}^N\frac{E_i\left[C\right]}{E_i\left[T\right]}\\ s.t.& 0<W_i\&le;T_i\end{array}\right.$

Wherein, W=(W ₁, W ₂..., W _n), T ₌(T ₁, T ₂..., T _n).

Compared with prior art; difference is fixed maintenance cost and is taken into account opportunity maintenance model by a kind of opportunity maintenance method considering that fixing maintenance cost is different of the present invention; thus make opportunity maintenance model have usable range widely, be specially adapted to the complication system of the different stop times that different faults causes.

Accompanying drawing explanation

Fig. 1 is classical opportunity maintenance principle schematic;

Fig. 2 is a kind of flow chart of steps considering the opportunity maintenance method that fixing maintenance cost is different of the present invention.

Embodiment

Below by way of specific instantiation and accompanying drawings embodiments of the present invention, those skilled in the art can understand other advantage of the present invention and effect easily by content disclosed in the present specification.The present invention is also implemented by other different instantiation or is applied, and the every details in this instructions also can based on different viewpoints and application, carries out various modification and change not deviating under spirit of the present invention.

Before introducing the present invention, the opportunity maintenance principle that first simple declaration is classical once.For opportunity maintenance understanding as shown in Figure 1, before parts move to opportunity maintenance threshold values W, if broken down, carry out failure replacement.When parts move between W and preventative threshold values T, if component malfunction, carry out failure replacement, if miscellaneous part breaks down, carry out preventative chance replacing.When parts move to T, which kind of situation all carries out preventative chance replacing.

What the present invention proposed is a kind of opportunity maintenance stragetic innovation model, supposes that the fixing maintenance cost magnitude relationship of parts is:

C _ol＞C _o2＞C _o3＞…＞C _oi

C in formula _oirepresent the dead loss expense of parts i.For chance replacement probability, by the failure replacement rate λ of other arbitrary parts _fior preventive replacement rate λ _picause, from both series connection of reliability.Can be similar to and regard following exponential distribution as, the present invention considers two kinds of situations: if the trouble unit j < i offered an opportunity, and it is larger namely to fix the maintenance cost source of trouble; If the trouble unit j > i offered an opportunity, the parts namely fixing maintenance cost acquisition opportunity maintenance are larger.

(1) as j < i,

g _1i(t)＝δ _iexp[-δ _i(t-W _i)]

In formula: ${\mathrm{\&delta;}}_i={\mathrm{\&Sigma;}}_{j<i}^N({\mathrm{\&lambda;}}_{\mathrm{fj}}+{\mathrm{\&lambda;}}_{\mathrm{pj}});$

(2) as j > i,

g _2i(t)＝δ _iexp[-δ _i(t-W _i)]

In formula: ${\mathrm{\&delta;}}_i={\mathrm{\&Sigma;}}_{j>i}^N({\mathrm{\&lambda;}}_{\mathrm{fj}}+{\mathrm{\&lambda;}}_{\mathrm{pj}});$

Fig. 2 is a kind of flow chart of steps considering the opportunity maintenance method that fixing maintenance cost is different of the present invention.As shown in Figure 2, the present invention is a kind of considers the opportunity maintenance method that fixing maintenance cost is different, comprises the steps:

Step 201, the replacement probability of calculating unit i.

Can by following analysis, the probability distribution function Ω that determining means i is replaced due to different reason _i(t).

(1) as t ∈ (0, W _i) time

${\mathrm{\&Omega;}}_i\left(t\right)={\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}$ Formula (1)

In formula, f _it () represents the fault probability function of parts.

(2) as t ∈ (W _i, T _i) time

1. the replacing that causes of own fault

${\mathrm{\&Omega;}}_i\left(t\right)=[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{f}_i\left(t\right)\right[1-{\&Integral;}_{W_i}^t{g}_i\left(u\right)\mathrm{du}\left]\mathrm{dt}\right\}$ Formula (2)

2. chance is changed

${\mathrm{\&Omega;}}_i\left(t\right)=[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{g}_i\left(t\right)\right[1-{\&Integral;}_{W_i}^t{g}_i\left(u\right)\mathrm{du}\left]\mathrm{dt}\right\}$ Formula (3)

(3) as t ∈ (T _i, ∞) time

${\mathrm{\&Omega;}}_i\left(t\right)=[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}][1-{\&Integral;}_{W_i}^{T_i}{f}_i\left(t\right)\mathrm{dt}][1-{\&Integral;}_{W_i}^{T_i}{g}_t\left(t\right)\mathrm{dt}]$ Formula (1)

Thus, the failure replacement probability of parts i is, t ∈ (0, W _i) time probability distribution function formula (1) and t ∈ (W _i, T _i) time probability distribution function formula (2) sum:

$P_i\left\{f\right\}={\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}+[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{f}_i\left(t\right)\right[1-{\&Integral;}_{W_i}^t{g}_i\left(u\right)\mathrm{du}\left]\mathrm{dt}\right\}$

Parts i chance replacement probability is divided into two classes, and the trouble unit fixed expense that the first kind is to provide chance is greater than the fixing maintenance cost of parts i, i.e. formula (3), but g _it () is transformed to g _1i(t), (i.e. aforementioned j<i) namely:

$P_i\left\{o1\right\}=[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{g}_{1i}\left(t\right)\right[1-{\&Integral;}_{W_i}^t{f}_i\left(u\right)\mathrm{du}]dt\}$

The trouble unit fixed expense that Equations of The Second Kind is to provide chance is less than the fixing maintenance cost in parts i, i.e. formula 3, but g _it () is transformed to g _2it () (i.e. aforementioned j>i) be namely:

$P_i\left\{o2\right\}=[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{g}_{2i}\left(t\right)\right[1-{\&Integral;}_{W_i}^t{f}_i\left(u\right)\mathrm{du}]dt\}$

The preventive replacement probability of parts i is, i.e. formula (4):

$P_i\left\{p\right\}=[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}][1-{\&Integral;}_{W_i}^{T_i}{f}_i\left(t\right)\mathrm{dt}][1-{\&Integral;}_{W_i}^{T_i}{g}_i\left(t\right)\mathrm{dt}]$ Formula (4)

In formula, P _i{ f} represents that parts i carries out the probability of failure replacement; P _i{ o1} represents that parts i obtains the probability of opportunity maintenance, and this chance is greater than the fixing maintenance cost of parts i by the trouble unit fixed expense offered an opportunity; P _i{ o2} represents that parts i obtains the probability of opportunity maintenance, and this chance is less than the fixing maintenance cost in parts i by the trouble unit fixed expense offered an opportunity; P _i{ p} represents the preventive replacement probability of parts; g _ithe density function of remaining part in (t) expression system.

Step 202, utilizes the replacement probability (failure replacement probability, chance replacement probability, preventive replacement probability) of above-mentioned parts i and dead loss expense C _oi, breakdown maintenance cost C _fiwith preventative maintenance expense C _pithe maintenance cost expectation value of calculating unit i.

System is shut down at every turn and all can be produced two kinds of expenses, dead loss expense C _oi, may be correlated with from the stop time of different parts; The maintenance cost of often kind of parts, is divided into breakdown maintenance cost C _fiwith preventative maintenance expense C _pi.Also relate to the fixing maintenance cost C of the trouble unit offered an opportunity herein _oj, the maintenance cost expectation value of parts i is:

E _i[C]＝P _i{f}*(C _fi+C _oi)+P _i{o1}*C _pi+P _i{o2}*(C _pi+C _oi-C _oj)

+P _i{p}*(C _pi+C _oi)

Step 203, the life expectancy of calculating unit i.

Life expectancy in the replacement cycle of parts i can be expressed as:

$\begin{array}{c}{E}_i\left[T\right]={\&Integral;}_0^{W_i}{\mathrm{tf}}_i\left(t\right)\mathrm{dt}+T_i{P}_i\left\{p\right\}+[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{\mathrm{tf}}_i\left(t\right)\right[1-\\ {\&Integral;}_{W_i}^t{g}_i\left(u\right)\mathrm{du}\left]\mathrm{dt}\right\}+[1-{\&Integral;}_0^{W_i}{f}_i\left(t\right)\mathrm{dt}]\left\{{\&Integral;}_{W_i}^{T_i}{\mathrm{tg}}_i\left(t\right)\right[1-{\&Integral;}_{W_i}^t{f}_i\left(u\right)\mathrm{du}\left]\mathrm{dt}\right\}\end{array}$

Step 204, utilizes the expect cost of parts i and the average maintenance scale of charges of life expectancy calculating unit.

The average maintenance scale of charges of parts i is:

$Z_i(W_i,T_i)=\frac{E_i\left[C\right]}{E_i\left[T\right]}$

Step 205, computing system average cost rate, Optimized model, makes system average cost rate minimize.

$\left\{\begin{array}{cc}\mathrm{Min}& Z(W,T)={\mathrm{\&Sigma;}}_{i=1}^N\frac{E_i\left[C\right]}{E_i\left[T\right]}\\ s.t.& 0<W_i\&le;T_i\end{array}\right.$

In formula: W=(W ₁, W ₂..., W _n)

T＝(T ₁，T ₂，...，T _N)。

In sum; difference is fixed maintenance cost and is taken into account opportunity maintenance model by a kind of opportunity maintenance method considering that fixing maintenance cost is different of the present invention; thus make opportunity maintenance model have usable range widely, be specially adapted to the complication system of the different stop times that different faults causes.

Above-described embodiment is illustrative principle of the present invention and effect thereof only, but not for limiting the present invention.Any those skilled in the art all without prejudice under spirit of the present invention and category, can carry out modifying to above-described embodiment and change.Therefore, the scope of the present invention, should listed by claims.

Claims (8)

1. consider to comprise the steps: the opportunity maintenance method that fixing maintenance cost is different

Step one, the replacement probability of calculating unit i, comprises failure replacement probability, chance replacement probability, preventive replacement probability;

Step 2, the maintenance cost expectation value of the fixing maintenance cost calculating unit i of trouble unit utilizing described failure replacement probability, chance replacement probability, preventive replacement probability and dead loss expense, breakdown maintenance cost, preventative maintenance expense and offer an opportunity;

Step 3, the life expectancy of calculating unit i;

Step 4, utilizes the expect cost of parts i and the average maintenance scale of charges of life expectancy calculating unit;

Step 5, according to the average maintenance scale of charges computing system average cost rate of each parts, Optimized model, makes system average cost rate minimize.

2. a kind of opportunity maintenance method that fixing maintenance cost is different of considering as claimed in claim 1, it is characterized in that, described failure replacement probability is:

Wherein, f _it () represents the fault probability function of parts, g _iu the failure density function of remaining part in () expression system, W is maintenance threshold values, and T is preventative threshold values.

3. a kind of opportunity maintenance method that fixing maintenance cost is different of considering as claimed in claim 2, it is characterized in that, described chance replacement probability comprises two classes: the first kind is the fixing maintenance cost that the trouble unit fixed expense offered an opportunity is greater than parts i, and its chance replacement probability is equations of The Second Kind is the fixing maintenance cost that the trouble unit fixed expense offered an opportunity is less than in parts i, and its chance replacement probability is P _i{ o2}=[1- wherein, g _1i(t)=δ _iexp [-δ _i(t-W _i)], g _2i(t)=δ _iexp [-δ _i(t-W _i)], λ _fifor failure replacement rate, λ _pifor preventive replacement rate.

4. a kind of opportunity maintenance method that fixing maintenance cost is different of considering as claimed in claim 3, it is characterized in that, described preventive replacement probability is:

5. a kind of opportunity maintenance method that fixing maintenance cost is different of considering as claimed in claim 4, it is characterized in that, described maintenance cost expectation value is:

E _i[C]＝P _i{f}*(C _fi+C _oi)+P _i{o1}*C _pi+P _i{o2}*(C _pi+C _oi-C _oj)

+P _i{p}*(C _pi+C _oi)

Wherein, C _oifor dead loss expense, C _fifor breakdown maintenance cost, C _pifor preventative maintenance expense, C _ojfor the fixing maintenance cost of trouble unit offered an opportunity, P _i{ f} represents that parts i carries out the probability of failure replacement; P _i{ o1} represents that parts i obtains the probability of opportunity maintenance, and this chance is greater than the fixing maintenance cost of parts i by the trouble unit fixed expense offered an opportunity; P _i{ o2} represents that parts i obtains the probability of opportunity maintenance, and this chance is less than the fixing maintenance cost in parts i by the trouble unit fixed expense offered an opportunity.

6. a kind of opportunity maintenance method that fixing maintenance cost is different of considering as claimed in claim 5, is characterized in that, in step 3, the life expectancy in the replacement cycle of parts i is:

7. a kind of opportunity maintenance method that fixing maintenance cost is different of considering as claimed in claim 6, it is characterized in that, in step 4, the average maintenance scale of charges of parts i is:

8. a kind of opportunity maintenance method that fixing maintenance cost is different of considering as claimed in claim 7, it is characterized in that, in step 5, Optimized model is:

Wherein, W=(W ₁, W ₂..., W _n), T=(T ₁, T ₂..., T _n).