TWI807427B - Real-time system reliability evaluation method - Google Patents

Abstract

A real-time system reliability evaluation method, the method adapted to a factory that includes a plurality of workstations to be implemented using a computing device, each of workstations has a plurality of machines, each of machines is related to a time period, the time period has N time points, N is positive integer and N ≧ 2, the method comprising steps of: (a) the computing device calculates machine reliability of each machine in each time points of the N time points according to a Weibull distribution (b) the computing device calculates the corresponding state probability of each workstation in multiple states according to a binomial distribution and the reliabilities of the machines, and generates a capacity probability table (c) the computing device calculates the capacity probability table and a minimal system level vector using a recursive sum of disjoint products to obtain a system reliability.

Description

Real-time System Reliability Evaluation Method

The invention relates to a system reliability evaluation method, in particular to a real-time system reliability evaluation method.

Most of the previous technologies are related to reliability assessment and system reliability monitoring, including defining system reliability assessment methods and monitoring methods. Prior art focuses on reliability calculation under different constraints. Four examples are listed below: the first example is to evaluate the reliability of the system under the given transmission time limit; the second example is that at different time points, the distribution of the probability of nodes being able to successfully transmit or fail is different; the third example is to calculate the probability that the system can complete the transmission as the reliability; the fourth example is to consider a computer network. When data is transmitted due to accidents such as voltage instability, magnetic field or lightning, packet transmission may be missed. In the event of an error, a backup transmission path can be used to maintain the operation of the entire system.

However, the prior art has the following disadvantages: it does not take into account that the component reliability will deteriorate with time, so the probability distribution of the components in each state does not change with time, but is fixed. Such considerations do not correspond to reality, and the resulting reliability assessment is thus inaccurate.

Therefore, the object of the present invention is to provide a real-time system reliability evaluation method under consideration of time operation when each component will be damaged.

Therefore, the real-time system reliability evaluation method of the present invention is implemented by a computing device to be applicable to a factory. The factory includes a plurality of workstations, each workstation includes a plurality of machines, and each machine is associated with a time period. The time period includes N time points, N≧2, and N is a positive integer. The method includes the following steps (a) to (c).

Step (a) The calculation device calculates the machine reliability of each machine at each time point of the N time points according to a reliability probability function of Weber distribution.

Step (b) The computing device calculates the state probabilities corresponding to each workstation in a plurality of states according to a binomial distribution formula and the reliability of the machines, and generates a production probability table, and these states are related to the available number of machines

Step (c) The computing device substitutes the capacity probability table and a minimum system-level vector into a probability calculation algorithm for calculation to obtain a system reliability. The minimum system-level vector is related to the minimum number of machines to satisfy an order.

The effect of the present invention is that: according to the reliability probability function of the Weber distribution The time parameter is included in the reliability of the machine for consideration, and then according to the binomial distribution formula and the reliability of the machines, the state probability corresponding to each workstation in multiple states is calculated to obtain the production probability table, and the production probability table and the minimum system-level vector are substituted into the probability calculation algorithm for calculation, and the system reliability is obtained. The reliability of the system will decline over time, which is consistent with the realistic results.

100~104: Steps to find out the minimum system is the vector

201~205: Steps to calculate the system reliability at each time point

Other features and effects of the present invention will be clearly presented in the implementation manner with reference to the drawings, wherein: Fig. 1 is a flow chart of an embodiment of the real-time system reliability evaluation method of the present invention; Fig. 2 is a flow chart of the embodiment; Fig. 3 is a network topology diagram of the workstation operation of a factory of the embodiment; and Fig. 4 is a relation diagram of a system reliability and time of the embodiment.

Before the present invention is described in detail, it should be noted that in the following description, similar elements are denoted by the same numerals.

Referring to FIG. 1 , FIG. 1 is a flowchart illustrating the steps of an embodiment of the real-time system reliability assessment method according to the present invention, starting from step 100 . The instant system of the present invention The system reliability evaluation method is implemented by a computing device and is suitable for a factory. The factory includes a plurality of workstations, each workstation includes a plurality of machines, and each machine is related to a time period. The time period includes N time points, N≧2, and N is a positive integer.

In step 101, a computing device calculates according to a current-carrying vector network model to obtain a demand rate. The current-carrying vector network model includes an order demand D and a time period t.

Referring to FIG. 3, FIG. 3 is a topological diagram of a workstation operation network of a factory in this embodiment. The factory is a shoe factory. a ₁ ~ a ₂₀ are the workstations of the factory, which can be called arcs (arc) in statistics. a ₁ ：縫製鞋舌頂部及鞋舌底部(stitch tongue top & tongue bottom)、a ₂ ：縫合繫帶環(stitch lace loop)、a ₃ ：縫製鞋舌頂部及鞋舌襯裡(stitch tongue top & tongue lining)、a ₄ ：黏合鞋舌底部(cement tongue bottom)、a ₅ ：黏貼鞋舌頂部及鞋舌底部(stick tongue top & tongue bottom)、a ₆ ：通過馬赫捶平鞋舌頂部及鞋舌底部(hammer flat by mach tongue top & tongue bottom)、a ₇ ：滾動鞋舌泡棉(rolling tongue foam)、a ₈ ：滾動鞋舌(rolling tongue)、a ₉ ：黏貼鞋舌泡棉及翻鞋舌襯裡(stick tongue foam & turn over tongue lining)、a ₁₀ ：通過馬赫捶平鞋舌(hammer flat by mach tongue)、a ₁₁ ：縫鞋舌邊線(stitch edge line tongue)、a ₁₂ ：縫製肩裡和鞋領口襯(stitch quarter lining & collar lining)、a ₁₃ ：使鞋面及鞋身側片內外腰彎曲(zigzag vamp & quarter med lat)、a ₁₄ ：縫合接縫(stitch seams foxing)、a ₁₅ ：通過馬赫捶平肩裡和鞋領口襯(hammer flat by mach quarter lining & collar lining)、a ₁₆ ：通過馬赫捶平且黏合接縫(cement and hammer flat by mach foxing)、a ₁₇ ：黏貼尼龍(stick nylon)、a ₁₈ ：剪裁鬆緊帶(cut elastic lace)、a ₁₉ ：縫製鞋眼攀帶至鞋眼片(stitch eyestay lat loop to eyestay)、a ₂₀ ：將鞋眼攀帶打孔(punching eyestay lat loop)。

The current-carrying vector network model includes the demand of the order D=50,000 pairs of shoes, and the time period t=50 hours. The demand rate d=D/t=50000/50=1000, that is to say, in order to satisfy the current-carrying vector network model, 1000 pairs of shoes need to be produced per hour.

，並滿足f_j

L_j，

，j=1,2,...,m，i是正整數，表示工作站的排序，W_i是正整數，表示在第i工作站的所有機台數，k_i表示在第i工作站的機台對應的產能，a_i表示第i工作站，P_j表示第j工廠。 In step 102, the calculation device calculates according to the demand rate d and the output corresponding to each machine, and obtains all feasible solutions of the flow vector F=(f ₁ , f ₂ , ... , f _m ). The flow vector F is related to finding the value closest to the minimum value of the product of the number of machines in each workstation and the output corresponding to each machine. The current-carrying vector network model also includes a factory quantity and a workstation quantity. The flow vector F=(f ₁ , f ₂ , ... , f _m ), m is a positive integer representing the number of factories, and all feasible solutions of the flow vector satisfy

, and satisfy f _j

L _j ,

, j=1,2,...,m, i is a positive integer, indicating the sorting of workstations, W _i is a positive integer, indicating the number of all machines at the i-th workstation, k _i is the corresponding production capacity of the i-th workstation, a _i is the i-th workstation, and P _j is the j-th factory.

Table 1 is the data of each workstation and the table of Weber parameters. α and β are Weber parameters obtained from historical data.

3×420；i=2，f₂

5×280；i=3，f₃

6×230；...；i=20，f₂₀

6×240。有一可行解F=(f₁)=(1000)。 Referring to Figure 3 and Table 1, the number of factories is 1, and the number of workstations is 20. Then the flow vector F=(f ₁ ). i=1, f ₁

3×420; i=2, f ₂

5×280; i=3, f ₃

6×230;...;i=20, f ₂₀

6×240. There is a feasible solution F=(f ₁ )=(1000).

。在步驟104中，該運算裝置利用一向量比較法找尋該等最小系統級向量的候選者X中的最小系統級向量。該向量比較法是相關於一向量空間中， 各向量彼此比較大小之方法。 In step 103, the computing device converts all feasible solutions of the flow vector F into a plurality of minimal system level vector (MSLV) candidates X=(x ₁ , x ₂ , ... , x _n ), n=1,2,...,i. The candidate X for each minimum system-level vector is related to the ratio of the flow vector to the output corresponding to each machine. Components of candidate X for each smallest system-level vector

. In step 104, the computing device uses a vector comparison method to find the smallest system-level vector among the candidates X of the smallest system-level vectors. The vector comparison method is related to the method of comparing the sizes of the vectors with each other in a vector space.

3；i=2，

；i=3，

；...；i=1，

。該最小系統級向量X₁=(x₁ ,x₂ ,...,x₂₀)=(3,4,5,5,4,3,3,4,4,3,3,3,3,4,4,4,4,3,4,5)。參閱圖2與表1，是該實施例的一流程圖。在步驟201中，該運算裝置根據一韋伯分配之可靠度機率函數計算每一機台在該N個時間點的每一時間點下的機台可靠度。該步驟201中的韋伯分配之可靠度機率函數即該機台可靠度

，i是正整數，表示工作站的排序，t^*是每一時間點，α、β是韋伯參數，預設同一工作站下的每一機台可靠度是一樣的。利用For迴路(For Loop)計算t*=1小時，每一工作站的每一機台可靠度，如下所示。

；

；r₃(1)=

；...；

。t^*=2小時，每一工作站的每一機台可靠度，如下所示。

；

；

；...；

。 Referring to FIG. 3 and Table 1, since there is only one factory, there is no need to use the comparison method to find the minimum system-level vector among the candidates X of the minimum system-level vectors. The feasible solution F=(f ₁ )=(1000) is transformed into the minimum system-level vector X ₁ =(x ₁ , x ₂ , ... , x ₂₀ ) that satisfies the requirement of producing 1000 pairs of shoes in one hour. It should be noted that the component _xi of the minimum system-level vector X ₁ is the smallest integer that can meet the requirement of producing 1000 pairs of shoes in one hour. The minimum system-level vector X ₁ may also be referred to as the minimum capacity lower bound vector in the factory. i=1,

3; i=2,

;i=3,

;...;i=1,

. The minimum system-level vector X ₁ =(x ₁ , x ₂ , ... , x ₂₀ )=(3,4,5,5,4,3,3,4,4,3,3,3,3,4,4,4,4,3,4,5). Referring to FIG. 2 and Table 1, it is a flow chart of this embodiment. In step 201, the calculation device calculates the machine reliability of each machine at each time point of the N time points according to a reliability probability function of Weber distribution. The reliability probability function of the Weber distribution in the step 201 is the machine reliability

, i is a positive integer, indicating the order of workstations, t ^* is each time point, α, β are Weber parameters, and the reliability of each machine under the same workstation is assumed to be the same. Use For Loop to calculate t*=1 hour, the reliability of each machine at each workstation, as shown below.

;

; r ₃ (1) =

;...;

. t ^* = 2 hours, the reliability of each machine for each workstation, as shown below.

;

;

;...;

.

，y_i是非負整數，表示在第i工作站的可工作機台數，W_i是正整數，表示在第i工作站的所有機台數，該產能機率表即是計算每一工作站在多個狀態下分別對應的狀態機率的結果。t^*=1小時的產能機率表

，i=1,2,...,20；y_i=0,1,...,W_i，如以下的表2。 In step 202, the computing device calculates state probabilities corresponding to multiple states of each workstation according to a binomial distribution formula and the reliability of the machines, and generates a production probability table, and the states are related to the available number of machines. The binomial distribution in step 202 is the state probability corresponding to each workstation in multiple states

, y _i is a non-negative integer, indicating the number of workable machines at the i-th workstation, W _i is a positive integer, indicating the number of all machines at the i-th workstation, and the productivity probability table is the result of calculating the state probabilities corresponding to each workstation in multiple states. t ^* = Production probability table for 1 hour

, i=1 , 2 , ... , 20; y _i =0 , 1 , ... , W _i , as shown in Table 2 below.

，i=1,2,...,20；y_i=0,1,...,W_i，如以下的表3。 t ^* = 2 hour capacity probability table

, i=1 , 2 , ... , 20; y _i =0 , 1 , ... , W _i , as shown in Table 3 below.

，d表示該需求率，k是正整數，表示工廠數量，X_r表示第r工廠的最小系統級向量。t^*=1小時的系統可靠度

。在步驟204中，判斷該時間點t^*是否小於最終時間點t，若是，則回到步驟201，繼續疊代，若否，則在步驟205中，輸出每一時間點的系統可靠度，也就是系統可靠度隨時間變化的資料，如圖4所示。 In step 203, the computing device calculates the production probability table and the minimum system-level vector using a recursive sum of disjoint products (RSDP) to obtain a system reliability. The minimum system-level vector is related to the minimum number of machines that satisfy the order. The system reliability in step 203

, d represents the demand rate, k is a positive integer representing the number of factories, and X _r represents the minimum system-level vector of the rth factory. t ^* = System reliability for 1 hour

. In step 204, it is judged whether the time point t ^* is smaller than the final time point t, if yes, return to step 201, and continue to iterate, if not, then in step 205, output the system reliability at each time point, that is, the data of system reliability changing with time, as shown in Figure 4.

Referring to Figure 4, the reliability of the system will decline with time, which is in line with the actual results. Taking the reliability of the system as an indicator, the threshold value of the reliability of the system is set according to the operating conditions of each factory, which can be used as the basis for maintenance or not.

To sum up, the above embodiments have the following advantages: the reliability of the system considers the time factor, so the reliability of the system will decline with time, which is in line with the actual results. Achieving efficacy is that the system reliability is a performance index of system capacity management. Managers can use this index to evaluate the possibility of the system fulfilling order requirements under limited conditions, and then adjust capacity or instant maintenance.

But the above are only embodiments of the present invention, and should not limit the scope of the present invention. All simple equivalent changes and modifications made according to the patent scope of the present invention and the content of the patent specification are still within the scope of the patent of the present invention.

201~205: Steps to calculate the system reliability at each time point

Claims (7)

A real-time system reliability evaluation method is implemented by a computing device to be applicable to a factory. The factory includes a plurality of workstations, each workstation includes a plurality of machines, and each machine is related to a time period. The time period includes N time points, N≧2, and N is a positive integer. The current-carrying vector network model is calculated to obtain a demand rate, and the current-carrying vector network model includes the demand of an order and the time period; (s2) the computing device calculates according to the demand rate and the output corresponding to each machine, and obtains all feasible solutions of the flow vector. All feasible solutions of flow vectors are respectively converted into candidates of a plurality of minimum system-level vectors, each candidate of the minimum system-level vector is related to the ratio of the flow vector to the output corresponding to each machine; and (s4) the computing device uses a vector comparison method to find the minimum system-level vector among the candidates of the minimum system-level vectors; (a) the computing device calculates the machine reliability of each machine at each time point of the N time points according to a reliability probability function of Weber distribution; (b) the computing device calculates the state probabilities corresponding to each workstation in a plurality of states according to a binomial distribution formula and the machine reliability, and generates a capacity probability table, and the states are related to the available number of machines; and (c) the computing device calculates the capacity probability table and the minimum system-level vector using a recursive disjoint method to obtain a system reliability, and the minimum system-level vector is related to the minimum number of machines that satisfy the order. The method for evaluating real-time system reliability as described in claim item 1, wherein, the reliability probability function of the Weber distribution in the step (a) is the reliability of the machine

, i is a positive integer, indicating the order of workstations, t ^* is each time point, α, β are Weber parameters, and the reliability of each machine under the same workstation is assumed to be the same. The instant system reliability evaluation method as described in request 2, wherein, the binomial distribution formula in the step (b) is the state probability corresponding to each workstation in multiple states

, y _i is a non-negative integer, indicating the number of workable machines at the i-th workstation, W _i is a positive integer, indicating the number of all machines at the i-th workstation, and the productivity probability table is the result of calculating the state probabilities corresponding to each workstation in multiple states. The instant system reliability evaluation method as described in claim 3, wherein, the system reliability in the step (c)

, d represents a demand rate, k is a positive integer representing the number of factories, and X _r represents the minimum system-level vector of the rth factory. The real-time system reliability evaluation method as described in claim item 1, wherein the demand rate d=D/t in the sub-step (s1), D represents the demand quantity of the order, and t represents the time period. The instant system reliability evaluation method as described in claim item 5, wherein, the flow vector F=(f ₁ , f ₂ , ... , f _m ) in the sub-step (s2), m is a positive integer representing the number of factories, and all feasible solutions of the flow vector satisfy

, and satisfy f _j

L _j ,

, j=1,2,...,m, i is a positive integer, indicating the sorting of workstations, W _i is a positive integer, indicating the number of all machines at the i-th workstation, k _i is the corresponding production capacity of the i-th workstation, a _i is the i-th workstation, and P _j is the j-th factory. The instant system reliability assessment method as described in Claim 6, wherein, in the sub-step (s3), each candidate of the minimum system-level vector X=(x ₁ , x ₂ , ... , x _n ), n=1, 2, ..., i, the components of each minimum system-level vector candidate

.

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