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Case study B: sensors unit of an HVAC

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R ELIABILITY A LLOCATION : T HEORY

5.10. Case study B: sensors unit of an HVAC

124

Finally, TABLE V. XIII shows the reliability allocation results using the developed iterative approach. As a result, lower reliability is allocated to components with high influence factors.

TABLE V.XIII

OUTPUT OF THE PROPOSED APPROACH FOR CASE STUDY A(WEIGHT FACTORS IN COMPLIANCE WITH 6-PARAMETER MEOWA).

BRANCH ALLOCATED RELIABILITY 1 0.878770 0.849513 0.853435

2 0.852271 0.861832 0.856324 0.846346 3 0.753006 0.797406

4 0.605013

5 0.906414 0.903343 0.921514 0.913622 0.908997

This case study highlights the huge benefits that are achievable using the conditional parameter, in particular when RA procedures are assessed during design phase with imprecise, incomplete or uncertain pieces of information.

The tool calculates also the failure rate to be apportioned to each item, assuming that all the blocks of the system are single elements and not subsystems in turn. Fig. 5 shows an example of the tool outcomes containing the simulation results for MEOWA technique.

125 The system is basically composed by two redundant branches. The top branch includes two temperature sensors in parallel configuration (identified by reliability R1 and R2) and three pressure transmitters in 2oo3 configuration (identified by reliability R3 R4 and R5). This branch also includes a series element called voter unit used to elaborate the output of the pressure sensors in 2oo3 architecture. The voter (identified by reliability R6) must diagnose any anomalies in the sensors output and guarantee the proper output in case of failure of one sensor. An example of application of voter system is illustrated in Fig. 5.12 considering three sensors S1, S2 and S3. In such case, the output of the 2oo3 architecture is equal to the intermediate value among the output of the three sensors. In case of failure of one single sensor (fail-to-low condition), the voter detect the failure and reconfigure the output which continue to be reasonable despite the failure of one sensor.

Fig. 5.12. Example of application of voting system in 2oo3 architecture.

Moving back to the RBD in Fig. 5.11., the second branch is composed by a single unit used for redundant and safety issues. Component R7 is a safety device able to measure temperature and pressure of the refrigerant gas and communicate the measurement data to the central unit. In case of failure of the main sensors included in the top branch, the safety device R7 provides redundant information to ensure continuity of service.

The system reliability goal to achieve through the Reliability Allocation procedure has been set as 95% reliability at the end of the HVAC life cycle, which is estimated after 20 years.

π‘…π‘…π‘†π‘†π‘†π‘†π‘†π‘†βˆ—(π‘‘π‘‘π‘Žπ‘Ž)|π‘‘π‘‘π‘Žπ‘Ž=20 π‘π‘π‘˜π‘˜π‘Žπ‘Žπ‘˜π‘˜π‘π‘= 0.95 (5.104) Time

Output of the sensors

Sensor S1 Sensor S2 Sensor S3 Voter Output

Failure of Sensor S3

126

The first step required to allocate the component reliability to the sensor unit of the HVAC under analysis is the system decomposition into hierarchical levels, as illustrated in Fig. 5.13. In this case, three different levels have been identified.

The top level is a simple parallel configuration between the first branch (equivalent item EQ1which stands for the temperature and pressure sensors) and the safety device R7.

Then, the second level includes the series configuration between the equivalent item EQ2, the equivalent item EQ3 and the voter unit R6.

Finally, the third level is used to model the two parallel temperature sensors and the 2oo3 configuration composed by three pressure transmitters.

Fig. 5.13. System decomposition of case study B into three hierarchical levels.

Also in this case, the influence factors of the 6-parameter MEOWA method have been used to evaluate the weight factors of the components. The complete assessment of the influence factors is reported in TABLE V.XIV.

Note that the same factors have been assigned to items R3, R4, and R5 because they are considered in 2oo3 configuration.

127 TABLE V.XIV

INFLUENCE FACTORS ACCORDING TO 6-PARAMETER MEOWA USED TO IMPLEMENT THE PROPOSED METHOD ON CASE STUDY B.

ITEM INFLUENCE FACTORS 𝐂𝐂 𝐄𝐄 𝐀𝐀 𝐊𝐊 𝐌𝐌 𝐑𝐑

R1 6 5 10 4 10 4

R2 8 5 6 5 6 5

R3 - R4 - R5 5 5 7 4 6 6

R6 3 2 3 2 4 2

R7 7 4 2 1 2 1

The estimation of the influence factors for the equivalent subunits according to the proposed model as in equations (5.62)-(5.68) is reported in TABLE V.XV.

TABLE V.XV

ESTIMATION OF THE INFLUENCE FACTORS FOR THE EQUIVALENT SUBUNITS. LEVEL ITEM ITEM USED TO

ASSESS THE FACTORS

INFLUENCE FACTORS 𝐂𝐂 𝐄𝐄 𝐀𝐀 𝐊𝐊 𝐌𝐌 𝐑𝐑

2nd level EQ2 R1 - R2 8 5 8 4 8 4

EQ3 R3 - R4 - R5 5 5 7 4 6 6 Top level EQ1 REQ2 - REQ3 - R6 8 5 6 2 7 2

Following the procedure illustrated in the previous case study (section 5.9), the item reliability has been allocated at the top hierarchical level (i.e. parallel configuration between equivalent unit EQ1 and component R7) using the proposed approach for parallel configuration as in section 5.8.3.2. The results varying the situation parameter Ξ± are illustrated in Fig. 5.14 where the reliability allocated to the safety unit R7 and to the top branch EQ1 are compared with system reliability goal (red dashed line).

As it is possible to see in Fig. 5.14, the extremely low influence factors of the safety unit R7 led to higher reliability with respect to the reliability of the equivalent unit EQ1 regardless the value of the situation parameter Ξ±.

The following step is the allocation of reliability requirements to the 2nd hierarchical level using the results of the equivalent unit EQ1 as input target.

In this case, model for series configuration has been implemented as in section 5.8.3.1. The results achieved varying the situation parameter Ξ± are illustrated in Fig. 5.15.

128

Fig. 5.14. Reliability allocated at the top hierarchical level of case study B varying the situation parameter Ξ±.

Fig. 5.15. Reliability allocated at the second hierarchical level of case study B varying the situation parameter Ξ±.

Finally, the procedure is repeated at the 3rd hierarchical level considering the two different architectures left.

Firstly, the proposed model for parallel configuration as in section 5.8.3.2. has been used to allocate reliability requirements to components R1 and R2 (parallel temperature sensors) starting from the reliability results achieved for the equivalent unit EQ2.

129 Then, the proposed model for k-ot-of-N configuration as in section 5.8.3.3. has been used to allocate reliability requirements to the 2oo3 architecture composed by the pressure transmitters R3, R4 and R5 starting from the results of the equivalent unit EQ3.

The overall results achieved for the seven considered items varying the situation parameter Ξ± are illustrated in Fig. 5.16. Note that the reliability of the three pressure transmitters has been illustrated using a single line (yellow trend).

This is due to the fact that the proposed RA procedure assigns the same reliability to all the items making up a 2oo3 configuration as required by the initial hypotheses of the k-out-of-N architectures.

What stands out from Fig. 5.16 is the extremely high reliability values assigned to both the voter unit (R6) and the safety instrumentation unit (R7). This is due to the very low influence factors assigned to both components.

Fig. 5.16. Results of the reliability allocation procedure to Case study B considering the proposed models.

The reliability results varying the situation parameter as in Fig. 5.16 are extremely helpful to designer during the allocation process. However, at the end of the procedure is necessary to provide a reliability at a certain time. In this case, according to equation (5.104) the allocation time has been set equal to π‘‘π‘‘π‘Žπ‘Ž= 20π‘π‘π‘˜π‘˜π‘Žπ‘Žπ‘˜π‘˜π‘π‘ = 175200 β„Ž.

Considering a situation parameter 𝛼𝛼 = 0.85 the reliability allocated to each component π‘…π‘…π‘£π‘£βˆ—(π‘‘π‘‘π‘Žπ‘Ž) is included in TABLE V.XVI.

130

TABLE V.XVI

RESULTS OF THE ALLOCATION PROCESS FOR CASE STUDY B: RELIABILITY VALUES. ITEM ALLOCATED RELIABILITY

AT 𝐭𝐭𝐚𝐚= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝐚𝐚𝟐𝟐𝟐𝟐

R1 0.6414731

R2 0.6439310

R3 - R4 - R5 0.7957998

R6 0.9403383

R7 0.8136760

Then, according to the final step of the proposed procedure (as in section 5.8.4) it is necessary to estimate the failure rate of the components making up the system. The temperature sensors (R1 and R2) and the pressure transmitter (R3, R4 and R5) are electronic components that can be easily described by an exponential failure distribution. Similarly, also the voter unit can be approximated to a constant failure rate item. Thus, the failure rate of such items can be estimated using equation (5.87). The results achieved for these components are reported in TABLE V.XVII. The unit of measurement of the failure rate is FPMH (Failure Per Million Hours).

TABLE V.XVII

ALLOCATED FAILURE RATE TO COMPONENTS OF CASE STUDY B THAT FOLLOW THE EXPONENTIAL FAILURE DISTRIBUTION.

ITEM ALLOCATED FAILURE RATE

R1 2.5341783 FPMH

R2 2.5123499 FPMH

R3 - R4 - R5 1.3036969 FPMH

R6 0.3511166 FPMH

After that, it is necessary to find a component on the market that allows to achieve the requirements as in TABLE V.XVII. Taking the temperature and pressure sensors as an example, the certification of the component failure rate under exponential failure distribution of many distributors are available on the Safety Automation Equipment List (SAEL) of the Exida certification company.

Quite the opposite, the safety unit used as redundant source of information about both temperature and pressure data is a complex equipment that could

131 be better described by a Weibull failure distribution. Thus, according to the proposed procedure as in section 5.8.4 an accelerated life test plan is required to ensure that the allocated reliability of the unit R7 as in TABLE V.XVI will be satisfied.

5.11. Case study C: lube oil console for Oil&Gas

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