R ELIABILITY A LLOCATION : T HEORY
5.11. Case study C: lube oil console for Oil&Gas systems systems
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
132
π π ππππππβ(π‘π‘ππ)|π‘π‘ππ=5 ππππππππππ= 0.9 (5.105)
In compliance with the proposed iterative approach, the first step of the procedure consists in the decomposition of the system RBD into different hierarchical levels. Each level must be assembled by a unique reliability architecture, such as series, parallel, standby or k-out-of-n. The decomposition of the lube oil under test is illustrated in Fig. 5.17, highlighting four levels.
Fig. 5.17. System decomposition of case study C into four different hierarchical levels.
The top level corresponds with the equivalent series architecture of the system under test, which means that each redundant block is grouped in a single equivalent series item. Then, the redundancies grouped in the top level are decomposed in the 2nd level. For instance, the 2oo3 PDIT item in the top level become the actual 2-out-of-3 architecture in the 2nd level. Quite the same the 1oo2 TIT and the 1oo2 FILTERS items. Instead, the pump unit is a more complex architecture that requires four decomposition levels. The 2nd level is composed by a cold standby architecture including the Pump Unit 1 (main unit) and the Pump Unit 2 (standby unit). Then, each unit is divided into a series configuration of three components: motor, pump and PSV. In particular, the Pump Unit 1 is composed by the main pump, the main PSV and the motor unit 1, while the Pump Unit 2 is composed by the auxiliary pump, the auxiliary PSV and the motor unit 2. Finally, the 4th level includes the decomposition of the motor units into a warm standby configuration each one including an active and a standby motor.
Seven influence factors (namely Complexity C, Environmental factor E, State of the Art A, Operative Time T, maintainability M, criticality K and safety
133 R) have been evaluated for each one of the components included in the RBD of the system under test based on expertβs judgments. Using these factors, it is possible to allocate the component reliability using many existing techniques, such as FOO, arithmetic AWM, 4-parameter MEOWA and 6-parameter MEOWA. The complete assessment report is included in TABLE V.XVIII.
TABLE V.XVIII
INFLUENCE FACTORS USED TO ASSESS THE WEIGHT FACTORS OF EACH COMPONENT INCLUDED IN THE CASE STUDY C.
ITEM C E A T M K R
PDIT 5 10 5 10 6 4 9
LIT 4 10 5 10 6 2 8
TIT 5 10 5 10 6 2 8
Heater 1 10 5 6 6 4 7
Main Pump 9 6 5 8 10 4 2
Main Motor 7 2 5 7 8 5 3
Std-by Motor 6 2 5 3 8 4 3
Main PSV 5 8 5 8 4 4 4
Aux Pump 9 4 5 2 10 1 1
Aux Motor 7 2 5 2 8 4 2
Std-by Motor 2 6 2 5 1 8 1 2
Aux PSV 5 4 5 2 4 1 4
PIT 5 8 5 10 3 2 8
PCV_1 3 8 5 10 4 1 8
TCV 3 8 5 10 3 2 6
TIT_1 5 8 5 10 3 5 9
TIT_2 5 8 5 10 3 5 9
PDIT_F 5 8 5 10 3 2 8
Main Filter 2 6 5 8 2 9 5
Std-by Filter 2 6 5 2 2 7 5
PCV_2 3 8 5 10 4 1 8
FAN 3 2 5 7 3 4 7
Analyzing the main motor and the standby motor it is easy to understand how the allocation is weighted in case of standby redundancy. The main motor is a more complex item working for longer period; therefore it is characterized by a higher complexity C and a higher Operating time O with respect to the standby motor. Moreover, it has also a higher criticality K which means it is a less critical component due to the presence of the standby unit. Such considerations have been drawn in order to extend the applicability of the RA process to standby redundancies according to the proposed method as in section 5.8.3.4.
134
The influence factors of the equivalent units can be estimated considering the principle of the βworst-case scenarioβ as detailed illustrated in section 5.8.2.
The results of the assessment are included in TABLE V.XIX.
TABLE V.XIX
INFLUENCE FACTORS OF THE EQUIVALENT UNITS: CASE STUDY C.
LEVEL UNIT ITEM USED TO
ASSESS THE FACTORS C E A T M K R 3rd Motor Unit 1 Main Motor - Std-by
Motor 7 2 5 7 8 4 3
3rd Motor Unit 2 Aux Motor - Std-by
Motor2 7 2 5 2 8 1 2
2nd Pump Unit 1 Main Pump - Motor
Unit1 - Main PSV 9 8 5 8 7 4 2
2nd Pump Unit 2 Aux Pump - Motor Unit2
- Aux PSV 9 4 5 2 7 1 1
TOP 2oo3 PDIT PDIT - PDIT - PDIT 5 10 5 10 6 4 9
TOP Pumps Unit Pump Unit 1 - Pump
Unit 2 9 8 5 8 7 1 1
TOP 1oo2 TIT TIT_1 - TIT_2 5 8 5 10 3 5 9
TOP 1oo2 Filters Main Filter - Std-by
Filter 2 6 5 8 2 7 5
The following steps require to calculate the weight factors and the allocated reliability to the component included in the top hierarchical level. The procedure has been repeated considering the weight factors of four different approaches:
β’ FOO method based on Complexty C, Environmental factor E, state of the art A and operative time O.
β’ 4-parameter MEOWA based on the same influence factor as FOO method.
β’ Arithmetic AWM based on Complexty C, Environmental factor E, state of the art A, Maintainability M, Criticality K and Safety R.
β’ 6-parameter MEOWA based on the same influence factor as arithmetic AWM.
The weight factors estimated for each hierarchical level in case of Arithmetic AWM and FOO methods are included in TABLE V.XX.
135 TABLE V.XX
WEIGHT FACTORS OF ARITHMETIC AWM AND FOO ASSESSED FOR DIFFERENT LEVELS.
136
Obviously, it is important to take into account that in case of series configuration the weight factor could be estimated directly using the equations proposed in each method, while in case of parallel configuration equations (5.69) - (5.70) must be used. Moreover, the 2oo3 configuration has been dealt with the method proposed in section 5.8.3.3. while the standby redundancies have been dealt with during the influence factors assessment as required by the method proposed in section 5.8.3.4.
Using the reliability target in equation (5.105) it is possible to calculate the reliability of the items composing the top hierarchical level simply applying the weight factors in TABLE V.XX to equation (5.71) since the top level is a series configuration. Then, in case of redundancies, the results achieved at the previous steps are used as reliability target for the evaluation of the component reliability at the 2nd level. In this case, it is important to evaluate the allocated reliability using the correct formula, such as Equation (5.71) in case of series architecture, equations (5.74) - (5.76) in case of parallel configuration or standby redundancies, and equations (5.84) - (5.85) in case of k-out-of-n configuration. Then, the same approach is repeated consecutively to the subsequent hierarchical levels, every time considering the results of the next higher level as input reliability target.
Fig. 5.18 shows the results of the procedure applied using the reliability models based on four influence factors, i.e. FOO and 4-parameter MEOWA. Quite the same, Fig. 5.19 shows the results of the procedure applied using the reliability models based on six influence factors, i.e. Arithmetic AWM and 6-parameter MEOWA.
Fig. 5.18. Reliability allocated using the proposed method to the components that make up the lube oil console by means of FOO and 4-parameter MEOWA.
0.5 0.6 0.7 0.8 0.9 1
Allocated Reliability Ri*(ta)
FOO 4-parameter MEOWA
137 Fig. 5.19. Reliability allocated using the proposed method to the components that
make up the lube oil console by means of Arithmetic AWM and 6-parameter MEOWA.
The FOO model cannot allocate the correct reliability to some critical components, such as the main motor, the main pump and the main PSV. In fact, using this model the impact of a great standby redundancy unit lead to untrustworthy reliability results for the main unit. Quite the opposite, MEOWA and AWM methods provides comparable results.
Finally, it is important to consider that there is a large uncertainty associated with known values of reliability parameters in commercially available devices.
The accelerated test (using for example temperature, vibration or humidity stress factors) proposed as final loop of the procedure presented in this work could provide more accurate reliability data about commercial components available on the market.