Operational reliability analysis applied to a gas turbine based on three parameter Weibull distribution

The first objective in gas and oil project is to increase efficiency in the use of equipment, with down time reduced and their startup with the application of sophisticated methods of exploitation to increase the life service of the used equipment. This work presents the development of tools for decision support, based on operational reliability analysis of the exploited equipment in oil installations, for the determination of maintenance actions. These equipments are subject to degradation mechanisms due to the operating conditions and / or environment: wear, fatigue, aging and various physic-chemical changes [1-3]. Given to these resulting failures, it is sufficient to perform robust reliability methods. In this paper, is more protective to implement the Weibull distribution to optimize the running time of an exploited gas turbine, deciding to intervene just in time, in the oil installations. For contribute to the development and the analysis of reliability of this system and to improving maintenance strategy for future applications. Nowadays, modern gas and oil installations are becoming more complex, at the same time, reliability, availability, and dependability have become very important and they are real challenges for businesses today. The reliability study appeared in order to improve the availability of its systems, from reliability models; these models can be static, such as fault trees, or behavioral, exploitable using analytical methods [4-7]. Several studies have been made in the literature to develop reliability methods, based on different information available to describe the behavior of systems. Moreover, the work developed in recent years by Osama Ashour et al, 2012 [8], Tung-Liang Chen, 2009 [9] Wenbin Dong et al, 2012 [10], Wenbin Dong et al, 2013 [11], have also invested in this area by developing a general methodological framework for modeling system reliability, to the implementation of its models in the planning of the maintenance strategy. In deterministic approaches developed in several studies [1, 12-14], the reliability is the system resistance to sustained loads is assumed to be known and time-invariant, regardless of the type of system. In fact, this capacity may differ depending on the type of equipment, and for various reasons; changes in system properties, dimensional tolerances and other factors that affect the conduct of a component or a system composed of several components, error in the manufacturing process [15-17]. In addition, the operating conditions are not, they either perfectly determined, these two elements of uncertainty, load and capacity, make random the proper functioning of the system. This work deals with a qualitative and quantitative analysis of operational reliability for the safe operation of gas and oil installations. Through a number of historic features and equipment used in gas and oil industry, by the examination of a gas turbine in our experimental investigation. The developed model was validated for different situations, to help the operator in design and optimize the reliability of the gas turbine studied. The studied approach in this work was validated by experimental testes to confirm their effectiveness.


Introduction
The first objective in gas and oil project is to increase efficiency in the use of equipment, with down time reduced and their startup with the application of sophisticated methods of exploitation to increase the life service of the used equipment.This work presents the development of tools for decision support, based on operational reliability analysis of the exploited equipment in oil installations, for the determination of maintenance actions.These equipments are subject to degradation mechanisms due to the operating conditions and / or environment: wear, fatigue, aging and various physic-chemical changes [1][2][3].Given to these resulting failures, it is sufficient to perform robust reliability methods.In this paper, is more protective to implement the Weibull distribution to optimize the running time of an exploited gas turbine, deciding to intervene just in time, in the oil installations.For contribute to the development and the analysis of reliability of this system and to improving maintenance strategy for future applications.
Nowadays, modern gas and oil installations are becoming more complex, at the same time, reliability, availability, and dependability have become very important and they are real challenges for businesses today.The reliability study appeared in order to improve the availability of its systems, from reliability models; these models can be static, such as fault trees, or behavioral, exploitable using analytical methods [4][5][6][7].Several studies have been made in the literature to develop reliability methods, based on different information available to describe the behavior of systems.Moreover, the work developed in recent years by Osama Ashour et al, 2012 [8], Tung-Liang Chen, 2009 [9] Wenbin Dong et al, 2012 [10], Wenbin Dong et al, 2013 [11], have also invested in this area by developing a general methodological framework for modeling system reliability, to the implementation of its models in the planning of the maintenance strategy.
In deterministic approaches developed in several studies [1,[12][13][14], the reliability is the system resistance to sustained loads is assumed to be known and time-invariant, regardless of the type of system.In fact, this capacity may differ depending on the type of equipment, and for various reasons; changes in system properties, dimensional tolerances and other factors that affect the conduct of a component or a system composed of several components, error in the manufacturing process [15][16][17].In addition, the operating conditions are not, they either perfectly determined, these two elements of uncertainty, load and capacity, make random the proper functioning of the system.This work deals with a qualitative and quantitative analysis of operational reliability for the safe operation of gas and oil installations.Through a number of historic features and equipment used in gas and oil industry, by the examination of a gas turbine in our experimental investigation.The developed model was validated for different situations, to help the operator in design and optimize the reliability of the gas turbine studied.The studied approach in this work was validated by experimental testes to confirm their effectiveness.

Industrial systems reliability
Reliability is the characteristic of a system expressed by the probability that perform the function for which it was designed, in given conditions for a given period [18,19].The lifetime of a industrial system is measured by the number of hours they actually worked, is a non-negative random variable, from which the act of degradation of the system can be determined.The equation (1) expresses the probability ( ) P t that the lifetime T of the industrial system is comprised between t and dt t + .

( ) ( )
with ( ) f t is the probability density associated to the life- times.As for the distribution of lifetimes ( ) F t and relia- bility function ( ) R t , they are related by the Eq. ( 2): ( ) ( ) The failure rate ( ) r t is the function to character- ize the degradation law system.This is the conditional probability of failure per unit time of a system that survived until t .However, the law of degradation of an in- dustrial system is completely defined by the knowledge of one of these four characteristics.For our application, we will use Weibull distribution, this law has the advantage of being very flexible and able to adjust to different experimental results [6,20].The reliability of a system expressed by Weibull is given by the following equation: with β is the shape parameter (unitless), η is the scale parameter (unit of time) and γ is the location parameter or origin (unit of time).For repaired equipment is intended to be reused after refurbishment, the reliability or the failure rate is a basic feature less common but nonetheless indispensable.Indeed, the failure rate reflects the frequency of failures that is not the availability (and this frequency becomes constant).The reliability is not enough to define the efficiency of a system; we must measure the availability when the system is multi-component and repair.The Fig. 1, shows that availability can be improved by an increase in average uptime through reliability and a lower average time to repair for maintainability.In the literature, there are several strategies to periodic replacement [3,6,14,18], those age when substitutions are made to the failure and after units of time without failure and those with block-replacements at predetermined times, regardless of age and type the condition of the equipment.In these strategies, the average repair time decreases as the preventive actions generally better prepared and faster, just reduce the need for corrective actions.

Industrial application
In this work, we consider a gas turbine type GE MS3002 installed in Hassi R'Mel, Algeria gas plant, shown in Figs. 2 and 3, used in the gas pipeline network activities to transport the gas along Hassi R'Mel pipeline.The objective of this work is to make an analysis of operational reliability, based on data feedback, to allow a better exploitation of the examined gas turbine.The entire turbine con-Fig. 2 Rotor failure in examined gas turbine  sists of three main components: the axial compressor, the combustor and turbine.This system is operated at about 50% of their maximum speed to maintain the compression cycle.The energy cost becomes very high when operating the compressor at idle or at low load.

Application results
The examined gas turbine at the Hassi R'Mel, Algeria are MS 5002 model, they are used to drive multistorey centrifugal compressors, where the data has been collected from the history of the studied gas turbine is given in Table 1.
From the times between failures (TBF), the general expression to calculate the average uptime MTBF is given by the flowing relation:  that is important to determine the number of classes.This rule varies the integer r classes or intervals to be based on the number n of data, we can determine the number of classes as follows:  ( ) ( ) with i n is the number of failures until time i t and N is the number of blackouts.
For the probability of failure and the non failure probability was given by the Table 3.To determine the failure rate in the examined gas turbine, we used the follows equation: with i n is the number of failures during s t ∆ and t N is the number of survirants early time slot i t , ie. it is the total number of failures decreased the number of failures to previous time ( ) Using the Eq. ( 2) and the history of the examined gas turbine in t ∆ time interval observed, we obtained the failure rate as Table 4 In this case the fit test is request, the failure rate results have tested using the Kolmogorov-Smirnov fit test, it consists in comparing the absolute error given by the difference between the actual and the theoretical static function, with ∞ , η ∆ reference selected, depending on the number total of failures η , knowing that the latter is the samples size of η with α risk of error.Assuming a risk of the absolute error between the actual and the theoretical function, we used the fit test as follows: with the function is given by 1 + n i , which i is the order of i t and n is the total number, in the examined system is 40.
The set function is given by: ( ) Effectively change the variable , by taking into account that ( ) ( )  5.

Table 5 Results of the standard deviation
. Therefore, it is confirmed that Weibull distribution is appropriate for the distribution of failures in the studied gas turbine GE MS5002, using the median ranks to determine the Weibull parameters of the law for the MTBF and to determine the associated reliability of the examined gas turbine.The Figs. 4, 5 and 6 showed the results of Weibull distribution with tow parameters for the sample times to failure, using the historical failure data of the investigated gas turbine.In Fig. 4 the evolution of the reliability function of the examined gas turbine GE MS5002 using Weibull with two parameters is shown, in Fig. 5 the cumulative failure using Weibull distribution with tow parameters of the examined system is presented, the results are given by two different curves in one graph, the first curve in continuous line represent the fitting tests using compared data by Sturge's rule in the second curve shown by discontinuous line.And the Fig. 6 showed the hazard function using Weibull distribution with tow parameters, this hazard function given the force of mortality in the examined gas turbine.The Figs. 7, 8 and 9 showed the results of Weibull distribution with three parameters for the sample times to failure, using the historical failure data of the investigated gas turbine.The Fig. 7 present the evolution of the reliability function of the examined gas turbine GE MS5002 using Weibull distribution with three parameters, in Figure 8 the cumulative failure using Weibull distribution with three parameters of the examined system is shown, the results are given by two different curves in one graph, the first   9 showed the hazard function using Weibull distribution with three parameters, this function given the survivor function of the examined gas turbine From the obtained results, we confirm that the reliability of the studied gas turbine for t = 2160 h, corresponding to the length of effective market for a quarter (3 months).The gas turbine GE MS5002, operate without failure for 3 months with a probability of 32.1%.

Conclusion
The developed model in this work, for operational reliability analysis applied to a gas turbine based on Weibull distribution with three parameters, was validated for different situations.The risk of the reliability error between the actual and the theoretical function of the examined system is equal to 05 0. = α is a very acceptable value.Also, the adequacy condition is equal to 194 0. D max = ∆ and after the fitting tests become 210 0. D max = ∆ , this confirms that Weibull distribution is appropriate for the distribution of failures in the studied gas turbine GE MS5002 in order to help the operator in design and optimize the reliability of the gas turbine.Indeed, the studied approach in this work, based on experimental investigation using Weibull distribution was validated by real tests to confirm their effectiveness.This work is carried out a proper analysis of operational reliability, based on data feedback to allow a better exploitation of the turbine.The proposed qualitative and quantitative analysis using operational reliability for the safe operation in oil and gas installations, using Weibull distribution with tow and three parameters give a good optimization of the operation of this system and meet the production in the examined installation.The used operational reliability found good results from a maintenance policy, which derive a planning revise (partial, full) and maintenance during this planning time.

Fig. 3
Fig. 3 Examined gas turbine in revision with the change in the functionality

.
According to the Sturges rule given in[12], to grouping in the order of magnitude of the amount of data Following these intervals time for each class for 40 items, easily we obtain the distribution of failures per class in the Table2.

Fig. 4 Fig. 6
Fig. 4 Reliability function using Weibull distribution with tow parameters of the examined gas turbine

Fig. 7 Fig. 8 Fig. 9
Fig. 7 Reliability function using Weibull distribution with three parameters of the examined gas turbine

Table 1
History data of the studied gas turbine MS 5002 model

Table 6
Results of the adequacy condition tests