Reliability based corrective maintenance activity timing.

Covo, Petar ; Grzan, Marijan ; Belak, Branko 等

Abstract: Corrective maintenance in the form of scheduled repairs has been increasingly used because of system reliability increase and a good maintenance technique. Mathematical presentation of a reliability indicator is related to the theory of probability and mathematical statistics. When reliability indicators are determined in practice, it is important that the causes of failure of any element in the series of components, based on which the conclusion on element reliability are made, are always the same. Such a series of components is statistically homogenous. Statistically homogeneous series may be realized in practice.

Key words: Reliability, Corrective Maintenance, Frequency of failures,

1. INTRODUCTION

Reliability can be fixed, assessed, extrapolated, predicted or actual, depending on the way in which the information on the reliability is formed. One of these versions is allocated to any reliability characteristics. The version "fixed" refers to the data obtained upon the inspection during which all the samples inspected were in operation. Version "assessed" refers to the data defined with an appropriate level of reliability and presents a limit of a reliability interval. Version "extrapolated" refers to the data on reliability under given operating conditions defined by extrapolation or interpolation of fixed or assessed data on the reliability under other operating conditions. Version "predicted" refers to the data calculated based on fixed, assessed or extrapolated reliability. Version "actual" refers to a data obtained upon the inspection during which all the samples stopped operating.

2. CORRECTIVE MAINTENANCE

Corrective maintenance is defined as a planned maintenance activity or as those activities caused by an operation failure of a system or a part of it. Corrective maintenance planned activity is a repair. As a rule there is a sudden system breakdown in case of a failure. After the failure, the failed component is replaced with a new one, or is repaired. In this case, the stochastic time of system part utilization causes also the stochastic failure duration time. These two times are interdependent. By this procedure, system part or a complete system is utilized until the final damage, i.e. the spare usability is used. Subsystem damages often result in the damages of other subsystems, so that total damages are considerably increased, especially with machinery (Baniae, N. & Eovo, P. 2006). A corrective approach to maintenance is the oldest form of maintenance and consists of numerous maintenance actions taken after the failure. This approach is called "wait and see".

The ship corrective maintenance is a base for a total utilization of system elements, and it application is decreasing, to be mainly carried out when a system element failure cannot adversely affect the crew, does not cause severe damages or breakdowns, does not cause long idle time, does not result in high costs and does not significantly influence the level of a system utilization. However, corrective maintenance in the form of planned repairs is increasingly used due to the reliability increase of a system and good maintenance technique.

During the system exploitation, the nominal characteristics are deteriorating and then the following actions should be taken: small, medium and general repairing actions. This is considered as the correction of a monitored element condition so to reach again the nominal characteristics in a radical way.

3. RELIABILITY INDICATORS

The concept of reliability indicators is related to a quantitative reliability expression issue (Eovo, P. 2007). This concept includes a quantitative characteristic of any feature that defines the reliability.

Quantitative data on reliability can be generally obtained in three ways. Firstly, the level of reliability can be determined based on the knowledge of component reliability and planned modes of operation. The reliability defined in this way is calculated reliability. Secondly, the data on reliability can be obtained in a laboratory. There are normal and accelerated, static and dynamic methods of reliability determination in laboratories. Tests are made in normal or special modes of operation. Thirdly, and also the most natural way to obtain data on reliability is based on the exploitation. A specific problem that arises in this case is the organization of data collection and their reliability.

The indicator selection generally depends on the system general application, but also the importance of functions that a system carries out can influence it. When selecting the reliability indicators of a technical system, attention should be paid to the following issues:

* Number of reliability indicators should be as small as possible, complex indicators obtained in the form of certain criteria groups should be avoided

* Reliability indicators selected must provide for possible checks in the designing stage

* Reliability indicators selected should be of a simple physical concept

* Reliability indicators selected must provide for statistical (experimental) assessment at special tests or against the exploitation results

* Reliability indicators selected must provide for the quantitative definition of reliability

System reliability prediction is a mathematical method based on experimentally determined data on component reliability. Depending on the aim defined and the level of development, the reliability prediction can be effected by following methods:

* Equipment similarity-based method,

* Prediction-based method,

* Loading-based method.

Equipment similarity-based method is applied when a system concept is created, and assesses the parameters of reliability that can be used in negotiations and setting up of technical requirements. As in the system content assessment there is only a function specification, and not the interactions forming that function, the reliability assessment is based on the reliability data of similar parts with similar functionalities. For this reliability prediction procedure a database, which will be used at a system definition outline when the elements have not been defined yet, but it is known what functions the system should met, is, of course, necessary. This assessment procedure should be carefully affected, with more alternative solutions and with a certain reserve, as there are technical requirements that should be fulfilled at designing.

Method of reliability prediction based on element listing enables a designer to compare the elements with identical functions, but with different execution. However, this prediction technique does not provide data on overloading of single elements, as the calculation method is based on average failure intensity for an appropriate class and type of element. This means that the designer uses this method as an orientation at optimizing, and as information on the quality, how many elements and which type of configuration he may use at most for his construction to meet the reliability requests.

Method of loading is used with the method based on element listing and is related to a specific calculation of a single element loading. The purpose of this method is to detect overloaded elements enabling other solutions to be taken for such cases already during designing, and also to make more realistic assessment of now already known specific environmental and operating conditions effects according to the device electrical and thermal stresses.

3.1. Functions of failure distribution, reliability and failure frequency

If T is a stochastic variable that indicates the time when a failure occurs, then the failure probability in the time function will be:

P(T [less than or equal to] t) = F(t) [greater than or equal to] 0 (1)

Function F(t) is called the failure distribution function and it shows the probability that a system will fail until time t. In the probability theory this function is known as a cumulative distribution function.

If system reliability is defined as the probability of a non-failure operation in the time interval t, it can be written:

R(t) = 1 - F(t) = P (T > t) (2)

Where R(t) indicates a reliability function.

Failure frequency function is indicated as f(t), and based on basic laws from the probability theory it can be written:

f(t) = dF(t)/dt (3)

According to the probability theory, this function is known as probability frequency function. Based on the above equations, an equation for reliability function can be written as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

Consequently, it is enough to know the form of f (t) function to get the reliability function R (t) (Eovo, P. 2007).

4. CONCLUSION

When defining the functions of failure frequency, failure intensity and reliability based on empirical data, two approaches may be employed:

* Choice of one of statistical distributions that is the most suitable for a given system (based on theoretical views and experience), or

* Determination of so-called empirical function of distribution frequency [f.sub.e] (t) based on the data given.

In the first approach, adopted distribution for data indicates that both failure intensity function and reliability function will be valid. This is the best method that should be used whenever possible. Of course, it may be checked whether the data collected comply with the adopted distribution, and if necessary select more appropriate distribution taking into consideration data collected for the previous period while the analysis and prediction are made for the next one, i.e. to the end of the system usage. Further data collection can be used for new corrections of the adopted distribution parameters or the correction of adopted parameters.

Empirical function of failure frequency is determined by considering n of the system and measurements made in time intervals of At duration, taking in consideration that when starting from t = 0 in any time t there are n(t) correct systems or elements. Adequate functions and failure frequency and intensity are determined by following equations:

[f.sub.e](t) = N([DELTA]t)/n[DELTA]t (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

Where:

n - total number of observed systems (elements) at t=0, [DELTA]t- time interval in which a reliability change is analyzed, N([DELTA]t)- total number of systems (elements) failed within the observed time interval,

n(t)- correct number of systems (elements) until time t, i.e. at the end of [DELTA]t interval.

Empirical function of reliability Re(t) and function of unreliability Fe(t) of the system are determined by equations:

[R.sub.e] (t) = n - N(t)/n = 1 - N(t)/n = n(t)/n (7)

[f.sub.e](t) = N(t)/n (8)

Where: n - total number of observed systems (elements) at t=0,

N(t)- total number of systems (elements) failed until the moment t,

N(t)- correct number of systems (elements) until time t.

For a practical analysis it is important that fe(t) presents the measurement of total rate of failure occurrence, while ee(t) is the measurement of current rate of failure occurrence. The choice of time intervals At is not strictly specified and depends on a specific problem. Generally, intervals may be of different or same duration. Optimal number of equal intervals k may be determined based on the number of failures N(t) using the following expression:

k = 1 + 3,3 log n (9)

Interval width At is determined against:

[DELTA]t [t.sub.max] - [t.sub.min]/1 + 3,3 log n (10)

Where: [t.sub.max.] - time when the latest system (element) failure occurred,

[t.sub.min]-time when the first system (element) failure occurred,

n-number of monitored systems (elements) at t=0.

5. REFERENCES

Eovo. P. (2007). Maintenance Model Interaction..., University of Rijeka, Rijeka

Baniae, N. & Eovo, P. (2006). Efficiency of maintenance, 12th International Conference HDO, Maintenance 2006, Rovinj