Failure Frequencies of the Transmitter System of the Nigerian Television Authority (NTA), Uyo
Chapter One
AIMS AND OBJECTIVES OF THE STUDY
The basic aim of this research work is to model the failure rate of non-repairable systems using probabilistic techniques with the view to improving the reliability of such systems and develop a preventive replacement schedule for the systems.
The objectives are to:
- Obtain the probability functions associated with reliability measures, such as the failure density function, the failure distribution function, the reliability function and the hazard function.
- Obtain the reliability indices of the transmitter system which include; the mean time to failure (MTTF), the mean time between failures (MTBF), the mean time to repair (MTTR), the availability (AI), and the maintainability (M) of the system.
CHAPTER TWO
LITERATURE REVIEW
INTRODUCTION
The lognormal distribution is a probability density function commonly used to model the lives of units whose failures are of a fatigue-stress nature. It is sometimes used as a first approximation to the Landau distribution describing the energy loss by ionization of a heavy charged particle.
According to Mann et al (1973), the plausibility of the log normal distribution was empirically demonstrated for semiconductors by Howard and Dodson (1961) and also by Peck (1961). Its acceptability as a failure distribution was indicated by the life-test sampling plans developed for it, Gupta (1962).
The log normal distribution received relatively minor attention in the statistical literature until the 1970s, Mann et al (1973). This, according to them, was basically because its applicability was limited to some rare situations in small-particles statistics, economics and biology.
In spite of this, they discussed the lognormal distribution as a failure model of physical processes wherein failures are due to fatigue cracks. They assumed a proportional effect model for the crack growth, where the crack growth at stage i, xi – xi-1, is randomly proportional to the size of the crack, xi-1, and that the item fails when the crack size reaches xn.
Burges et al (1975) compared two methods of estimating the threshold parameters of the log normal distribution, one using the first three moments, the other substituting the median for the third moment. They concluded from a 1000 Monte Carlo samples of sizes 50 that the three-moment method gave a less biased and less variable estimator of the threshold parameters for samples encountered in the operational hydrology.
Kapur and Lamberson (1977) in “Reliability in Engineering Design” discussed the log normal distribution as a model for reliability and hazard function. They obtained the reliability measures, the mean and variance of the lognormal distribution.
Hallberg (1977) while working with failure rate as a function of time due to lognormal life distribution(s) of weak part, pointed to the presence of damages within a batch of components as the major cause of high initial failure rate which the decrease with time he assumed a lognormal failure rate (a log normal life distribution and developed a calculator program for easy computation, to predict the failure rate during normal use from data retained from life-test.
Stedinger (1980) reported a substantial Monte Carlo comparison of five different methods of estimating the two-parameter lognormal distribution and four different methods of estimating those of the three-parameter lognormal distribution. The criteria adopted were Root-Mean-Square error of 99% quantile pertinent to estimating the 100-year flood. The same for the 1% quantile pertinent to reliable yields of the reservoirs and the integrated-mean-square error of the whole distribution, also of interest for the reservoir yields. The superiority of the maximum likelihood method for the two- parameter case was confirmed except that there was a little difference for sample sizes as low as 10. For the three-parameter case, the results were not as clear cut but the use of three symmetric quantiles to estimate the threshold parameter only is recommended.
Reinius (1982) compared graphical methods of estimating flood flows using the lognormal model (log-Pearson Type III and Weibull being mentioned also). He proposed a new plotting position formula.
CHAPTER THREE
METHODOLOGY
INTRODUCTION
A handful of parametric models exist which have been successfully used as population models for failure times both for repairable and non-repairable system, arising from a wide range of products and failure mechanism. Examples of such models are exponential, weibull, gamma, and lognormal models. These distributions are exhibited by systems according to their mode of failure and or failure mechanism. Sometimes, there are probabilistic arguments based on the physics of the failure mode that tends to justify the choice of models. Other times, the models are used solely because of its empirical success in fitting actual failure data.
Based on the failure modes of systems, we will consider three different life distribution models as follows;
Firstly, we consider systems which has constant rate of failure, that is, the event of failure keeps happening at the same time interval e.g. the arrival rate of cosmic ray alpha particles. Here, we are interested in the random variable which is the interval between successive arrivals. Since the failures are random, it accords to the postulates of a Poisson process, hence the exponential model works well for such event, Kaminskiy and Krivtsov (1998).
Secondly, we consider a system whose components do not exhibit constant failure rate. Its operational efficiency degrades with time and usage. That is, it deteriorates or wears with usage like that found in ball bearings and machine/vehicle tyres. These types of failures are modeled using the Weibull distribution as discussed by Weibull (1951) in Mann (1973).
CHAPTER FOUR
DATA PRESENTATION, ANALYSIS AND INTERPRETATION
INTRODUCTION
In this chapter, we will analyze and interpret statistically, the result of the analysis of the lognormal model on the inter-failure times of the transmitter system, a typical non-repairable system with sudden but not constant failure attribute. We will also test for the goodness of fit of the lognormal model to the inter-failure times of the system.
PRESENTATION OF DATA
Table 3A shows the inter-failure times (in hours) of the transmitter system of the NTA Uyo with their corresponding failure dates.
THE GOODNES- OF-FIT TEST
Table 3D shows the observed frequency of failures of the transmitter system at the given intervals of time t.
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATIONS
INTRODUCTION
In this chapter, we shall give the summary of the findings based on the results of the analysis in the previous chapter.
We shall also make recommendations based on the results of the analysis to the NTA Uyo, and other users of transmitter system in other establishments, of which if strictly adhered to and properly made use of, will help to provide a preventive replacement schedule for the system and hence improve the reliability of the system.
SUMMARY OF FINDINGS
The following are the summary of the findings from the results of the analysis in this research work;
- The goodness-of-fit test shows that the empirical failure data of the transmitter system follow lognormal distribution, hence the application of the log normal model to our reliability study of the system.
- The failure rate of the transmitter system is log-normally distribution with mean = 7.7hours and 2 = 1.4hours.
- The mean time to failure (MTTF) of the transmitter system of the NTA Uyo, is approximately 4395 hours.
- The mean time between failures in the system is approximately 3393hours.
- The mean time to repair of the system after failure is approximately 115hours
- The availability of the system is approximately 97%.
- The maintainability of the system is approximately 3%.
RECOMMENDATIONS
Based on the findings of this research work, the following recommendations were made;
- That the NTA Uyo and other transmitter system users should preventively replace the mean time to failure(MTTF)= 4395 hours, to prevent failure maintenance which is usually costly than preventive maintenance.
- That the lognormal model gives a good fit for the failure rates of non-repairable systems with sudden but not constant failures and is therefore recommended for probability modeling of similar systems.
CONCLUSION
From the result in (3.3), this work shows that the reliability of the transmitter system of NTA Uyo can be improved by replacing the non- repairable component before 4395 hours of operation. Also, from the result of the Goodness- of -fit test, we conclude that the failure rates of non- repairable systems follow the lognormal distribution.
REFERENCES
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