Comparative Study to Estimate the Effect of Parameter and Reliability of the Exponential Distribution on the Failure time of the ATM using Bayes Method (Case study: A.T.M in Sudan)

Abstract

The consequent of non-application the reliability system on the ATM will lead to big problems which are non-increase of productivity and the lack of optimal utilization of machines and reflect on economic development. The aim of this paper is to apply lifetime models on the failure time of the automatic teller machine (ATM) in Sudan and estimate the parameter and reliability of the machines, in order to compare between machines. failure's data has been taken from Central Bank of Sudan, which is, type of machine, type of failure, Downtime, Uptime and outage duration in Hrs. during the period of time (1/1/2017-30/6/2017).The comparison between five machines selected randomly out of 28 machines have done. Through the lifetime models estimation (failure distribution, reliability, hazard rate, and mean time to failure (MTTF)), using Bayes method in estimate the parameters and reliability of exponential distribution. The comparison is executed through reliability values; from analysis results it is clear that, the failure time of all machines follow exponential distribution with one-parameter, according to the Kolmogorov-Smirnov test and Chi-Squared test for goodness of fit result. The machines no (B5 and B35) have high reliability compered by other machines. When we predict the reliability according to the time we found that the reliability decrease and hazard rate increase and there is relationship between MTTF and reliability. Finally to the extending of study span the authors recommended to include all types of ATM faults (out of cash and out of serves). Furthermore, the authors recommended that when expanding or adding a new machine, it is preferable to buy the machine with high reliability.