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This research determined time to failure rate and number of successful transaction of selected banks in Nigeria, using Log normal distribution. Transformation technique was applied to the log-normal model to obtain a quadratic equation or polynomial regression that assisted in determining the parameters of the log-normal model. In addition, one-way ANOVA was used to test for equality of the average (or mean) time to failure rate and average number of successful service time of the banks. The research fitted the log-normal models of the banks with the help of SPSS 21 statistical software and the result showed that GT-Bank model has the highest variation of 90.3% for number of successful service time (t), while Fidelity bank model has the highest variation of 56.6% for time of failure rate. The one-way ANOVA result of the number of successful service time (min) showed a significant difference. The Tukey comparison tests showed that GT bank is significant at 5% and 10% from other banks. Hence, the number of successful service time (min) were not the same for all the five banks. However, the one-way ANOVA result of the banks in term of number of Time to Failure (t) (min) showed no significant difference among the five banks.
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