I. The Human Resource Office of an Organization processes payroll in three t app
ID: 435216 • Letter: I
Question
I. The Human Resource Office of an Organization processes payroll in three t approval, payment authorization. All steps: time sheet submission, time sheet three steps must function properly for an employee to be paid on time. Pas data indicates the first step is completed promptly 96% of the time, the second 89% of the time, and the third 68% of the time. a. Compute the reliability of the payroll system -i.e. determine the likelihood that employees will be paid on time. A backup group of human resource officials who are equal in performance to the first will be added to help ensure timely payment. The backup group will be alerted promptly most of the time by a designated employee if the first payroll system does not complete their tasks promptly. In the past the designated employee has proven to be 85% reliable. Including this backup, what is the reliability that employees will be paid on time? Show your calculations. b.Explanation / Answer
a) The three steps are in series. This makes the process to have a reliability of a serial system. Now on a serial system, the reliability of the total system is calculated by the product of the reliability of each component.
This means that the likelihood that employees will be paid on time is
0.96*0.89*0.68 = 0.58 or 58%
b) A backup group will add redundancy to the system and put the process in parallel. In parallel processes we need to calculate reliability by first calculating the probability of failure. We know that the probability of success of the previous arrangement is 0.58. This makes the probability of failure to 0.42. With another backup we have a total probability of failure as
0.42*0.42 = 0.176
This means the probability of success is 1-0.176 = 0.8236 or 82.36%.
Now there is another factor. This success rate is only possible if the designated employee gives the signal successfully. His reliability is 85% or 0.85. This means the total success reliability of this backup arrangement is
0.8236*0.85 = 0.7 or 70%