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Cycle availability of a system. In the jargon of system
Chapter 4, Problem 150E(choose chapter or problem)
Problem 150E
Cycle availability of a system. In the jargon of system maintenance, cycle availability is defined as the probability that the system is functioning at any point in time. The DoD developed a series of performance measures for assessing system cycle availability (START, Vol. 11, 2004). Under certain assumptions about the failure time and maintenance time of a system, cycle availability is shown to be uniformly distributed between 0 and 1. Find the following parameters for cycle availability: mean, standard deviation, 10th percentile, lower quartile, and upper quartile. Interpret the results.
Questions & Answers
QUESTION:
Problem 150E
Cycle availability of a system. In the jargon of system maintenance, cycle availability is defined as the probability that the system is functioning at any point in time. The DoD developed a series of performance measures for assessing system cycle availability (START, Vol. 11, 2004). Under certain assumptions about the failure time and maintenance time of a system, cycle availability is shown to be uniformly distributed between 0 and 1. Find the following parameters for cycle availability: mean, standard deviation, 10th percentile, lower quartile, and upper quartile. Interpret the results.
ANSWER:
Solution 150E
Step1 of 3:
Let us consider a random variable ‘X’ it presents the number of cycles availability.
Here X follows uniform distribution with parameters
Here our goal is:
1). We need to find mean,
2). We need to find standard deviation,
3). We need to find 10th percentile,
4). We need to find lower quartile, and
5). We need to find upper quartile.
Step2 of 3:
We know that X follows uniform distribution. That is,
X U(a, b)
X U(0, 1)
The probability distribution function of X is:
1). The mean of Uniform distribution is given by: