An engineering topic that catch my interest  is reliability engineering. It mainly because of this topic seems to have intimate relation with safety engineering, maintenance engineering, can be implemented with enterprise resource software, and use mathematical modeling as its tools.

According to wikipedia, reliability engineering is an engineering field that deals with the study of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time.

Hm .. sounds interesting. But how could we quantify the “ability”? Are there any performance indicator that can help us to indicate that one system is more reliable than the other? What are tools, preferrably mathematical tools, that we can used to analyze the reliability of a complex system? How can we improve reliability, given a not reliable system. It seems that we need to give a more “formal “treatment. Here I try to explain in formal fashion, or better to say: to re-write, by mainly refer to [1]

Definition 1.1 (reliability): Reliability is the probability that a device will operate successfully for a specified period of time, and under specified conditions when used in the manner, and for purposes, intended.

Theorem 1.2 (series system): The system reliability $R_s$ for $n$ devices connected in series is $R_s = R_1 times R_2 times ... times R_n$, where $R_n$ is the reliability of the $n$th components.

Example 1.3:  The following figure is the simple example of control system loop

Let $R_x$ is the reliability of system $x$. Given the probabilityof failure over a 10-year period is 0.25 for the transmitter, 0.05 for the controller, and 0.3 for the valve. Thus, according to Definition 1.1:

$R_{transmitter} = 1-0.25 = 0.75$

$R_{controller} = 1-0.05 = 0.95$

$R_{valve} = 1-0.3 = 0.7$

According to Theorem 1.2 then the complete system reliability for the next 10 years is:

$R_{system} = R_{transmitter} times R_{controller} times R_{valve} = 0.75 times 0.95 times 0.7 = 0.499$

To be continued …

References

1. Cheddie, H.L., Reliability Engineering Concepts, in Instrument’s Engineer Handbook: Process Software and Digital Networks, Liptak, B.G-Editor in Chief, CRC Press, 2000

2. As one of the resource from the computer science point of view, I find a nice course by prof. Stefan Kowalewski from RWTH Aachen on Safety and Reliability Engineering. The video presentation are also provided on the website.