Reliability

NPHS 1530: Analytics

Reliability

Lesson Outline
Introduction	20 minutes
Series System Reliability	30 minutes
Parallel System Reliability	20 minutes
n of N Parallel Component Reliability R_n/N	30 minutes
Complex Series/Parallel System Reliability	40 minutes
Factors Affecting Reliability	15 minutes
Reliability in Design	20 minutes

Objectives

The purpose of this lesson is to establish an in-depth understanding of the concept of reliability in the context of emergency situations. The lesson will present the mathematical basis for reliability theory. The goal is not for the student to learn the math but through doing the math the student will develop skills and knowledge to design reliability into and enhance the reliability of exiting emergency and mission critical systems.

Reliabilty

The concept of reliability is ubiquitous in our everyday life. Perfect reliability is, in practice, unattainable. We have systems that we require to have very high reliability. For example:

Critical infrastructure
Electrical
Water supply
Communications
Financial
Food
Transportation
Emergency

Some examples:
When we flip our light switch, we expect the lights to go on.
When we turn the tap, we expect water to flow.
When we drop a letter into the mailbox or hit SEND on our email or our text system, we expect the message to go through.
We expect to have the ATM working and available.
We expect the grocery store to have shelves stocked.
When we turn the key we expect the car to start. We expect the roads to be open.
We expect Emergency Services to respond as quickly as possible when we dial 911.

A key question is "How much reliability is enough?" We can answer this question from the perspective of a rational economic decision maker. "How much are we willing to spend to achieve a higher reliability".

From an operational standpoint we can take a simple view that a system is in a state of either working (reliable, R) or not working (failed, F). Since these are mutually exclusive and collectively exhaustive:

R = 1 - F

System costs can be separated into two categories:

Costs associated with failure (expected costs)
Costs related to preventing or mitigating failure (out of pocket costs)

Consider the case of a small convenience store.

Failure costs include damage, loss of business, reduced customer goodwill, etc.(C_F)

For a natural disaster (i.e. storm) reliability potential costs (C_R) include backup generators, reinforced construction, insurance, etc.

For a man-made emergency (e.g. theft, vandalism, etc.) (C_R) potential costs include walls/fences, razor wire, alarm systems, barred windows, surveillance cameras, armed guards, pull-down gates, police patrols, etc.

In our rational economic model the expected cost of failure should equal the cost spent to achieve reliability.

C_R = F * C_F

In other words, if I expect failure costs to be $1 million and the failure liklihood to be once per 3 years, then I should be willing to spend $300,000 on enhanced reliability in that same period. If I have a conservative economic posture, then I should be willing to pay more.

Preparation

Before taking the sections on decision making and risk, please read the following:

Reading

Evaluating the Reliability of Emergency Response Systems for Large-Scale Incident Operations, Brian A. Jackson, Kay Sullivan Faith, Henry H. Willis, RAND Corporation, 2010.

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