Question

1. A factory line has three lathe processing stations 1, 2, and 3, with reliabilities of 0.99, 0.96, and 0.93, respectively. The lathe stations are arranged so that if one breaks down, the others will stop working as well. To increase the reliability of the production line managers are experimenting two different plans. Plan A involves adding an identical backup line in series layout, and plan B is to provide backup in parallel layout for each machine. In either case, three additional machines (1, 2, and 3) would be used with reliabilities equal to the original three.

1. Which plan will provide higher reliability? Show your reasoning and calculations.

2. Explain why the two reliabilities are not the same.

3. What other factors might enter into the decision of which plan to adopt?

Answer 1

A. Which plan will provide higher reliability? Show your reasoning and calculations.

Reliability is a broad term that focuses on the ability of a product to perform its intended function. Mathematically speaking, assuming that an item is performing its intended function at time zero, reliability can be defined as the probability that it will continue to perform its intended function without failure for a specified period under stated conditions

Plan A involves a series system which means the system works only if all the component works. The status of the series function is given by the equation:

, Series reliability = Reliability of Device 1 * Reliability of device 2 * Reliability of Device 3

that is series reliability = 0.99 *0.96*0.93 = 0.88

Plan B involves a parallel system which means the system works even if at least one component is working. The parallel system can be indicated using the function

Parallel Reliability = 1- [(1- Reliability of Device 1 )(1-Reliability of Device 2)(1- Reliability of Device 3)

that is parallel reliability = 1-[(1-0.99)(1-0.96)(1-0.93)

= 1-[0.01*0.04*0.07]

= 1- 0.000028

Parallel system reliability = 0.999

So the plan B reliability is better

Question b.Explain why the two reliabilities are not the same.

The two reliabilities are not the same since one is a series system that needs all the components of a system to work simultaneously. The second reliability is a parallel system which needs only any one of the component to work

Question c. What other factors might enter into the decision of which plan to adopt?

The other factors which enter into the decision are

• Minimal Path set(MPS)- Minimal Path set is the subset of the component of the system such that operation of all the component in the subset implies the operation of the system
• Minimal Cut Set(MCS)-Minimal cut set is the subset of the component of the system such that failure of all the component in the subset does not imply the operation of the system