Question

A Subway shop evaluated its reliability for each of its processes and showed the following:

Service                                                Reliability Percentage

Baking Bread                                                  .97

Cutting Bread for sandwich                          .88

Selecting proper meats/cheese                  .95

Selecting proper vegetables/sauces         .92

Cutting sandwich and wrapping                 .98

Compute the over-all reliability of preparing a sandwich correctly (round to 2 decimals):

Answer 1

To calculate the reliabiility of a system firs step is to note if there are any sub systems that work together and can be the backup if in case one part of the subsystem fails.

In this case all the operations are in series (performed one after other) and there are no replacements to the performed functions this means the reliability of the system will be calculated as follows:

0.97 * 0.88 * 0.95 * 0.92 * 0.98 = 0.73

Thus, The reliability of the system is 0.73. Now to understand the concept behind reliability calculation look at the following examples:

For example: If there are two machines with 0.90 reliability and they both perform the same function such that any one of the machines could be used to generate the output then the total reliability of the system would be calculated as:

1-probability of the whole system failing

1-(probability of 1st machine failing * probability of 2nd machine failing)

1-[(1-Reliabulity of 1st machine) * (1-Reliabulity of 2nd machine)]

1-[(1-0.9)*(1-0.9)]

1-[0.01]

0.99 this is the reliability of the system

Now consider another example where the two machines with 0.9 reliability are in series and they perform independent function such that the whole system will shut down even if one of the machined will break. In this case reliabuluty will be measured as:

Reliabulity of 1st machine * Reliabulity of 2nd machine

0.9*0.9

0.81 will br the reliability of the whole system.