Question

Reliability & Maintenance Tbay University has set up printing stations on campus, which are currently maintained by their Tech Service Unit. The table below recorded the breakdowns over past months under the current maintenance policy.

Number of breakdowns 0 1 2 3 4 5

Monthly frequency of breakdowns 4 8 5 2 1 0

Each breakdown would cost an average of $200 for repairs. The printer manufacturer has recently approached to the university for a $250 monthly service contract, in which they guarantee repairs on any breakdowns.

What is the expected number of breakdowns per month with the maintenance by Tech Service Unit?

Answer 1

The expected number of breakdowns per month with maintenance by Tech Service Unit is 1.4, determined by calculating the weighted average from the recorded frequencies of breakdowns over the past months.

Step-by-step explanation:

To determine the expected number of breakdowns per month with maintenance by Tech Service Unit, we need to calculate the weighted average of breakdowns based on the given frequencies. Here's the data:

• 0 breakdowns - 4 times
• 1 breakdown - 8 times
• 2 breakdowns - 5 times
• 3 breakdowns - 2 times
• 4 breakdowns - 1 time
• 5 breakdowns - 0 times

The expected number of breakdowns (E) is calculated using the formula:

E = (0*4) + (1*8) + (2*5) + (3*2) + (4*1) + (5*0)

E = 0 + 8 + 10 + 6 + 4 + 0

E = 28 breakdowns over 20 months, so:

E = 28 / 20 = 1.4 breakdowns per month

The reliability of the printing stations with the current maintenance scheme averages to 1.4 breakdowns per month.