A company purchased and installed 1000 identical relays for use in radio transmi

Question

A company purchased and installed 1000 identical relays for use in radio transmitters. The company maintained detailed records on the failure pattern of the relays in the field as shown below in the attached table. Answer the following questions using the data provided in this table: The probability that a capacitor chosen at random lasts more than 8 years. Assuming an exponential distribution, estimate the value of A and calculate the expected number of failures for each year. Prove that exponential failure distribution has no memory. Substantiate your results with the date given in the table also. The proportion of capacitors that survive 3 years those also survive at least three additional years. For a system with k components in parallel, the expected lifetime of the system is increased by [1/((k + 1)*lambda)] by adding one additional component.

Explanation / Answer

Probability column calculated such that we have given total 1000  transmitters company installed and outof that number of failures transmitters, then the probability column = Number of failures / 1000.

a]

Probability that a capacitor chosen at randam lasts more than 8 years.

Pr ( X > 8) = Pr (X = 9) + Pr ( X = 10) + Pr (X >10)

= 0.035 + 0.025 + 0.09

= 0.15

Number of years of operation Number of failures Probability of Failures 1 230 0.23 2 160 0.16 3 125 0.125 4 90 0.09 5 80 0.08 6 75 0.075 7 50 0.05 8 40 0.04 9 35 0.035 10 25 0.025 > 10 90 0.09

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