Reliability Calculations in Excel

In Operations Management today we used Excel to calculate product reliability. Reliability is defined as "the ability of a product, service, part, or system to perform its intended function under a prescribed set of circumstances" (Stevenson, 2009). In order to calulate reliability over a given length of time we need to use the following formula:

P(no failure) = e-t/MTBF

where:

e = 2.7183
t = Length of service before failure
MTBF = Mean Time Between Failures

One of the cases we did in class involved an auto detailing company that wanted to calculate the reliability of its vacuum cleaners. Excel provides an "EXP" funtion that we can easily apply here. After entering all data for the problem as shown on the spreadsheet below, we type the formula =EXP(-A5/$B$2) in cell B5 and copy down. Next we plot the distribution for t=0 to the maximum life expectancy of 20 years using a line graph. What we end up with looks like a classic case of "exponential decay"...



Based on this this information, we can answer questions such as what is the probability that any one of these vacuums will:

Last one year? (Answer: 77.88%)

Last four years? (Answer: 36.79%)

Fail before four years? (Answer: 1-36.79% = 63.21%)

Last between two and five years? (Answer: 60.65%-28.65% = 32.00%)

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