As one of the four key functions related to reliability engineering, the reliability function is often confused or misunderstood. Let’s spend a few minutes exploring the reliability function and how to use it.
Reliability generally means that the product or item is durable. This involves the passing of time and the continued useful functioning of the product. Reliability has a careful definition that includes function, environment, probability, and duration. It is the probability element of reliability that is where the reliability function comes to play.
The reliability function mathematically defines the probability over the duration. It is a function of time (or cycles, or miles, or whatever unit of time passing makes sense). It is a coupling of probability and time. Always.
The function starts with all items working or 100% functioning at time zero. Time zero is when the unit is placed into service. We often describe the idea with 100 units started at time zero and they are all working. And over time, eventually, all the units fail. When the last unit fails, the reliability function is 0%. We can also say the reliability function ranges from 1 to 0.
A common question that the reliability function answers is “how many units will survive over the warranty period?”. If a product operates 24/7, it will operate 8760 hours in a year. R(t) becomes R(8760 hours) and depending on the particular life distribution the formula differs. The result, in this case, provides the probability of units surviving 8760 hours. Let’s say this is 0.78. The 0.78 (78%) means that 78 out 100 are expected to survive 8760 hours. It also can mean that one unit has a 78% chance of surviving out to 8760 hours.
78 out of 100 customers in the above example are expected to experience product failure. That may or may not be acceptable. That is a business decision.
Now back to the idea of reliability and some of the confusion. Reliability is not just the probability of success or failure rate. It involves the other elements of the definition of reliability, function, environment and duration, too. Simply using MTBF (a representation of failure rate) does not include duration and implies function and environment. To avoid confusion, I recommend always thinking about all four elements and specifically stating the couplet of probability and duration as the reliability function suggests, a function that describes the probability of success as a function of time, R(t).
Rather than setting a single product reliability goal, I recommend setting three. One for the early failure period, R(one month), and, the warranty period, R(1 year), and, for the expected useful or design life, R(5 years). The examples here, one month, 1 year, and five years vary depending on the technology, market, customer expectations, and business objectives. The goals provide an envelope to describe the reliability objectives. It also provides three points, possibly tied to business and customer needs, that describe a curve related to the reliability function.
As the product is developed and tested, and eventually fielded, the information should be compared to the reliability goals. The data creates a mathematical description of the time to failure or reliability function. From this function we can calculate the number of units that survived a period of time of interest.
The Four Functions (article)
Reliability Goal (article)
Series reliability question (article)