Reliability Concept

[As of April, 2011]

Reliability and Time

Of the three factors discussed in the section "Defining and Quantifying Reliability,"spatial conditions and the definition of failure for each device are constant. Therefore, reliability can generally be defined as a function of time (t).
Reliability concerns the normal functioning of a product over time, while quality mainly concerns the normal functioning of a product initial stage (at time 0).
Reliability, as described above, is expressed as a probability value with time as a variable. Depending on whether the product is a component or system and depending on its purpose and application, the following functions can be used as measures of reliability quantification.

1. Reliability (or Reliability Function)   R(t)
   This function defines reliability as the ratio of non-defective units after t hours of use to the total number of units at the start of use, i.e., the product survival rate. It is expressed as:
   
   
   
2. Non-Reliability (or Cumulative Failure Distribution)   F(t)
   This equation calculates the Cumulative Failure Rate from time 0 to time t. Its distribution complements that of R(t), as shown in Figure 1.
   

   

   Figure 1 Relationship Between Reliability and Non-Reliability

   
   
   
   
3. Failure Density Function   ƒ (t)
   This is the differential of the cumulative failure rate F(t) with respect to time. It shows the rate of failure increase at time t.
   
   
   
   Reliability and cumulative failure rate can be expressed in terms of ƒ(t) as follows:
   
   
   
   
4. (Instantaneous) Failure Rate (or Hazard Rate)   λ (t)
   This represents the rate of failure per unit time at time t.
   
   
   
   Reliability can be expressed in terms of λ (t) as follows:
   
   
   
   According to the MIL standard, failure rate is expressed as "%/1000h" using 1000h as the unit of time. For semiconductor products, however, failure rate is expressed using the unit FIT, where 1 FIT = 10⁻⁹ (failures/hour) = 10⁻⁴ (%/1000h), because the failure rate is very low.
   The failure rate of electronic parts generally exhibits a uniform trend, as indicated in Figure 2. This figure can be divided into three periods: the initial failure period, a random failure period and a wear-out failure period. (The figure is referred to as the “bathtub curve.”) The number of failures in the initial failure period can be decreased using a process known as “burn-in” (i.e., aging, heat run, etc.), and the number of failures in the wear-out period can be decreased by preventive maintenance. Random failures, however, cannot be foreseen. Thus, one of the objectives when ensuring reliability is to decrease to the extent possible the failure rate during the random failure period.
   Semiconductors products, based on past experience, undergo a gradual decrease in failure rate during the random failure period, as shown in Figure 2.
   

   

   Figure 2 Semiconductor Failure Rate Over Time

5. Product Life
   Product life can be expressed in many ways. Mean Time to Failure (MTTF) is used with non-repairable devices and parts, and Mean Time Between Failure (MTBF), which shows the mean lifetime, and Useful Life, which shows the length of time until the failure rate will remain below a specified value, is used with repairable devices and parts.
   For devices and parts that cannot be repaired, MTTF is found as follows:
   
   
   

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