The ‘Probability’ In The Definition Of Reliability (& Availability)

There are four (4) key elements in the definition of Reliability (and Availability). These are:

1. A Probability (any number between 0 and 1);

2. Specific Function;

3. Specific Time Period; and

4. Specific Support Conditions.

Stringing these together: "Reliability (and Availability) is a probability that a process/system/equipment/component/part will perform a specific function over a specific time period and under specific support conditions."

Element number one (1) in the definition of reliability is given by the reliability formula.

Pragmatic Application Of The Reliability Formula Leveraging Experience

Reliability is one of the key maintenance metrics and is given by the Reliability Formula. In the article below, they showed how 'lamda' or Failure Rate (λ) is derived from MTBF and MTTR and then plugged into the Reliability Formula to produce the 'Probability' in the definition of Reliability (and Availability).

In comments under that above article, I commented about the pragmatic use of the reliability formula leveraging experience especially when MTBF or MTTR data or both are not readily available.

My comment was especially on how the failure rate can be alternatively derived from other than MTBF and MTTR by drawing from experience to be later plugged into the common reliability formula. The approach in the above article assumes a constant failure rate (λ) or lambda, which corresponds to the exponential distribution (i.e. when the shape factor (β) or 'beta' value of 1). In reality, the failure rate of most components is not constant and usually varies over time. The Weibull distribution is generally preferred because it can model different failure behaviors and the variables in the formula can be inserted based on experience.

To be more pragmatic and apply the Weibull parameters, we expand the failure rate (λ) multiplied by time in the reliability formula.

Failure rate x time = (characteristic life/time)^shape factor.

That is, failure rate x time = “open bracket characteristic life divided by specified time period close bracket raised to the power of shape factor”.

✳️Characteristic life = can be obtained from OEM or as we know 63% of life where most failure occur. Or we can opt to use the derived MTBF.

✳️Time = is one of the four (4) elements in the definition of reliability. Reliability cannot be stated without referencing a specific time period. This is the time period in hours where we want to know the reliability of a process/system/equipment/component/part.

✳️Shape factor = this is the ‘beta value’ on the Bathtub Curve for various failure modes which, with experience, can be easily assigned. For example, a ‘failed bearing’ gets a beta of 1 and a ‘worn bearing’ gets a beta of greater than 2 (maybe 3 or 4 or 5 which in-depth data analysis can later affirmed).

In this way we can use experience to place any failure mode on the Bathtub Curve then use the reliability formula with the Weibull shape factor (β) parameter of 'beta' to quantify reliability.

Additionally by applying shape factor based on experience, we would already have a fair idea on what maintenance strategy to apply.

The Weibull Parameter 'Beta' In the Reliability Formula And Indicative Maintenance

This reliability formula was invented by Waloddi Weibull in 1937. This formula could describe the different shaped graphs in each of the three zones of the Bathtub Curve. The three zones are: high probability of failure when new (burn-in); steady state probability of failure (random or constant); and increase probability of failure when old (wear-out).

The shape factor tells you the location of the failure mode on the Bathtub Curve and the maintenance strategies to apply. The failure is 'burn-in' if the shape factor is less than 1 and is often the result of improper installations/rebuild and precision maintenance is the strategy to mitigate this failure. The failure is random (or constant) when the shape factor is equal to 1 and a run-to-fail strategy could be applied if the risk of failure is acceptable, but if the risk is not acceptable, then on-line condition monitoring can be the maintenance strategy to be applied. The failure is slow aging or wearing at constant rate if the shape factor is equal to 2. If the shape factor is greater than 2 and less than 4, the failure mode is wear-out (i.e. aging) and condition-based maintenance will be the strategy. If the shape factor is 5 and above, the failure is very predictable and a time based schedule changeout should be the maintenance strategy to mitigate the risk of this failure mode in the maintainable item.

The bottom line is that, for RCM Practitioners, if you know the practical application of this formula, you can read a lot from it (i.e. where it is on the Bathtub Curve and the appropriate maintenance strategy to apply to preserve the function of the process/system/equipment/component/part) when you see the formula with the functional variables and take quick decisive pragmatic actions knowing what you know.

As Deming said "It is not enough to do [our] best, [we] must know what to do and then do [our] best."