Binomial

Discovered in 1663 by John Newton, the simple formula for the binomial distribution requires only that the proportion that each of two outcomes is expected and the number of samplings or trials that are to be made are known. The binomial distribution applies to counted events that can have only two outcomes. It is used extensively in quality control and test planning, and it can be used in all discrete situations, such as yes/no, on/off, good/bad, pass/fail, etc.. An example of binomial distribution is coin tossing.

Poisson

Often used as an approximation for the binomial distribution when the values are within appropriate limits, the Poisson distribution is used to model rare events in a continuum. Requiring only one-parameter, the average or mean value, the Poisson distribution is based on counted events that are random in time. The Poisson distribution is used for nuclear emissions, accidents, spare parts prediction for low-demand components, etc.. An example of Poisson distribution is a lightning strike.

Kaplan-Meier

Long-used in the medical industry, the Kaplan-Meier survival function estimates the cumulative survival distribution without making any distribution assumptions. This method is non-parametric, meaning that it does not assume a distribution that uses parameters like the and in the Weibull distribution. The Kaplan-Meier estimate of the survivor curve looks like a stair pattern rather than a smooth curve. It works well for grouped, uncensored or right-censored data. Each time you have a failure, you multiply by a fraction. The fraction is determined by the total units at the start of the test, minus the number that are no longer on test after time t (failures and censored observations), divided by the number at risk of failure before t. A tie is taken into account in the fraction by the numerator. If you do not know what distribution the data comes from and do not want to assume a distribution, consider using the Kaplan-Meier method. It is the best practice for snapshot data and is often useful for tracking warranty data by age as well as for analysing inspection data.

Crow-AMSAA

The Crow-AMSAA model is used to track the growth of reliability in a development programme as a function of time. Requiring less information than Weibull analysis, the Crow-AMSAA model indicates instantaneous failure rate changes by plotting a straight line on a log-log plot. Although may reliability growth models are available, the Crow-AMSAA model is considered the best practice because of the powerful statistical capabilities that Dr. Larry Crow added to J. T. Duane’s postulate for learning curve modelling. The charts note trends that are used to forecast failures as a function of additional test time or calendar time, thereby making spares ordering and maintainability planning easier. This model can be used to track critical parameter rates such as warranty claims, outages, fires and accidents. It is also now being applied to tracking maintainability for fleets of repairable systems and ranking significant management events. It can handle mixed failure modes and well as missing portions of data.