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Reliability probability and statistics is a complex, diverse area that people spend years mastering, so don't expect to get the analysis right the first time through! Properly applied statistics can help clarify an issue; but if misused or misapplied, they can generate misleading results. So be skeptical and pessimistic regarding reliability data. Reliability statistics require careful, honest interpretation. Statistical probability should be used only when there is a lack of knowledge about a situation and if the knowledge cannot be obtained at a reasonable cost in a reasonable amount of time. In other words, when trying to determine a course of action, the best path is to acquire knowledge. Do not rely primarily on predictive statistics and probabilities. Use these tools only as a last‐resort strategy or in conjunction with other tools. Don't gamble with product reliability. Much like the stock market, past performance does not guarantee future results. Since excellent resource material on reliability statistics exists (Abernethy 2000; Wunderle and Michel 2006, 2007), this section intends to reintroduce and provide a brief refresher of some key concepts, basic recommendations, and common pitfalls.

Reliability statistics are used to describe samples of populations. If the sample size is small, every member can be tested, and representative statistics are not needed. For reliability statistics to be valid, samples must be chosen randomly, and every member must have an equal chance of being selected. For example, when testing to failure, if testing is ended before all items have failed, the sample is not random. The data is referred to as censored data. Censored data may use Type I censoring (time censored) or Type II censoring (failure censored). Censored data must be analyzed using special techniques.

Here are some views on statistics from masters of their fields:

A statistical relationship, however strong and however suggestive, can never establish a causal connection. Our ideas on causation must come from outside statistics, ultimately from some theory.

Kendall and Stuart, The Advanced Theory of Statistics

Ultimately, all our understanding should be based upon real knowledge (scientific, human, etc.). The statistical methods can provide tools to help us gain this knowledge.

Patrick O'Connor, Practical Reliability Engineering

When you can measure what you are speaking about and express it in numbers, you know something about it.

But when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind.

It may be the beginning of knowledge, but you have scarcely in your thoughts, advanced it to the state of science, whatever the matter may be.

Lecture to the Institution of Civil Engineers, 3 May 1883, William Thomson – Lord Kelvin

Common statistical pitfalls include sample‐size errors, distribution or model errors, and failure‐to‐validate‐data errors. Using sample sizes too small to be statistically significant or valid (and using that data to make long‐term decisions!) is a common error in high‐reliability systems design due to availability, time, complexity, and cost of hardware and testing. Distribution or model errors are also frequently seen. Using normal distributions for non‐normal data is often done due to the ease of calculations and over‐reliance on easy spreadsheet statistics. Using limited, scrubbed, or unvalidated data is also common. Repeating analyses and modeling at various intervals are highly recommended as more and more credible data is obtained. For example, consider repeating the analysis after product release, after a specific number of product builds, after a certain volume has been manufactured, and after some time in the field.