# Reliability Goal and Confidence

We establish reliability goals and measure reliability performance.

They are not the same thing. Goals and measures, while related, are not the same nor serve the same purpose.

Recently, I’ve seen a few statements that seem to confuse the role of statistical confidence when establishing a goal. Thus, I would like to relate how I think about the difference of goals and statistical confidence along with how they are related.

## The Purpose of a Reliability Goal

Setting any goal provides tangible direction or a meaningful target for the team. A reliability goal is a balance of

- what the customer expects,
- what is technically possible,
- and an expression of the business objectives.

A reliability goal establishs the probability a function will successfully operate over a specific duration given a specific use and environment. For example, my smart phone will make and receive calls in Northern California with a 99% probability of successful operation over 2 years.

The purpose of the goal to define to the engineering team, to the marketing team, to customers, the item’s expected or desired reliability performance.

It is not the actual reliability performance. It is what we would like to have happen. It’s a goal, objective, target, etc.

The purpose to provide guidance, alignment, and requirements for the creation of a new product or system.

## The Purpose of Statistical Confidence

Statistical confidence is a statement of the acceptable risk we are willing to accept. The risk is based on the ability of a specific sample to accurately represent the entire population.

The chance that a single sample’s reliability performance will be the same as the population’s average reliability performance is very low. As we measure more samples from the population the ability of the sample to estimate the population’s performance increases.

There is some statistical law about this phenomenon.

Some organizations set a policy concerning the amount of risk they are willing to accept when using a sample to create an estimate. Other times we determine the statistical confidence based on how many samples we have evaluated.

The purpose of a statistical confidence is to manage the risk of the sample providing misleading information.

The goal is often to minimize sample size related risk within the constraints that exist limiting sample sizes.

## The Relationship Between Goals and Confidence

Reliability goals are a desired state of performance. Confidence reflects the risk a sample based results is close to being true.

Stating a reliability goal that includes a confidence in effect defines the desired sample size to measure the reliability performance. That is not a bad relationship. Yet stated we want a reliability goal of 90% reliability over 2 years with 90% confidence, is not, in my mind, a goal.

We would like the actual reliability of the item to have a 90% chance of surviving 2 years. We may want to minimize sample risk by measure the reliability performance with a 90% confidence.

The estimate from a sample of the actual reliability performance will always be an estimate. The confidence provides a figure of risk that the results we are viewing actually reflect the real and unknown reliability performance.

If we use a one-sided lower bound for the confidence, we are looking for evidence that the reliability is at least above the lower bound value. We could set the threshold for the lower bound at the goal value. With a 90% confidence we are accepting the risk the actual population reliability is less then 90% and the sample results end with a value higher than the goal, thus we believe the product’s reliability performance is better than actual.

The relationship between a goal and confidence is they are both providing information about the unknown actual reliability performance. The former is the desired state, the later is a reflection of sample risk during measurement.

Let me know if this makes sense, or if there is a better way to describe the relationship between goals and confidence. Please comment and join the conversation.

It seems to me that the specified reliability is a goal, and confidence limits are a measure concerning that goal. Consider the following.

Another way of stating this is to specify the lowest reliability you want (say 0.90 at 2 years), and to design a measurement that will tell you that you are 80% (or 60% or 90%) confident that the true reliability is at least 0.90 at 2 years.

Assume that you have a test where you know (with absolute certainty) that the test duration is equivalent to 2 years of operation. Then you could adopt any one of several test strategies to assess the probability of failure during the test. Specifically, you would want to determine if the probability of failure during testing is less than 0.10. That’s just a statistical problem.

There are a number of side issues, of course. If you use the Arrhenius equation to compute an acceleration factor, you probably don’t actually know either (1) that the Arrhenius equation applies or (2) the activation energy. This brings up a related issue: you don’t know that all the failure modes will be accelerated in the same way by the test conditions, that is, it is possible that each component has a different activation energy even if all the failure modes accelerate according to Arrhenius (which is uncertain anyway).

The bottom line, at least IMO, is that you can know if a product will survive a test with some specified probability (e.g., 0.90) and you can compute a confidence level (i.e., the probability that the true reliability is greater than or equal to the specified reliability. You also need to understand how the confidence limits are computed (i.e., are they Poisson, normal, binomial, distribution free, etc.) and state those assumptions clearly. If you can do all this, then you have a goal (a specified reliability) and a way to measure it (some sort of confidence).

What do you think?

Hi Paul,

Interesting idea – if we know it will survive the test, why run the test?

I’ll have to read your note a few more times, yet keep in mind that confidence has a general meaning (trustworthiness) while in statistics it has a specific and different meaning.

I tried to stay away from type I and type II errors, etc – yet may have to try sorting out a clearer way to explain the difference in the belief that something will happen and statistical confidence.

Cheers,

Fred