I believe colleagues who are engaged in reliability work have a question: How to choose the number of samples in the research and development stage? In the product development stage, there will inevitably be product test specifications, which describe what temperature range our products can meet, how much shock and vibration stress values they can withstand, etc.
Then we started arranging tests to verify whether our products could meet the requirements of the product specifications. So for each test item, how many samples do we test before we can say that our product meets our product specifications?
Share a method introduced in the book Practical Reliability Engineering that I am reading, and also share the explanation and calculation cases of some basic reliability measurement terms.
Selection of the number of test samples in the R&D stage
First refer to the concept of binomial distribution: the binomial distribution is repeated n independent Bernoulli trials. There are only two possible outcomes in each trial, and whether the two outcomes occur are opposite to each other and independent of each other. They have nothing to do with the results of other trials. The probability of the event occurring or not remains unchanged in each independent trial. .
In the product development stage, it is considered that the probability of the test result (Pass) or (Fail) of each R&D sample in each test item remains unchanged in each independent test. According to the binomial distribution theory, quote Practical Reliability Engineering 14.3 2 The formula for item distribution confidence is as follows:
The above formula assumes that the number of failures k=0, and the simplified formula is as follows: C=1-R^N; the number of test samples is N = Ln(1-C)/Ln(R); the screenshot below is quoted from Practical Reliability engineering.
For the screenshot example above, note: R here refers to the probability of demonstrating the reliability of product test specifications. Do not confuse it with the reliability of exponential distribution. R=e^(-λt) of exponential distribution; changes with time. .
Taking the above example as R=90% and C=50%, the calculated number of test samples in the R&D stage is 7. The popular meaning is as follows: when 7 test samples are selected, if the test results of all 7 samples pass, there is 50% confidence that the product we develop will meet the product test specifications with a 90% probability (no matter how many products we sell in the future In the market, as long as all 7 samples tested in the R&D stage pass, we can declare to the outside world that we are 50% confident that 90% of the products on the market can meet the test specifications of our products. Of course, the premise here is to ensure that the R&D stage is Same as batch segment).
After reading the introduction in the book, the industry standard for industrial automation is to use R=97% & C=50%, which results in N=23. Some people here may have questions, which department defines the values of R and C? How to define it? This is also my question, and it is also a difficulty in the development of reliability and quality work... For example, the research and development costs of some products are too high. Usually, the project will only provide one product for research and development testing. If it passes the test based on this sample, it can only Say C=50%, R=50%... I believe this is also the current situation of most companies...
Explanation of basic reliability measurement terms and calculation examples
Recently, I encountered a customer at work who asked about the calculation of PPM, MTBF and reliability probability R. I won’t talk about the customer’s case, but share what I saw in Practical Reliability Engineering;
MTBF: Meantime between failure; R(t) = e^(-1/MTBF*t) in exponential distribution;
PPM: Parts Per Million; R(t)=1-PPM(t)/(10^6);
BX-Life: If x=10 here, it means R=90%;
Analysis of the above example: The product requires the life of B10 to be 5 years, which means that the reliability of the product after 5 years is 90%. In the example, it is MTTF (MeanTime To Failure), which satisfies the exponential distribution. Substitute it into formula 14.2 in the above figure to obtain, MTTF = 47.5 years, which means the annual failure rate λ = 0.021, (another statement is introduced here, because MTTF = 47.5 years, then the annual repair rate = 1/47.5 = 2.1%, which is very high... Usually consumer products are lower than 0.3 %...); the PPM value is 100,000, which means that after 5 years, 100,000 products per million will fail.