This article presents a summary of the techniques available to use the cumulative binomial distribution to assist in the design of effective reliability demonstration tests and also to determine the reliability that has been demonstrated in a test with few or no failures.
Although these tests yield minimal meaningful information about the product's life characteristics, they are a common requirement for many engineers in the design and manufacturing arena. Therefore, these engineers need to be able to design and allocate resources for these tests without having a great deal of detailed information beforehand. Fortunately, the cumulative binomial distribution can be put to use to help develop a rough estimate of the test design, which includes test duration and the number of units to be tested, without having to develop a complete life test. Otherwise, a large quantity of failures must be achieved before any conclusions can be drawn about the reliability of the product. The cumulative binomial distribution can also be used to analyze the results of tests in which there were few or no failures.
where: *C.L.*is the confidence level for the test. This can be thought of as the probability of more than the maximum number of allowable failures occurring on test.*N*is the number of units on test.*r*is the maximum allowable number of failures on test.*R*is the reliability of the product for the duration of the test.
Essentially, the test design process involves solving the cumulative
binomial equation for one variable, given that the other variables are
known or can be assumed. This is particularly important for the variable
R.
Then, given the desired confidence level (C.L.), the maximum allowable
failures (r) and the reliability value (R), the cumulative binomial
equation can be solved for the number of units (N). Similarly, if the test
is to demonstrate a required MTTF (mean time to failure), at least one of
the parameters of the product's life distribution must be known in order
to solve for R. The exception to this is for the one-parameter exponential
distribution, where the parameter is assumed to be the specified MTTF.
Then, the MTTF and the parameter are used to calculate the value of R for
substitution in the cumulative binomial equation and the procedure is the
same as that described above.
N), the number of allowable failures (r) and the
desired confidence level (C.L.). With this information, the cumulative
binomial equation can be solved for R. Once the reliability value (R) has
been determined, it can be substituted into the appropriate reliability
equation and the test time can be solved for given the distribution
parameters and the reliability value.
N), the number of failures on the test (r) and the desired
confidence level (C.L.). With this information, the cumulative binomial
equation can be solved for R, which is the reliability demonstrated on the
test. However, the reliability value is associated only with the test
duration.
N), the number of failures (r) and the calculated
or estimated reliability (R), the value of the confidence level (C.L.) can
easily be calculated with the cumulative binomial equation. |