How to carry out the reliability test plan design?
The purpose of the reliability test is different, and the plan design is also different. This article focuses on how the reliability qualification test plan is designed?
Reliability appraisal test is to assess whether the reliability of the product meets the specified reliability requirements. It is a test conducted by the ordering party with representative products under specified conditions, and this is used as one of the basis for approving the design and finalization. A sampling inspection.
Since the sampling inspection judges the quality of the whole batch of products by inspecting the quality of the samples, the following two types of errors may be made: ① The qualified product batch is misjudged as an unqualified product batch, which is called the first type of error; The misjudgment of a qualified product batch as a qualified product batch is called a category 2 error. Making the first type of error will cause the producer to suffer losses, so the probability of making this type of error is called the producer’s risk, generally expressed by α, when making the second type of error, the user will suffer losses, so it is called making this type of error. The probability of is the user's risk, which is generally expressed by β.
The ideal sampling inspection plan requires α=β=0, but such a test plan does not exist. Because it is necessary to make α=0, that is, the qualified batch must not be mistakenly judged as the unqualified batch. It is enough to judge any batch of products as qualified, but this will increase β. On the contrary, if β=0, it will lead to α increases. In addition, the test is also subject to time, funding, test resources and other conditions. Therefore, in actual work, the manufacturer and the user often negotiate and weigh together to formulate the test plan.
Two values θ1 and θ0 (θ0>θ1) are given for a certain inspected parameter θ of the product (such as life, mean time between failures, reliability, success rate, etc.). When the average value of the sample parameters is greater than θ0, in order to protect the interests of the producer, the entire batch of products should be received with a high probability. Record L(θ) as the probability of acceptance, that is, when the average value is required to be greater than θ0
When the average value ≤ θ1, in order to protect the interests of the user, the entire batch of products should be received with a small probability, that is, when the average value ≤ θ1
According to these two conditions, the test plan for sampling inspection can be determined. The above is the basic idea for the formulation of reliability qualification test plans, and all the formulation of reliability qualification test plans follow this principle.
So how to operate for specific success or failure products (binomial distribution or hypergeometric distribution)?
The following is a brief introduction to the program formulation process using binomial distribution as an example. First, give the simultaneous equations:
Where n is the sample size, c is the maximum number of failures, r is the number of failures, α is the risk of the producer, β is the risk of the user, p0 is the acceptable quality (1-the upper limit of reliability), and p1 is the allowable unqualified quality ( 1- Lower limit of reliability).
The formulation process of the sampling plan is the process of determining n and c by α, β, p0 and p1. The above equations are non-linear integer equations without analytical solutions, and can only be approximated by computer simulation, traversal or trial-and-error.
Commonly used test schemes are given in GB5080.5 "Verification Test Scheme for the Success Rate of Equipment Reliability Tests". However, if the actual situation does not meet the standard requirements, a computer program is required to solve it.
Example: For a certain type of missile, the lower reliability limit of 0.62 is required for its autonomous flight reliability during the design and finalization stage, and the upper limit of its reliability is 0.80. Because the cost of this type of missile is expensive. It should be possible to use a smaller number of products for identification. After negotiating with Party A, it is agreed to use a high-risk solution of about 30%. Therefore, another constraint condition in designing the qualification test plan is to try to make the risk borne by both parties in the test close to 30%. Since there is no plan that satisfies this condition in the standard, we can put the above conditions into the equations, and we can get
Solving the above equations through a computer program can be obtained, when n=9, c=2, the test requirements can be met. At this time, the producer's risk α is 26.18%, and the user's risk β is 27.13%.