Calculate the acceptance and rejection line for the SPRT test.This is comparable to α 1 in the previous section. If the component’s reliability is 82% or less, the probability ofĪccepting it (i.e., Type II error or β error) should be less than 0.1. A minimum reliability of 82% at 200 hours.This is comparable to α 2 in the previous section. (i.e., Type I error or α error) should be less than 0.05. If the component meets or exceeds the target reliability, the chance of rejecting it A target reliability of 92% at 200 hours.We will use SPRT to determine if the component meets the following reliability requirements: Let's assume the lifetime of a component is described by a Weibullĭistribution with the shape parameter b = 1.5. The decision equation for the log-likelihood ratio R is:Įqns. When b 1 = b 2, the above equation becomes: For the test for vendor A, since it is less than C 1, we accept thatįor the test for vendor B, since it is less than C 2, we accept that μ η 1). When we take samples for the life test, the resulting sample mean has one of If a sample mean is greater than C 2, then we accept that the component is from vendor B otherwise, we accept , The bottom plot is for the second test (vendor B).Ĭ 2 is the critical value at a significance level of α 2. That the components are not from vendor A. If we take some samples and the sample mean is less than C 1, The top plot is for the first hypothesis test (vendor A).Ĭ 1 is the critical value at a significance level of These two separate hypothesis tests are shown graphically below: Therefore, we need to conduct two statistical hypothesis tests. Wrong claim that it is from vendor A should be less than α 2 = 0.05. If the component is indeed from vendor B, the chance of making a.Wrong claim that it is from vendor B should be less than α 1 = 0.01. If the component is indeed from vendor A, the chance of making a.We want to determine if the components are from vendor A orįrom vendor B by conducting a test. Components from vendor A have a mean lifeĪnd components made by vendor B have a mean life of μ 2 = 20.Īn unlabeled box of components was received by the company. Although theĬomponents from the two companies look exactly the same, their lifetimeĭistributions are different. Two vendors provide the same component to a company. Let's first use a simple example to explain the principal behind Of significance are applied to the data accumulated up to that time. The test results are reviewed after each test. Sequential test is a method by which items are tested in sequence (oneĪfter another).

Whether a given lot meets the production requirements. SPRT was originally developed as an inspection tool to determine We will explain the theory behind this method and illustrate its use in reliability engineering, especially in It is widely used in quality control in manufacturing and detection ofĪnomalies in medical trials. The Sequential Probability Ratio Test (SPRT) was developed by Abraham Wald more than a half century ago.

Erliability sequential testing