Tham khảo tài liệu 'engineering statistics handbook episode 5 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . The random errors follow a normal distribution. Non-Normal Random Errors May Result in Incorrect Inferences Of course if it turns out that the random errors in the process are not normally distributed then any inferences made about the process may be incorrect. If the true distribution of the random errors is such that the scatter in the data is less than it would be under a normal distribution it is possible that the intervals used to capture the values of the process parameters will simply be a little longer than necessary. The intervals will then contain the true process parameters more often than expected. It is more likely however that the intervals will be too short or will be shifted away from the true mean value of the process parameter being estimated. This will result in intervals that contain the true process parameters less often than expected. When this is the case the intervals produced under the normal distribution assumption will likely lead to incorrect conclusions being drawn about the process. Parameter Estimation Methods Can Require Gaussian Errors The methods used for parameter estimation can also imply the assumption of normally distributed random errors. Some methods like maximum likelihood use the distribution of the random errors directly to obtain parameter estimates. Even methods that do not use distributional methods for parameter estimation directly like least squares often work best for data that are free from extreme random fluctuations. The normal distribution is one of the probability distributions in which extreme random errors are rare. If some other distribution actually describes the random errors better than the normal distribution does then different parameter estimation methods might need to be used in order to obtain good estimates of the values of the unknown parameters in the model. NIST SEMATECH HOME tools AIDS search l ACK next http div898 handbook pmd section2 2 of 2 5 1 2006 10 21 .
