Parameter estimation plays a very important role in the quantitative evaluation of system reliability and maintainability. Fig. 18.1 is a typical flow chart for data analysis in reliability and maintainability engineering. From field operation or from lab tests, data such as times to (or between) failure(s) or times to repair can be collected. Through failure analysis or using statistical techniques, the outlier or unusual data in the sample can be found. With the purified data, we then evaluate the system's reliability, or maintainability, parametrically. To do this, the most important task is to find the best, or the most appropriate distribution to describe or represent these data. The optimum distribution can be obtained using the following process:
Choose one of the distributions summarized in Fig. 18.1. Write down its pdf.
Estimate the parameter(s) of this chosen distribution from the sample data using any one or more of the following methods: least squares, matching moments, modified moments, maximum likelihood, probability plotting, or others.
Conduct goodness-of-fit test(s) to ascertain that the selected distribution fits the data. Such tests are the chi-squared, Kolmogorov-Smirnov, modified Kolmogorov-Smirnov, correlation coefficient, likelihood ratio, Anderson-Darling, Cramer-von Mises tests, or others.
If the selected distribution is rejected, then go to Step 1 in Fig. 18.1, choose another distribution, and repeat Steps 2 and 3. If the selected distribution is not rejected, then take it as a possible candidate and repeat Steps 1, 2 and 3 by choosing another distribution.
After exhausting all of the possible distributions by...
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