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Distribution Fitting in NCSS

Researchers at a company would like to better understand the time to failure of a medical device the company produces. 104 devices are followed for 3 years (or 1,095 days). At the end of 3 years, 86 of the devices have failed and 18 are still functioning. The researchers would first like to determine the distribution that best fits the failure data, and then they would like to estimate the parameters of that distribution. The Time Variable is the Time Column. The 18 devices that are still working are given a time of 1,095, a censor value of 0, and a Count of 18. Equivalently, 1,095 could have been listed 18 times with no count variable used. The Censor variable is the Censor Column. A Failed response is a 1, and a right-censored response is a Zero. A comparison of the distributions will be made using the specification ‘Find Best.’ All the available distributions will be compared. The Options are left at the defaults. All reports and plots are checked. The first section of the report is a summary. The second section shows the comparison of distributions. The distribution with the highest likelihood is the log-Logistic. The probability plots also show that the log-Logistic distribution has the best fit. The density formula of the log-Logistic distribution is shown in the documentation. This distribution can take on many shapes, depending on the values of its 3 distribution parameters. Now we re-run the procedure with the Distribution set to log-Logistic. After the data summary, the parameters of the distribution are estimated in detail. This is followed by a general survival analysis, with Kaplan-Meier details, Hazard Rate details, the failure distribution, Reliability, and Percentiles. The Survival Plot and Hazard Function Plot at the end give a good visual representation of the device failure.