Talk:Survivor function

Hello. I see that survivor function and survival analysis were both started last month. I was working on survival analysis in ignorance of survivor function. There is some terminology in survivor function which isn't present in survival analysis, so I think I will merge that in. Since survival analysis is substantially more developed, I would suggest that further edits be made on that article rather than duplicating the effort on this one. For what it's worth, Wile E. Heresiarch 04:33, 15 Feb 2004 (UTC)

Thanks for this. I had missed survival analysis. I've added it to list of statistical topics. I agree that we need to align and that the two articles need merging. As I'd missed survival analysis, I'd been working on my own version which starts from a slightly more "upstream" point that yours. My version is not quite finished. I feel that the merged article might fit survivor function better than survival analysis but have a go merging because we can always rename and move later. Would it help if I posted where I have got to with survival analysis here? Cutler 10:59, 15 Feb 2004 (UTC)

Thanks for posting the material below, it's very inspirational. I've merged terminology and some other stuff from survivor function into survival analysis, and some of the discussion points (defn of survival, inferences to be made from the survival function) from the work below. I've tried to merge in all the points that were not already present in the survival analysis article. You can check the page history to see what I've done. -- As to organization, I guess I don't see a good reason to make separate articles for hazard function, etc., since the various terms are not really comprehensible in isolation. Also, at present biological survival and mechanical reliability are treated by the same article. Although the basic discussion is the same, at some point maybe detailed or in-depth points peculiar to one or the other could be split off into specialized articles. FWIW, & thanks for your help, Wile E. Heresiarch 16:33, 15 Feb 2004 (UTC)

Well, here it is:

Survival analysis is that branch of statistical theory that deals with the longlevity of artifacts, natural phenomena or organisms.

Bases

Survival analysis starts in a probability space (E,P) that satisfies the usual axioms. Here the sample space E is a set of possible failure events in the real world. Each element of the set is a potential failures that are of interest. It might be the set of all possible ways that a man's life could end or all potential ways in which a mechanical bearing could give trouble to its owner. Now, in the first case, the events are fairly unambiguous. In the second case, there is room for extensive disagreement and uncertainty about what would constitute a failure. For this reason, any practical use of survival analysis in statistical practice must begin with an operational definition of "failure".

Survival analysis is concerned with death, not recurrent faults in a system that can be repaired. Is is thus adapted to the study of parts reliability in engineering but, though it is relvant, it is not to be confused with systems reliability.

The most important concept in survival analysis is that of life. Life is a random variable that maps E onto time. Without loss of generality, we can fix the origin of time at the birth of an item and conveniently express life on the real interval [0,&inf;). Thus, we can think of the random variable life as a process that looks at a failure (death) and extracts the time at which it occurred.

Elementary problems in survival analysis

• What is the probability that an item will survive beyond a given time? (see Survivor function)
• How many of a population (statistics) of items will survive beyond a given time? (see Survivor function)
• By what time will a given percentage of items in a population (statistics) have failed? (see Survivor function
• What is the average (expected) time to failure of an item? (see Mean time to failure)
• Is failure becoming increasingly probable or not so? (see Hazard rate)
• What can we learn about the underlying mechanisms from failure data? (see Hazard rate)
• When would be a good time to replace an item with a new one? (see Age-replacement problem)

• Which of two items is the better when durability is important?
• Given an existing item, is it better to replace it with an alternative where durability is important?

• What are the causes of variation in life?

Issues of statistical practice

See also:

Cutler 11:02, 15 Feb 2004 (UTC)