Data analysis

[Francisco Anes]

[Originally Posted: 10/31/00--Transferred by ReliaSoft Moderator]

I have four fuel feed pumps. I observed all at the same time and I stoped observation also at the same time. At starting time all four had accumuled operation time(do not know by observer). For all pumps is considered a renewal process. So from maintenance files I got the following failure and right censored data.

(a)Pump 1: 1709,16401(RC) (b)Pump 2: 18330(RC) (c)Pump 3: 4835, 1699, 2271, 1085(RC) (d)Pump 4: 911, 5990, 1085(RC)

As renewall processes I put all data together and I ajusted a Weibull distribution, according to the statements below:

(1)I treated data as six failures and four right censored data points. I got by MLE (90% confidence) to = 0 ; B = 0.825(0.5513 - 1.235); n = 9147(4683 - 17290).

(2)I treated times to first failures as censored left (1709, 4835 and 911)as well as failure data (three data points) and censored right (four data points). I got the following results: t0 = 0; b = 0.906(0.5193 - 1.581);n = 19480(7642 - 49660).

So I would get ansewers for the following questions:

(a)On (1) I treated the suposed left censored data as failure data. Do you agree? Why? (b)On (2)do you agree to treat left and right censored data as the same way?Why? (c)What method do you select (1) or(2)? Why? (d)What is really the best method to treat this kind of data?

I would like to thank all of you.

Francisco Anes

[Dean Ford]

[Originally Posted: 11/3/00--Transferred by ReliaSoft Moderator]

If I understand you problem correctly, you had four pumps running at the beginning of the observation period. Correct? Then, you only have 3 pumps for which you know a failure time. Those failure times being 1699,2271, and 5990. Each of the remaining pumps, you know a time which is only known to be less than the actual failure time.

1709,16401,18330,4385,1085,911, & 1085.

Each of those 7 should be treated as right censored. The fact that for some of them the unknown hours are at the start of the observation rather than the end does not make them left censored parts.

[Dr. Dave Olwell]

[Originally Posted: 11/5/00--Transferred by ReliaSoft Moderator]

I agree with Dean's characterization of the data as 3 failures and 7 right suspensions.

A more interesting problem is what model to fit to the data. You chose a Weibull; a case can be made for the exponential or lognormal based on goodness of fit tests with different estimation methods. What information are you trying to extract from your madel? Do you have reason ahead of time to prefer one distribution over another? You will get significantly different answers with different models and estimation techniques.

Because of the early suspensions, MLE methods will underestimate the slope of a Weibull model. You should keep that in mind. For that reason, I prefer the RRX estimate.

Dr. Dave