TABLE 1 Fictitious Developmental and Operational Test Data

Developmental Test Data

Operational Test Data

28.73

18.01

13.48

21.76

1.55

18.63

6.01

35.54

4.54

46.68

22.06

23.51

7.58

2.58

5.34

11.27

20.89

8.39

16.08

7.15

39.97

8.06

10.19

7.79

9.97

67.03

33.14

41.66

7.79

6.14

training) cannot be developed. The estimation approach described by Steffey is (Bayesian) hierarchical modeling using a relatively simple characterization of relatedness of conditions of use.

A dataset motivated the discussion. Consider the following (fictitious) lifetimes of experimental units (hours to failure) from developmental and operational testing (DT and OT) as displayed in Table 1. For developmental testing, the mean time to failure is 19.53, whereas for operational testing, it is 16.09.

The statistical model used assumes that there exists a probability distribution with mean μD that generates DT mean times to failure. Likewise, there also exists a probability distribution that generates OT mean times to failure. These means of the distributions that generate mean times to failure (μD, μO) are referred to as grand means. Then, to obtain the observed time to failure for a given system for either developmental or operational test, one draws a random waiting time from a distribution with the appropriate mean. This can be considered a staged process in which the second and final stage represents the variability of an individual system’s waiting times to failure about each individual system’s mean, and the initial stage represents the variability between the mean times to failure for individual systems (from the same manufacturing process) about a grand mean time to failure. It makes sense to assume that the DT grand mean is some factor larger than the OT grand mean, since operational test exposes a system to more opportunities for failure. This multiplicative factor is designated λ. (There are non-Bayesian approaches in which a λ factor is used to convert



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