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Estimation of the reliability function for an object that is improved on the basis of data on the life-lengths and types of failures of an object that is not improved

100%

Domsta J.

Mathematica Applicanda

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1983

|

tom 11

|

nr 22

PL

W pracy podaje się twierdzenia, które mogą być podstawą do oszacowania(zgodnie z zasadami statystyki matematycznej) funkcji niezawodności obiektu poprawionego. Korzysta się przy tym z danych o obiekcie przed jego poprawieniem. Wyrózniono dwa rodzaje metod poprawiania: -przez selekcję, -przez uszlachetnienie. Omówiono niektóre interpretacje rozważanych modeli.

EN

The author considers a population Π of devices which can fail due to one of the modes of failure Ui, i=1,2,...,k. Assume that each device e in Π has a life which will terminate at time T(e) due to mode Uj. When a device is drawn at random from Π, the pair [T(e),j] is a two-dimensional random variable with probability distribution P(T,j) which determines the marginal survival function R(t)=P{T>t}, called the "reliability function before improvement". The author discusses possible improvement of such a population by procedures of two types. Type I consists of removing from Π all devices with certain unfavorable qualities, for example, those that fail due to Uj within a test period tj for specified j and tj, or those for which one can tell beforehand that they will fail due to a specified Uj. Type II consists of modifying the devices (e.g., by changing the manufacturing process) in a way that will change the probability distribution P(T,j) into some P~(T,j). In view of the multiplicity of modes of failure, this leads to questions dealing with competing risks.

2

Review: D. Stoyan, D. Konig; Queuing theory

100%

Domsta J.

Mathematica Applicanda

|

1983

|

tom 11

|

nr 22

PL

Artykuł nie zawiera streszczenia

EN

The article contains no abstract

3

The first exit of almost strongly recurrent semi-Markov processes

63%

Domsta J., Grabski F.

Applicationes Mathematicae

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1995-1996

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tom 23

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nr 3

285-304

EN

Let $\stackrelnX(·)$, n ∈ N, be a sequence of homogeneous semi-Markov processes (HSMP) on a countable set K, all with the same initial p.d. concentrated on a non-empty proper subset J. The subrenewal kernels which are restrictions of the corresponding renewal kernels $\stackrelnQ$ on K×K to J×J are assumed to be suitably convergent to a renewal kernel P (on J×J). The HSMP on J corresponding to P is assumed to be strongly recurrent. Let [$π_j$; j ∈ J] be the stationary p.d. of the embedded Markov chain. In terms of the averaged p.d.f. $F_{ϑ}(t) :=\sum_{j,k ∈ J} π_jP_{j,k}(t)$, t ∈ i$ℝ_+$, and its Laplace-Stieltjes transform $\widetilde F_ϑ$, the above assumptions imply: The time $\stackrel{n}{T}_{J}$ of the first exit of $\stackrel{n}{X}(·)$ from J has a limit p.d. (up to some constant factors) iff 1 - $\widetilde F_ϑ$ is regularly varying at 0 with a positive degree, say α ∈ (0,1]. Then the transform of the limit p.d.f. equals $\widetilde G^{(α)}(s) = (1+s^{α})^{-1}$, Re s ≥ 0. This extends the results by V. S. Korolyuk and A. F. Turbin (1976) obtained for α = 1 under essentially stronger conditions.

Ograniczanie wyników

2 Mathematica Applicanda

1 Applicationes Mathematicae

3 Domsta J.

1 Grabski F.

1 1995

2 1983

Estimation of the reliability function for an object that is improved on the basis of data on the life-lengths and types of failures of an object that is not improved

Review: D. Stoyan, D. Konig; Queuing theory

The first exit of almost strongly recurrent semi-Markov processes