Shock models leading to increasing failure rate and decreasing mean residual life survival

1982 ◽  
Vol 19 (01) ◽  
pp. 158-166 ◽  
Author(s):  
Malay Ghosh ◽  
Nader Ebrahimi
Keyword(s):  
Poisson Process ◽  
Failure Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Increasing Failure Rate ◽  
Shock Models

Shock models leading to various univariate and bivariate increasing failure rate (IFR) and decreasing mean residual life (DMRL) distributions are discussed. For proving the IFR properties, shocks are not necessarily assumed to be governed by a Poisson process.

Shock models leading to increasing failure rate and decreasing mean residual life survival

1982 ◽  
Vol 19 (1) ◽  
pp. 158-166 ◽  
Author(s):  
Malay Ghosh ◽  
Nader Ebrahimi
Keyword(s):  
Poisson Process ◽  
Failure Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Increasing Failure Rate ◽  
Shock Models

Shock models leading to various univariate and bivariate increasing failure rate (IFR) and decreasing mean residual life (DMRL) distributions are discussed. For proving the IFR properties, shocks are not necessarily assumed to be governed by a Poisson process.

The hazard and vitality measures of ageing

1989 ◽  
Vol 26 (03) ◽  
pp. 532-542 ◽  
Author(s):  
Joseph Kupka ◽  
Sonny Loo
Keyword(s):  
Sudden Death ◽  
Failure Rate ◽  
Residual Life ◽  
Ageing Process ◽  
Mean Residual Life ◽  
Absolutely Continuous ◽  
Intrinsic Interest ◽  
Increasing Failure Rate ◽  
Time Period ◽  
The Relationship

A new measure of the ageing process called the vitality measure is introduced. It measures the ‘vitality' of a time period in terms of the increase in average lifespan which results from surviving that time period. Apart from intrinsic interest, the vitality measure clarifies the relationship between the familiar properties of increasing hazard and decreasing mean residual life. The main theorem asserts that increasing hazard is equivalent to the requirement that mean residual life decreases faster than vitality. It is also shown for general (i.e. not necessarily absolutely continuous) distributions that the properties of increasing hazard, increasing failure rate, and increasing probability of ‘sudden death' are all equivalent.

scholarly journals Reversed Preservation Properties for Series and Parallel Systems

2007 ◽  
Vol 44 (4) ◽  
pp. 928-937 ◽  
Author(s):  
Félix Belzunce ◽  
Helena Martínez-Puertas ◽  
José M. Ruiz
Keyword(s):  
Failure Rate ◽  
Residual Life ◽  
Parallel Systems ◽  
Mean Residual Life ◽  
Convex Order ◽  
Increasing Failure Rate ◽  
Decreasing Failure Rate ◽  
New Better Than Used ◽  
Better Than

Recently Li and Yam (2005) studied which ageing properties for series and parallel systems are inherited for the components. In this paper we provide new results for the increasing convex and concave orders, the increasing mean residual life (IMRL), decreasing failure rate (DFR), the new worse than used in expectation (NWUE), the increasing failure rate in average (IFRA), the decreasing failure rate in average (DFRA), and the new better than used in the convex order (NBUC) ageing classes.

scholarly journals Preservation of some partial orderings under Poisson shock models

1989 ◽  
Vol 21 (03) ◽  
pp. 713-716 ◽  
Author(s):  
Harshinder Singh ◽  
Kanchan Jain
Keyword(s):  
Poisson Process ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Mean Residual Life ◽  
Survival Functions ◽  
Constant Intensity ◽  
Variable Ordering ◽  
Shock Models ◽  
Partial Orderings ◽  
Likelihood Ratio Ordering

Suppose each of the two devices is subjected to shocks occurring randomly as events in a Poisson process with constant intensity λ. Let Pk denote the probability that the first device will survive the first k shocks and let denote such a probability for the second device. Let and denote the survival functions of the first and the second device respectively. In this note we show that some partial orderings, namely likelihood ratio ordering, failure rate ordering, stochastic ordering, variable ordering and mean residual-life ordering between the shock survival probabilities and are preserved by the corresponding survival functions and .

The hazard and vitality measures of ageing

1989 ◽  
Vol 26 (3) ◽  
pp. 532-542 ◽  
Author(s):  
Joseph Kupka ◽  
Sonny Loo
Keyword(s):  
Sudden Death ◽  
Failure Rate ◽  
Residual Life ◽  
Ageing Process ◽  
Mean Residual Life ◽  
Absolutely Continuous ◽  
Intrinsic Interest ◽  
Increasing Failure Rate ◽  
Time Period ◽  
The Relationship

A new measure of the ageing process called the vitality measure is introduced. It measures the ‘vitality' of a time period in terms of the increase in average lifespan which results from surviving that time period. Apart from intrinsic interest, the vitality measure clarifies the relationship between the familiar properties of increasing hazard and decreasing mean residual life. The main theorem asserts that increasing hazard is equivalent to the requirement that mean residual life decreases faster than vitality. It is also shown for general (i.e. not necessarily absolutely continuous) distributions that the properties of increasing hazard, increasing failure rate, and increasing probability of ‘sudden death' are all equivalent.

scholarly journals Preservation of some partial orderings under Poisson shock models

1989 ◽  
Vol 21 (3) ◽  
pp. 713-716 ◽  
Author(s):  
Harshinder Singh ◽  
Kanchan Jain
Keyword(s):  
Poisson Process ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Mean Residual Life ◽  
Survival Functions ◽  
Constant Intensity ◽  
Variable Ordering ◽  
Shock Models ◽  
Partial Orderings ◽  
Likelihood Ratio Ordering

Suppose each of the two devices is subjected to shocks occurring randomly as events in a Poisson process with constant intensity λ. Let Pk denote the probability that the first device will survive the first k shocks and let denote such a probability for the second device. Let and denote the survival functions of the first and the second device respectively. In this note we show that some partial orderings, namely likelihood ratio ordering, failure rate ordering, stochastic ordering, variable ordering and mean residual-life ordering between the shock survival probabilities and are preserved by the corresponding survival functions and .

scholarly journals Reversed Preservation Properties for Series and Parallel Systems

2007 ◽  
Vol 44 (04) ◽  
pp. 928-937
Author(s):  
Félix Belzunce ◽  
Helena Martínez-Puertas ◽  
José M. Ruiz
Keyword(s):  
Failure Rate ◽  
Residual Life ◽  
Parallel Systems ◽  
Mean Residual Life ◽  
Convex Order ◽  
Increasing Failure Rate ◽  
Decreasing Failure Rate ◽  
New Better Than Used ◽  
Better Than

Recently Li and Yam (2005) studied which ageing properties for series and parallel systems are inherited for the components. In this paper we provide new results for the increasing convex and concave orders, the increasing mean residual life (IMRL), decreasing failure rate (DFR), the new worse than used in expectation (NWUE), the increasing failure rate in average (IFRA), the decreasing failure rate in average (DFRA), and the new better than used in the convex order (NBUC) ageing classes.

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