A study on mean residual life and failure rate functions for exponentiated weibull distribution

Firmware is embedded software in hardware devices and they play important role for many critical systems' function. Firmware failure rate in operation should be quite lower than the application software which is operating on it. Most of the study on software reliability deals with systems during development, and it is also important to study the integrated system during operation. Complex systems usually have a bathtub-shaped failure rate over the lifecycle of the product. This paper discusses the parametric analysis of model given by Haupt and Schäbe (1992), exponentiated Weibull distribution and models generated from Pareto and Weibull distribution, as well as their possible application to modeling firmware system failure. In addition, the Safety Integrity Levels (SIL) stipulated in IEC 61508 are taken into account in the modeling since the safety-critical systems in general are firmware-dominated.

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The Generalized Gamma – Exponentiated Weibull Distribution with its Properties

Al-Mustansiriyah Journal of Science ◽

10.23851/mjs.v31i2.775 ◽

2020 ◽

Vol 31 (2) ◽

pp. 30

Author(s):

Salah Hamza Abid ◽

Nadia Hashim Al-Noor ◽

Mohammad Abd Alhussein Boshi

Keyword(s):

Weibull Distribution ◽

Simulated Data ◽

Quantile Function ◽

Cumulative Distribution ◽

Generalized Gamma ◽

Distribution Probability ◽

Exponentiated Weibull Distribution ◽

Exponentiated Weibull ◽

Rate Functions ◽

Special Case

In this paper, we present the Generalized Gamma-Exponentiated Weibull distribution as a special case of new generated Generalized Gamma - G family of probability distribution. The cumulative distribution, probability density, reliability and hazard rate functions are introduced. Furthermore, the most vital statistical properties, for instance, the r-th moment, characteristic function, quantile function, simulated data, Shannon and relative entropies besides the stress-strength model are obtained.

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MEAN RESIDUAL LIFE AND OTHER PROPERTIES OF WEIBULL RELATED BATHTUB SHAPE FAILURE RATE DISTRIBUTIONS

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539304001397 ◽

2004 ◽

Vol 11 (02) ◽

pp. 113-132 ◽

Cited By ~ 24

Author(s):

C. D. LAI ◽

LINGYUN ZHANG ◽

M. XIE

Keyword(s):

Failure Rate ◽

Residual Life ◽

Weibull Model ◽

Parameters Estimation ◽

Mean Residual Life ◽

Bathtub Shape ◽

Reliability Characteristics ◽

Rate Functions ◽

Life Distributions ◽

The Relationship

The two-parameter Weibull distribution is widely used in reliability analysis. Because of its monotonic ageing behaviour, its applicability is hampered in certain reliability situations. Several generalizations and extensions of the Weibull model have been proposed in the literature to overcome this limitation but their properties have not yet been described in a unified manner. In this paper, graphical displays of the mean residual life curves of several families of Weibull related life distributions are given together with their corresponding failure rate functions. The relationship between these two functions are visibly demonstrated. We focus our attention on the Weibull related families that have bathtub or modified bathtub shape failure rates. Important reliability characteristics such as burn-in, change point and flatness of bathtub of these families are examined. Model selection and parameters estimation are also discussed.

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