Estimation of a distribution function with increasing failure rate average

2021 ◽  
Vol 213 ◽  
pp. 179-192
Author(s):  
Hammou El Barmi ◽  
Ganesh Malla ◽  
Hari Mukerjee
Keyword(s):  
Distribution Function ◽  
Failure Rate ◽  
Increasing Failure Rate

ACKNOWLEDGMENT OF PRIORITY: “On the conditions for mixtures of increasing failure rate distributions to have an increasing failure rate”

2003 ◽  
Vol 17 (1) ◽  
pp. 153-153
Author(s):  
James Lynch
Keyword(s):  
Failure Rate ◽  
Applied Probability ◽  
Increasing Failure Rate

The above-mentioned article by James Lynch was published in Probability in the Engineering and Informational Sciences (1999), 13: 33–36.It has recently been brought to the author's attention that the results in that paper were preceded and superseded by the results in Thomas H. Savits' paper, “A multivariate IFR class,” which appeared in the Journal of Applied Probability (1985), 22: 197–204. This acknowledgment is to correct this contretemps.

scholarly journals ДОСЛІДЖЕННЯ ПОКАЗНИКА ЕФЕКТИВНОСТІ ЕКСПЛУАТАЦІЇ ЗАСОБІВ ВИМІРЮВАЛЬНОЇ ТЕХНІКИ МЕТОДОМ КОМПʼЮТЕРНОГО МОДЕЛЮВАННЯ

2020 ◽  
pp. 166-169
Author(s):  
Олександр Володимирович Томашевський ◽  
Геннадій Валентинович Сніжной
Keyword(s):  
Computer Simulation ◽  
Distribution Function ◽  
Normal Distribution ◽  
Failure Rate ◽  
Random Variable ◽  
Operational Efficiency ◽  
Distribution Law ◽  
Maintenance System ◽  
Wide Range ◽  
Calibration Interval

The operational efficiency of measuring equipment (ME) is important in determining the cost of maintaining ME. To characterize the operational efficiency of the ME, an efficiency indicator has been introduced, an increase of which will reduce costs caused by the release of defective products due to the use of ME with unreliable indications. Over time, the ME parameters change under the influence of external factors and the ME aging processes inevitably occur, as a result of which the parameters of the ME metrological service system change. Therefore, in the general case, the parameters of the metrological maintenance system of ME should be considered as random variables. Accordingly, the efficiency indicator of measuring instruments is also a random variable, for the determination of which it is advisable to apply the methods of mathematical statistics and computer simulation. The performance indicator depends on the parameters of the metrological maintenance ME system, such as the calibration interval, the time spent by the ME on metrological maintenance, and the likelihood of ME failure-free operation. As a random variable, the efficiency indicator has a certain distribution function. To determine the distribution function of the efficiency indicator and the corresponding statistical characteristics, a computer simulation method was used. A study was made of the influence on the indicator of the effectiveness of the parameters of the metrological maintenance system ME (interesting interval, the failure rate of ME). The value of the verification interval and the failure rate of MEs varied over a wide range typical of real production. The time spent by ME on metrological services is considered as a random variable with a normal distribution law. To obtain random numbers with a normal distribution law, the Box-Muller method is used. After modeling, the statistical processing of the obtained results was done. It is shown that in real production, the efficiency indicator has a normal distribution law and the value of the efficiency indicator with an increase in the calibration interval does not practically change.

CLASSIFICATION OF MULTIVARIATE LIFE DISTRIBUTIONS BASED ON PARTIAL ORDERING

2002 ◽  
Vol 16 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Present Article ◽  
Failure Rate ◽  
Partial Ordering ◽  
Increasing Failure Rate ◽  
Multivariate Generalization ◽  
Partial Orderings ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

Barlow and Proschan presented some interesting connections between univariate classifications of life distributions and partial orderings where equivalent definitions for increasing failure rate (IFR), increasing failure rate average (IFRA), and new better than used (NBU) classes were given in terms of convex, star-shaped, and superadditive orderings. Some related results are given by Ross and Shaked and Shanthikumar. The introduction of a multivariate generalization of partial orderings is the object of the present article. Based on that concept of multivariate partial orderings, we also propose multivariate classifications of life distributions and present a study on more IFR-ness.

A multivariate IFR class

1985 ◽  
Vol 22 (01) ◽  
pp. 197-204 ◽  
Author(s):  
Thomas H. Savits
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Random Vector ◽  
Increasing Failure Rate ◽  
Rate Distribution ◽  
Weak Limits ◽  
Multivariate Exponential Distribution ◽  
Multivariate Exponential

A non-negative random vector T is said to have a multivariate increasing failure rate distribution (MIFR) if and only if E[h(x, T)] is log concave in x for all functions h(x, t) which are log concave in (x, t) and are non-decreasing and continuous in t for each fixed x. This class of distributions is closed under deletion, conjunction, convolution and weak limits. It contains the multivariate exponential distribution of Marshall and Olkin and those distributions having a log concave density. Also, it follows that if T is MIFR and ψ is non-decreasing, non-negative and concave then ψ (T) is IFR.

Failure distributions of shock models

1980 ◽  
Vol 17 (03) ◽  
pp. 745-752 ◽  
Author(s):  
Gary Gottlieb
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Shock Model ◽  
Life Distribution ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Damage Process

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate.

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.

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