Four-Parameter Weibull Distribution with Lower and Upper Limits Applicable in Reliability Studies and Materials Testing

Kohout, Jan

doi:10.3390/math11030544

Cited by 9 publications

(4 citation statements)

References 24 publications

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“…Based on the above embedded optimization, the data distribution of the time between failures can be ensured. (5) The distribution feature of the failure-grade index is analyzed firstly based on the calculation implemented in the example cases of the above section. Figure 5a,b shows the interval distributions of the failure-grade index for the machine tool and the cooling system, respectively.…”

Section: Modified Adaptive Small-sample-expansion Methods and Example...mentioning

confidence: 99%

“…According to research experiences, the time between the failures or service life of electromechanical equipment such as computer numerical control (CNC) machine tools is subject to certain probability distribution types. Typical distribution types mainly include exponential distribution [4], Weibull distribution [5,6], Rayleigh distribution [7], normal distribution [8], and extremum distribution [9]. For example, under the complete maintenance assumption of "repair as new", exponential distribution and Weibull distribution are often used for faultdata modeling.…”

Section: Introductionmentioning

confidence: 99%

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A Statistical Evaluation Method Based on Fuzzy Failure Data for Multi-State Equipment Reliability

Xu,

Yan,

Pei

et al. 2024

Mathematics

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For complex equipment, it is easy to over-evaluate the impact of failure on production by estimating the reliability level only through failure probability. To remedy this problem, this paper proposes a statistical evaluation method based on fuzzy failure data considering the multi-state characteristics of equipment failures. In this method, the new reliability-evaluation scheme is firstly presented based on the traditional statistical analysis method using the Weibull distribution function. For this scheme, the failure-grade index is defined, and a fuzzy-evaluation method is also proposed by comprehensively considering failure severity, failure maintenance, time, and cost; this is then combined with the time between failures to characterize the failure state. Based on the fuzzy failure data, an improved adaptive-failure small-sample-expansion method is proposed based on the classical bootstrap method and the deviation judgment between distributions of the original and newborn samples. Finally, a novel reliability-evaluation model, related to the failure grade and its membership degree, is established to quantify the reliability level of equipment more realistically. Example cases for three methods of the scheme (the failure-grade fuzzy-evaluation method, the sample-expansion method, and the reliability-evaluation modeling method) are presented, respectively, to validate the effectiveness and significance of the proposed reliability-evaluation technology.

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Section: Modified Adaptive Small-sample-expansion Methods and Example...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Statistical Evaluation Method Based on Fuzzy Failure Data for Multi-State Equipment Reliability

Xu,

Yan,

Pei

et al. 2024

Mathematics

View full text Add to dashboard Cite

show abstract

“…About the catastrophe rate, the value that this distribution has is a greater number of early failures, which declines over the period as the faulty samples are removed from the model. Since these failures occur in the early period of an item's life, it is referred to as “infant mortality" [ [113] , [114] , [115] , [116] , [117] ]. In this review hereafter, the scale parameter,

is replaced with

the shape parameter,

is replaced with

and the threshold parameter, γ is replaced with

Fig.…”

Section: Overview Of Weibull Analysis (Wa)mentioning

confidence: 99%

“…As a product age, wear out increases the failure rate. The life cycles of many consumer electronics goods exhibit the bathtub curve [ 115 , 127 , 128 ].…”

Section: Overview Of Weibull Analysis (Wa)mentioning

confidence: 99%