Weibull and lognormal Taguchi analysis using multiple linear regression

2019

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In this paper, the formula to estimate the sample size n to perform a random vibration test is derived only from the desired reliability (R(t)). Then, the addressed n value is used to design the ISO16750‐3 random vibration test IV for both normal and accelerated conditions. For the normal case, the applied random vibration stress (S) is modeled by using the Weibull stress distribution [W(s)]. Similarly, for the testing time (t), the Weibull time distribution [W(t)] is used to model its random behavior. For the accelerated case, by using the over‐stress factor fitted from the W(t) and W(s) distributions, four accelerated scenarios are formulated with their corresponding testing's profiles. Additionally, from the W(s) analysis, the stress formulation to perform the fatigue and Mohr stress analysis is given. Since the given Weibull/fatigue formulation is general, then the formulas to determine the W(s) parameters, which correspond to any principal stresses values and/or vice versa, are given. Although the application is performed to demonstrate R(t) = 0.97 by testing only n2 = 6 parts, the guidelines to use the values given in columns n, S, and t of the Weibull analysis table to generate several accelerated testing plans are given.

Section: Discussionmentioning

confidence: 99%

“…9. On the other hand, it is important to mention that if the time Weibull family W (β t , η t ) or the stress Weibull family W (βs, ηs) are determined based on several stress variables, then the Taguchi method given in 26 can be used to determine the corresponding Weibull parameters. 10.…”

Section: Discussionmentioning

confidence: 99%

Weibull analysis for normal/accelerated and fatigue random vibration test

2019

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“…Therefore, since in Equation , only η is unknown, then it should also be possible to estimate η on the basis of n . Fortunately, from Equation and Piña et al, the n value that holds with the given R(t) , t , and β values is given by

n = \frac{1}{- ln ([],, R ((),, t))} .

…”

Section: Weibull Sample Size Nmentioning

confidence: 99%

“…As a consequence, the Weibull family, which the PCIs shall represent is W(3, 4356.388). Therefore, since in Equation 14, only η is unknown, then it should also be possible to estimate η on the basis of n. Fortunately, from Equation 15 and Piña et al, 17 the n value that holds with the given R(t), t, and β values is given by…”

Section: Weibull Sample Size Nmentioning

confidence: 99%

Unbiased Weibull capabilities indices using multiple linear regression

Baro

Ortiz-Yañez³

2017

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Although the recently proposed Weibull process capability indices (PCIs) actually measure the times that the standard deviation (σx) is within the tolerance specifications, because they not accurately estimate neither the log‐mean (μx) nor the σx values, then the actual PCIs are biased. This actually because μx and σx are both estimated without considering the effect that the sample size (n) has over their values. Hence, μx is subestimated and σx is overestimated. As a response to this issue, in this paper, μx and σx are estimated in function of n. In particular, the PCIs' efficiency is based on the following facts: (1) the derived n value is unique and it completely determines η, (2) the μx value completely determines the η value, and (3) the σx value completely determines the β value. Thus, now, since μx and σx are in function of n and they completely determine β and η, then the proposed PCIs are unbiased, and they completely represent the analyzed process also. Finally, a step by step numerical application is given.

“…In Eqn (5), n is the sample size to be tested, which based on R(t) (see Piña et al 11 Section 3.3.1), is given by…”

Section: Weibull and Process Parameter Relationshipsmentioning

confidence: 99%

Conditional Weibull Control Charts Using Multiple Linear Regression

2016

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Because in Weibull analysis, the key variable to be monitored is the lower reliability index (R(t)), and because the R(t) index is completely determined by both the lower scale parameter (η) and the lower shape parameter (β), then based on the direct relationships between η and β with the log-mean (μ x ) and the log-standard deviation (σ x ) of the analyzed lifetime data, a pair of control charts to monitor a Weibull process is proposed. Moreover, because the fact that in Weibull analysis, right censored data is common, and because it gives uncertainty to the estimated Weibull parameters, then in the proposed charts, μ x and σ x are estimated of the conditional expected times of the related Weibull family. After that both, μ x and σ x are used to monitor the Weibull process. In particular, μ x was set as the lower control limit to monitor η, and σ x was set as the upper control limit to monitor β. Numerical applications are used to show how the charts work.