Why shape parameter in Weibull distribution difficult to model or estimate?

I have different wind speed data and I want to find both Weibull and Rayleigh PDF scale and shape parameters in Excel sheet. Simplest method for these calculations on Excel through only wind speed data??

We have failure data, and we need to calculate the scale and shape parameters.

The Sumerian term 𒌦 (kalam), which means ''homeland" or "mainland," has possible linguistic ties to Proto-Altaic and Proto-Turkic concepts that evoke notions of proximity, family, and permanence. The Proto-Turkic term "kiāl" suggests the idea of "to stay behind and front," encompassing a sense of staying or remaining within a particular space, which is central to the concept of a homeland (Starostin et al., 2003: 71). Further, the Proto-Altaic word "kalu" implies being "near" or "to come near" (Starostin et al., 2003: 637), reinforcing the theme of closeness associated with the idea of a homeland. Additionally, another Proto-Altaic term "kala" is linked to "family" and "gathering" (Starostin et al., 2003: 634), which are inherently connected to the notion of a homeland as a central place where families and communities come together and reside.

The Sumerian verb 𒋾 (til3), meaning "to live," shows linguistic parallels to Proto-Turkic terms that carry similar life-affirming meanings. The Proto-Turkic word "dīri" particularly resonates with this concept, encompassing meanings such as "to live," "be alive," and "revive." This connection illustrates a shared linguistic and cultural valuation of life and vitality across these ancient language families. Additionally, in some Turkic dialects, the terms "tilin" and "tillij" are used specifically with the meaning "to revive" (Starostin et al., 2003: 1371-1372), suggesting a nuanced extension of the basic concept of living towards rejuvenation and renewal. These terms enrich the semantic field related to life and living, indicating that the concept was multifaceted and culturally significant, with specific lexical items developed to express different aspects of life and vitality.

In this expression, the sequence shows a complex sentence structure with a series of noun and verb phrases that cumulatively build a comprehensive thought. The sentence seems to be structured around a series of conditions or actions leading to an outcome. Proto Turkic Structure follows a similar complex pattern, using a series of descriptive terms that progressively build up to a conclusion. It uses a mixture of verbs and nouns to create a narrative flow.

✓ Both languages use a complex narrative structure that layers multiple concepts to build towards a culminating action or state (reviving the homeland).

✓ The use of temporal markers at the beginning sets the stage for a sequence of events or conditions.

✓ The construction in both languages reflects a deep narrative style, where each component adds semantic depth to the sentence.

16th Phrase:

𒀀𒊮𒆜𒅗𒄊𒅗𒉇𒉆𒁀𒂊𒌍𒀳𒊒𒍣𒁑

𒂵𒀀𒀭

❖ a-šag4 kaškal ka-ĝiri3-ka ba-e-ur11-ru zi

bulug-ga- am3(a.an)

❖ basıg kaç-kal kajirikan nam baejuru azun

puluggang (Proto Turkic Reconstruction)

❖düz yol kayırır iken azının bayır neyini

pulluklayan (Turkish Reconstruction)

❖ while a straight/cleared off road would favor

[one], one ploughs the life’s steepness up

❖ you should not plough a field at a road or a

path (Accredited Translation)

In Sumerian, the term 'a-šag4' translates to 'field.' This term is etymologically connected to the Proto Turkic word 'basɨg,' which also means 'field' or 'cornfield.' Furthermore, in the Zonguldak dialect of Turkish, the term 'bâsu-raχ' is used to describe a 'fenced garden' or 'yard,' showing the semantic evolution of this concept from ancient to modern times within Turkic languages.

The Sumerian term 'kaškal', combining 'kaš' (to run, walk) with 'kal' (a suffix indicating 'to remain'), means 'road'. This term corresponds to the Proto Altaic root 'aja' and the Proto Turkic 'kaj', which both reflect the concepts of movement such as 'to go', 'to run', 'to walk', or 'to pass'. The ending 'kal' in Turkish, derived from Proto Altaic 'kial', serves as an affirmative suffix, reinforcing the idea of 'remaining' or persisting in a state or action. This

layered meaning highlights a conceptual link between physical movement and permanence across these languages.

The Sumerian compound 'ka-ĝiri3', which combines 'ka' (meaning 'mouth') and 'ĝiri' (meaning 'path'), is interpreted as 'to favor'. This compound reflects a metaphorical usage, where speaking ('mouth') favorably influences the 'path' or direction of something or someone. This interpretation aligns with various related terms in Proto Altaic and Turkic languages (Starostin et al., 2003):

✓ The Proto Altaic root 'ak' and the Proto Turkic '(k)ag', both meaning 'mouth', correspond to the Sumerian 'ka'. In modern Turkish, 'ağız' continues to carry the meaning 'mouth'.

✓ The Old Turkic word 'qaj', meaning 'crossroad', and Proto Altaic 'giru', meaning 'road', along with Tungusian 'giri' (also 'road') and Turkish 'yürü' ('walk'), all relate to the Sumerian 'ĝiri' as aspects of paths or ways.

Thus, the semantics of 'ka-ĝiri3' are reflected in modern Turkish through the verb 'kayır-', which means 'to favor' or 'to let go of', illustrating how the concept of guiding or favoring someone

linguistically evolved from describing physical paths to metaphorical guidance.

In Sumerian, the tag for the cuneiform sign 𒅗 (KA) suggests an unknown meaning (besides well known meaning of ‘mouth’), possibly used as a time-indicating suffix. This function could correspond to the Turkish word ‘iken’, which is used to indicate temporal conditions such as 'when' or 'while'. The parallel suggests a potential linguistic link, where both the Sumerian suffix and the Turkish conjunction express aspects of time in a sentence.

The Sumerian phrase "nam ba-e-ur11-ru" resonates with the dialectal Turkish term "bayırı-nım," which denotes the 'steepness' of a place. According to Black et al. (1998), the component "ur11-ru" in Sumerian is associated with the verb 'to plough', linking it to the Turkish verb "-sür," which carries a similar meaning. In this specific Sumerian construction, the prefixes "ba-e" suggest an action of 'going up or down'. Consequently, the term "ba-e-ur11" can be interpreted as describing a 'steep' place or road, analogous to the Turkish word "bayır," which also refers to a slope or incline. This comparison highlights a nuanced linguistic correspondence between the Sumerian description

of physical terrain and its modern Turkish counterpart.

In Sumerian, the term "zi" denotes both the action "to live" and the noun "life." This corresponds to the Proto Altaic term "zela," which encompasses meanings such as "to be awake" and "to live." Further, there is a linguistic thread extending into Old Turkic with the word "azun" and into modern Turkish with "azı," both of which also mean "life." These connections illustrate the thematic continuity and linguistic evolution from ancient to modern languages in how concepts related to life and living are expressed.

The term "bulug-ga-am3" is identified by Black et al. (1998) as denoting 'a sharp object.' Specifically, "bulug" in Sumerian is traditionally understood to mean 'needle.' This interpretation is likely influenced by the action associated with "ul," which means 'to sew' in various Tungusic dialects. This semantic thread ties back to Proto-Altaic "(b)iṓĺe," which encompasses actions such as to weave, bind, or sew, further extending into Proto-Turkic "(b)iēĺ(mik)" and Proto-Tungusian "(b)ul." The Turkish word "ilmik" (knot, stitch, or to knit) also aligns with this semantic field. However, the term "bulug" also encompasses actions like 'pulling,' 'grabbing,' and 'blowing,' along with nouns like "bulug," which means 'mud' and 'wet.' Such varied meanings suggest an additional, possibly secondary, interpretation of "bulug" as 'plough' in Turkish, known as "pulluk." This reflects a broader and more dynamic usage of "bulug" in Sumerian, which may align with both the sharp, precise function of a needle and the robust, soil-turning capability of a plough. This comparative morphology analysis demonstrates how a single Sumerian term can evolve across related languages, developing multiple, context-dependent meanings that reflect both cultural and practical aspects of ancient and modern life (Starostin et al., 2003).

The Sumerian term 𒀳 'apin', which translates to 'plough', is etymologically derived from the verbal clause 𒀀𒉈 'a-pil'. This origin reflects a deep-rooted connection to agriculture in Sumerian culture. Correspondingly, in Proto Turkic, the related term 'apɨl' signifies 'hoe', highlighting a shared focus on agricultural tools among these language families. Further enriching this linguistic landscape, the Kirghiz term 'abɨl-qasɨm' specifically refers to a component of the plough, namely one of its pegs, demonstrating the nuanced understanding and specialization of agricultural implements in Turkic languages. This etymological thread illustrates how fundamental agricultural practices

were common among Sumerians and Proto Turks.

In Sumerian, the compound term 𒊕𒀳 'saĝ-apin' specifically refers to the 'plough beam' or 'plough head,' key components of the plough that highlight its structural importance. This term corresponds closely with the Turkish word 'saban', which is also used broadly to mean 'plough,' similar to another Turkish term, 'pulluk'. Additionally, the Turkish language includes the term 'yaba', which describes a fork used for holding grass. This diversity in terminology indicates a rich agricultural vocabulary that reflects both the practical aspects of farming equipment and the linguistic connections between these ancient and modern cultures.

In Sumerian, the term 𒄑𒆪 [ĝeš] 'KU' carries the meaning of 'plough,' an essential agricultural tool. This term's semantics extend into Proto Altaic, where 'guk ̔à~u' captures concepts such as 'curve,' 'hook,' and 'to cling.' These meanings suggest a functional aspect of the plough related to its curved and hooking parts, which are vital for its operation in tilling soil. Further connecting these linguistic dots, the Proto Tungusian word 'guk' specifically denotes 'plough thill,' which is the horizontal beam of a plough, indicating direct parallels in agricultural terminology and technology across these language families. This cross-linguistic

consistency underlines the importance of ploughing in these cultures and the specialized vocabulary developed to describe its various components.

In Sumerian, the term 𒄑𒃮 [ĝeš] 'gaba' notably corresponds to the concept of a hoe, a fundamental agricultural tool, and encompasses the action of digging. This specific term finds its counterpart in the Turkish word 'çapa' [or yaba, as identified before], which similarly refers to both the hoe as an implement and the digging action it performs. This correlation illustrates the continuity and persistence of agricultural terminology and practices from ancient Sumerian into modern Turkish. The semantic overlap underscores the integral role that such tools have played in both societies, bridging ancient and contemporary agricultural vocabularies .

In Sumerian, the term 𒌆𒋽, tug2-gur8, is another designation for the 'plough', highlighting the variety of terms used to describe this essential agricultural tool. This term aligns with the Proto Turkic word (b)okursɨ, which specifically denotes a 'wooden plough' and 'ploughshare', indicating a more detailed description of the plough's components and materials. Furthermore, the Proto Tungusic term 'suk' encompasses multiple related meanings: a 'chisel', used metaphorically to describe the plough's action in soil; 'to carve' or 'engrave', evoking the plough's effect on the earth; and 'to hit', suggesting the impact necessary in traditional ploughing techniques. This is complemented by the Orchon Tungusic 'tūku', further cementing the extensive linguistic and cultural importance of ploughing and its tools across these regions. These connections illustrate a deep, shared understanding of agriculture and toolmaking, reflected in the specific vocabulary used to describe various aspects of the plough's function and form.

In Sumerian, the expression 𒀀𒈨 a-me, is employed to denote various parts of a plough, highlighting the detailed terminology used to describe this essential agricultural implement. This precise use of language reflects an intricate understanding of the plough's structure and functionality within Sumerian society. This concept finds a parallel in the Proto Altaic term amča and the Proto Turkic amač, both of which also refer to the plough in a broader sense. These terms underscore the importance of the plough across these linguistic groups, indicating a shared agricultural heritage and technological knowledge. The alignment of these terms across cultures not only underscores the vital role of agriculture but also showcases the linguistic connections that point to deeper historical and cultural identical commonalities.

Please some examples for WASPAS,CRITIC ,COPRAS in optimizing machining parameters!

How does crack develop in Laser powder bed fusion additive manufacturing after solidification of material.?

How does the dendritics growth occur?

Is it due to small pores or residual stress while cooling down or cooling rate?

Assuming the electrical breakdown probability follows the two-parameter Weibull

distribution function:

See attached document

How do we combine the COVs of two independent, uncorrelated variables of different probability distributions?

Question

Weather-related loadings on electrical transmission lines involves incidence of wind on an iced conductor, separately and combined. Current US codes require transmission wires and structures be checked for the following load cases:

L1 Extreme Wind (high wind loads on bare conductors, upto 150 mph or 230 kmph)

L2 Extreme Ice (accumulated radial freezing ice, sometimes upto 2” to 4” in thickness)

L3 Combined Ice and Wind (¼” to ½” ice with variable winds, usually 20 mph to 40 mph)

Wind speeds are often considered to follow a Weibull or Extreme Value type distributions) while ice is generally known to be a Normal distribution. Some known COVs (coefficients of variation) are:

C1 Ice: 0.09

C2 Wind: 0.18 to 0.20

If one considers the load case L3, as shown in the sketch below, the Resultant of the ice load (V) and wind load (T) – both in force units per unit length of cable – can be expressed as:

Force Resultant R = √(V2 + T2)

Can this vectorial approach be valid for a resultant COV? Say COVR = √(C12+ C22)?

Note: Ice and Wind are totally independent variables and possess no statistical correlation whatsoever.

📷

Equations to calculate ice and wind loads are available in standard textbooks. Wind pressure p (psf) is generally approximated as p = 0.00256*S2 where S is the wind speed in miles per hour.

Hello,

Let's imagine we're using a Weibull law to study experimental dispersions and we've evaluated these laws for 3 loading levels, say 1 MPa, 5 MPa and 10 MPa. Is there a method that can predict the probability law for the experimental dispersion at, say, 3 MPa or 12 MPa?

Best regards,

Benjamin Martin

We are trying to compare results from a cell culture analysis. we have done 3 or 4 replicates per condition which is common practice.

Student's t-test is often used in similar publications, however, I'm not sure if is the best option, as 3 replicates per condition we cannot assume a normal distribution.

Which is the optimal statistical test you would use in such experimental conditions?