A mass of 150g was hung in turn from 250 pieces of a certain yarn, and 12 of the pieces broke. A load of 200g was then hung from the previously unbroken pieces and a further 213 pieces broke. Assume that yarn strength is distributed normally. Estimate the mean and standard deviation of the yarn strength.

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The proportion of yarn that can withstand 150g of load, = 238/250 = 0.952 The proportion of yarn that cannot withstand = 1-0.952= 0.048 or 12/250 = 0.048 The proportion of yarn that can withstand 200g of load, = 25/250 = 0.1 Let µ and σ be mean and standard deviation of yarn’s strength Therefore, … Read more

A manufacturing company produces knitted sports goods. It is found that 2% of the goods produced are defective. What is the probability that in a shipment of 100 such goods 4% or more will prove to be defective?

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Answer: To solve this problem, we can use the binomial probability distribution formula. The binomial distribution is applicable when there are two possible outcomes (defective or non-defective) and each trial is independent with a constant probability of success (defective in this case). Let’s denote: – (p) as the probability of a single item being defective … Read more

GATE TF Syllabus 2025: Textile Engineering & Fibre Science

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A. General Aptitude Verbal Aptitude Basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb-nounagreement, and other parts of speech Basic vocabulary: words, idioms, and phrases in contextReading and comprehension Narrative sequencing Quantitative Aptitude Data interpretation: data graphs (bar graphs, pie charts, and other graphs representing data), 2-and 3-dimensional plots, maps, and tables Numerical computation and … Read more

A manufacturing company produces knitted sports goods. It was found that 2% of the goods produced were defective. What is the probability that in a shipment of 100 such goods, 4% or more will prove to be defective?

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To solve this problem, we can use the binomial probability distribution formula. The binomial distribution is applicable when there are two possible outcomes (defective or non-defective) and each trial is independent with a constant probability of success (defective in this case).Let’s denote: (p) as the probability of a single item being defective (0.02 in this … Read more

Mean count of 100 samples of yarn was found to be 40’s with a SD of 6’s Ne. How many tests are required to make at 95% confidence limit, error in yarn count be 2.56 %.

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Answer: To determine the number of tests required to achieve a certain level of confidence with a given margin of error, we can use the formula for the confidence interval of the mean: Margin of Error = (Z_(α/2) *σ) / √n Where: –  Z is the z-score corresponding to the desired confidence level, – σ is … Read more

Textile Statistics: The mean yarn count of 200 samples is 20.46 Ne, and the standard deviation is 0.5. The tolerance limit for yarn count variation is 19.7 Ne to 21.22 Ne. Determine the off-count percentage.

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To determine the off-count percentage, we need to find the proportion of samples that fall outside the tolerance limits.First, let’s find the z-scores corresponding to the lower and upper tolerance limits:For the lower limit (19.7 Ne):ZLower = (19.7 – 20.46)/0.5 [As Z = (X-μ)/σ ]= -1.52For the upper limit (21.22 Ne):ZUpper = (21.22 – 20.46)/0.5= … Read more

Textile Statistics: In a normal distribution, 10% of the yarn fault (thick/thin places/neps) is under 4mm in length, and 90% of the yarn is under 20 mm long. What are the mean and standard deviation of the distribution?

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To solve this problem, we can use the properties of the normal distribution, specifically the z-score formula. Given that: 10% of the yarn faults are under 4 mm in length, this corresponds to the area to the left of 4mm. 90% of the yarn faults are under 20 mm in length; this corresponds to the … Read more

Reuse of denim garments, a step towards sustainability

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The History of Denim: Global denim market – statistics & facts: Indian denim market – statistics & facts: Environmental impacts of denim processing: Sources of denim waste – statistics & facts: Ways to Reuse, Repurpose, and Re-imagine: Frayed denim pouch: Use a portion of a pair of old jeans to create this simple frayed edge … Read more

Evolution of technology for shirt button attachment & ROI (Return on investment)

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Earlier, button attaching was time-consuming, with more defects when done manually. Now, with advancements in technology, it has become very convenient to do the job. Automated button attachments have helped to reduce the cycle time to a great extent. Different types of buttons like buttons with two holes and four holes could be sewn on … Read more