GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- IV (New) EXAMINATION - WINTER 2019
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Subject Code: 2142905Subject Name: Statistical Quality Control & Textile Costing
Time: 10:30 AM TO 01:00 PM
Date: 12/12/2019
Total Marks: 70
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Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
Q.1 (a) Define the term:
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- Mode
- PMD
- Coefficient of variation
(b) The following table shows test results pertaining to yarn count. (Marks 04)
| Test No. | Count |
|---|---|
| 1 | 24 |
| 2 | 20 |
| 3 | 18 |
| 4 | 21 |
| 5 | 22 |
| 6 | 23 |
| 7 | 19 |
| 8 | 20 |
Find the quartile deviation. (Marks 07)
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Q.2 (a) Following are the results of the fabric strength (in 10 gm) obtained from the samples of two different fabrics. (Marks 03)
Fabric A |22.0|21.5|22.8|21.0|23.0|20.9|21.6|22.0|22.8|21.2
Fabric B |22.3|21.6|22.0|22.1|22.0|22.3|21.8|21.8|21.6|21.8
Find out using above data which fabric is more consistent in terms of the strength.
(b) Describe various types of scatter diagram. (Marks 04)
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(c) Find out D7 & P35 for the following frequency distribution. (Marks 07)
| Class | 30-34 | 35-39 | 40-44 | 45-49 | 50-54 | 55-59 | 60-64 |
|---|---|---|---|---|---|---|---|
| Frequency | 3 | 5 | 12 | 18 | 14 | 6 | 2 |
OR
(a) An experiment was conducted to study the effect of a dye produced by four different companies (A, B, C, and D) on the strength of the fabric and following results were obtained. (Marks 03)
| Dye | A | B | C | D |
|---|---|---|---|---|
| Fabric strength | 250 | 225 | 250 | 300 |
| 275 | 250 | 275 | 250 | |
| 275 | 225 | 250 | 275 | |
| 300 | 300 | 250 | 300 |
Carry out the analysis (One way ANOVA) of the above data and write the conclusion. (Table value of F for 3, 12 degree of freedom at 5% level= 3.49)
(b) A 4 X 4 LSD was conducted to study the effects of four different dyes A, B, C, and D on the strength of the fabric. To remove the variation of the laboratory and the operators conduced the experiment in four different laboratories and the results obtained are as follows: (Marks 04)
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| Lab | I | II | III | IV |
|---|---|---|---|---|
| I | 66 (B) | 74 (D) | 70 (A) | 72 (C) |
| II | 75 (D) | 63 (A) | 68 (C) | 65 (B) |
| III | 69 (A) | 72 (C) | 63 (B) | 75 (D) |
| IV | 70 (C) | 65 (B) | 74 (D) | 70 (A) |
Carry out analysis of the above data and write the conclusion. (Table value of F for 3, 6 degree of freedom at 5% level =4.76) (Marks 07)
Q.3 (a) What is meant by correlation? Explain types of correlation. (Marks 03)
(b) Explain Binomial distribution with their properties (Marks 04)
(c) Calculate the coefficient correlation of the following data and comment on it. (Marks 07)
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Y | 2 | 6 | 7 | 8 | 10 | 11 | 11 | 10 | 9 |
OR
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(a) State the properties of Normal distribution. (Marks 03)
(b) Explain Poisson distribution with their properties. (Marks 04)
(c) Two judges in a fabric assessment rank 6 fabric samples in the following order. Find out spearman’s rank correlation coefficient. (Marks 07)
| Sample | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| Judge A | 2 | 1 | 3 | 5 | 6 | 4 |
| Judge B | 3 | 2 | 6 | 4 | 5 | 1 |
Q.4 (a) Briefly explain about the small sample t-test. (Marks 03)
(b) Five knitted garments each were selected at eight different times during the production and following results of number of defective garments were obtained. (Marks 04)
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| Sample nos. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| No. of defective garments | 0 | 2 | 1 | 1 | 2 | 0 | 0 | 0 |
Draw the np-chart for the above data.
(c) The following data are related to the percentage of humidity and the warp breakage rate recorded for a week in a loom shed. (Marks 07)
| % Humidity | 54 | 85 | 86 | 50 | 42 | 75 | 65 | 56 |
|---|---|---|---|---|---|---|---|---|
| Warp breakage rate | 2.45 | 1.21 | 1.12 | 2.84 | 3.25 | 1.86 | 1.90 | 2.32 |
Using equation of line of regression, find warp breakage rate if humidity percentage on a specific day is 60 for given data.
OR
(a) Explain about collection and types of data. (Marks 03)
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(b) Following data represents average and range of linear density of the yarn obtained from eight different samples each size five, selected during a spinning process. (Marks 04)
| Sample nos. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Avg. Linear density | 19.6 | 20.1 | 20.5 | 19.4 | 22.3 | 21.7 | 20.3 | 19.9 |
| Range | 1.2 | 1.24 | 1.6 | 1.8 | 2.0 | 1.7 | 2.0 | 1.8 |
Draw the mean charts for the above data.(A2=0.577)
(c) Ten ring bobbins selected from the production of the day shift and fifteen ring bobbins selected from the production of the night shift have shown following results. (Marks 07)
| Day shift | Night shift | |
|---|---|---|
| No. of tests | 10 | 15 |
| Average count | 40.2 | 39.3 |
| Std. dev. of count | 2.5 | 3.8 |
From these sample results, is there any evidence that the yarn spun during night shift is coarser than the day shift? Use 10% los. (Table value t23,0.1=1.319)
Q.5 (a) Ten strength test made on certain yarn have shown the following results; 22.8,23.2,22.9,22.6,23.4,23.0,23.1, 23.0, 22.9, 23.0 (Marks 03)
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Find the median for the above data and comment on it.
(b) Write short note on Material cost. (Marks 04)
(c) For spinning 18s warp carded yarn, three qualities of cottons are used. Their proportions and rates/kg. are as shown below. (Marks 07)
| Cotton Variety | % in mix | Cost/kg. (in Rs.) |
|---|---|---|
| A | 8 | 5.84 |
| B | 88 | 5.00 |
| C | 4 | 3.00 |
Waste of cotton aggregate to 5% and other spinning waste is 12% on mixing. If saleable waste per 100kg. put through, 8kg. are saleable at 1.75 Rs./kg.
OR
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(a) Discuss about population and sample. (Marks 03)
(b) Write short note on labour cost. (Marks 04)
(c) Explain in detail about DMAIC process. (Marks 07)
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