Cover image of Ignou MST-013 Solved Assignment 2023

IGNOU MST-014 Solved Assignment 2023 | MSCAST

Solved By – Narendra Kr. Sharma – M.Sc (Mathematics Honors) – Delhi University

365.00

Share with your Friends

Details For MST-014 Solved Assignment

IGNOU MST-014 Assignment Question Paper 2023

untitled-document-16-9cbde385-ad0a-4c74-864f-362c1a2d74cc
  1. (a) State whether the following statements are True or False. Give reason in support of your answer:
(i) The R R R\mathrm{R}R – chart is suitable when subgroup size is greater than 10 .
(ii) In single sampling plan, if we increase acceptance number then the OC curve will be steeper.
(iii) If the effect of summer and winter is not constant on the sale of AC then we use the additive model of the time series.
(iv) If a researcher wants to find the relationship between today’s unemployment and that of 5 years ago without considering what happens in between then the partial autocorrelation is the better way in comparison to autocorrelation.
(v) A system has four components connected in parallel configuration with reliability 0.2 , 0.4 , 0.5 , 0.8 0.2 , 0.4 , 0.5 , 0.8 0.2,0.4,0.5,0.80.2,0.4,0.5,0.80.2,0.4,0.5,0.8. To improve the reliability of the system most, we have to replace the component which reliability is 0.2 .
(b) Differentiate between the autoregressive and moving average models of time series.
2(a) A manufacturer of men’s jeans purchases zippers in lots of 500 . The jeans manufacturer uses single-sample acceptance sampling with a sample size of 10 to determine whether to accept the lot. The manufacturer uses c = 2 c = 2 c=2c=2c=2 as the acceptance number. Suppose 3% nonconforming zippers are acceptable to the manufacturer and 8 % 8 % 8%8 \%8% nonconforming zippers are not acceptable. Find
(i) Probability of accepting a lot of incoming quality 0.04 .
(ii) Average outing quality (AOQ), if the rejected lots are screened and all defective zippers are replaced by non-defectives.
(iii) Average total inspection (ATI).
(b) An office supply company ordered a lot of 400 printers. When the lot arrives the company inspector will randomly inspect 12 printers. If more than three printers in the sample are non-conforming, the lot will be rejected. If fewer than two printers are nonconforming, the lot will be accepted. Otherwise, a second sample of size 8 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second sample. Also AQL and LTPD are 0.05 and 0.10 respectively. Let incoming quality be 4 % 4 % 4%4 \%4%.
(i) What is the probability of accepting the lot at the first sample?
(ii) What is the probability of accepting the lot at the second sample?
3(a) A system has seven independent components and reliability block diagram of it shown as follows:
original image
Find reliability of the system.
(b) The failure data for 40 electronic components is shown below:
Operating Time (in hours)  Operating Time (in   hours)  {:[” Operating Time (in “],[” hours) “]:}\begin{array}{l}\text { Operating Time (in } \\ \text { hours) }\end{array} Operating Time (in  hours)  0 5 0 5 0-50-505 5 10 5 10 5-105-10510 10 15 10 15 10-1510-151015 15 20 15 20 15-2015-201520 20 25 20 25 20-2520-252025 25 30 25 30 25-3025-302530
Number of Failures 5 7 6 4 5 4
Operating Time (in hours)  Operating Time (in   hours)  {:[” Operating Time (in “],[” hours) “]:}\begin{array}{l}\text { Operating Time (in } \\ \text { hours) }\end{array} Operating Time (in  hours)  30 35 30 35 30-3530-353035 35 40 35 40 35-4035-403540 40 45 40 45 40-4540-454045 45 50 45 50 45-5045-504550 50 50 >= 50\geq 5050
Number of Failures 4 0 2 1 2
” Operating Time (in hours) ” 0-5 5-10 10-15 15-20 20-25 25-30 Number of Failures 5 7 6 4 5 4 ” Operating Time (in hours) ” 30-35 35-40 40-45 45-50 >= 50 Number of Failures 4 0 2 1 2 | $\begin{array}{l}\text { Operating Time (in } \\ \text { hours) }\end{array}$ | $0-5$ | $5-10$ | $10-15$ | $15-20$ | $20-25$ | $25-30$ | | :— | :—: | :—: | :—: | :—: | :—: | :—: | | Number of Failures | 5 | 7 | 6 | 4 | 5 | 4 | | $\begin{array}{l}\text { Operating Time (in } \\ \text { hours) }\end{array}$ | $30-35$ | $35-40$ | $40-45$ | $45-50$ | $\geq 50$ | | | Number of Failures | 4 | 0 | 2 | 1 | 2 | |
Estimate the reliability, cumulative failure distribution, failure density and failure rate functions.
  1. At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the 8-hour working day. The data below shows the waiting time in seconds:
Time Sample Number
1 1 1\mathbf{1}1 2 2 2\mathbf{2}2 3 3 3\mathbf{3}3 4 4 4\mathbf{4}4 5 5 5\mathbf{5}5
9 a.m 8 9 15 4 11
10 7 10 7 6 8
11 11 12 10 9 10
12 12 8 6 9 12
1 p.m. 11 10 6 14 11
2 7 7 10 4 11
3 10 7 4 10 10
4 8 11 11 11 7
Time Sample Number 1 2 3 4 5 9 a.m 8 9 15 4 11 10 7 10 7 6 8 11 11 12 10 9 10 12 12 8 6 9 12 1 p.m. 11 10 6 14 11 2 7 7 10 4 11 3 10 7 4 10 10 4 8 11 11 11 7| Time | Sample Number | | | | | | :—: | :—: | :—: | :—: | :—: | :—: | | | $\mathbf{1}$ | $\mathbf{2}$ | $\mathbf{3}$ | $\mathbf{4}$ | $\mathbf{5}$ | | 9 a.m | 8 | 9 | 15 | 4 | 11 | | 10 | 7 | 10 | 7 | 6 | 8 | | 11 | 11 | 12 | 10 | 9 | 10 | | 12 | 12 | 8 | 6 | 9 | 12 | | 1 p.m. | 11 | 10 | 6 | 14 | 11 | | 2 | 7 | 7 | 10 | 4 | 11 | | 3 | 10 | 7 | 4 | 10 | 10 | | 4 | 8 | 11 | 11 | 11 | 7 |
(i) Use the data to construct control charts for mean and comments about the process. If process is out of control, then calculate the revised control limits.
(ii) Construct the CUSUM chart when the process is under control and draw the conclusion about the process.
(iii) If the specification limits as the 8 ± 2 8 ± 2 8+-28 \pm 28±2, then calculate the process capability index C p k C p k C_(pk)\mathrm{C}_{\mathrm{pk}}Cpk and impetrate the result.
(iv) Also find the percentage of calls lie outside the specification limits assuming that calls follow the normal distribution.
5(a) Consider the time series model
y t = 10 + 0.5 y t 1 0.8 y t 2 + ε t y t = 10 + 0.5 y t 1 0.8 y t 2 + ε t y_(t)=10+0.5y_(t-1)-0.8y_(t-2)+epsi_(t)\mathrm{y}_{\mathrm{t}}=10+0.5 \mathrm{y}_{\mathrm{t}-1}-0.8 \mathrm{y}_{\mathrm{t}-2}+\varepsilon_{\mathrm{t}}yt=10+0.5yt10.8yt2+εt
where ε t N [ 0 , 1 ] ε t N [ 0 , 1 ] epsi_(t)∼N[0,1]\varepsilon_{\mathrm{t}} \sim \mathrm{N}[0,1]εtN[0,1]
(i) Is this a stationary time series?
(ii) What are the mean and variance of the time series?
(iii) Calculate the autocorrelation function.
(iv) Plot the correlogram.
(b) The marketing manager of a company recorded the number of mobiles sold quarterly for which are given in the following table:
Quarter Q 1 Q 1 Q_(1)\mathbf{Q}_1Q1 Q 2 Q 2 Q_(2)\mathbf{Q}_{\mathbf{2}}Q2 Q 3 Q 3 Q_(3)\mathbf{Q}_{\mathbf{3}}Q3 Q 4 Q 4 Q_(4)\mathbf{Q}_{\mathbf{4}}Q4
2 0 1 8 2 0 1 8 2018\mathbf{2 0 1 8}2018 48 41 60 65
2 0 1 9 2 0 1 9 2019\mathbf{2 0 1 9}2019 58 52 68 74
2 0 2 0 2 0 2 0 2020\mathbf{2 0 2 0}2020 60 56 75 78
Quarter Q_(1) Q_(2) Q_(3) Q_(4) 2018 48 41 60 65 2019 58 52 68 74 2020 60 56 75 78| Quarter | $\mathbf{Q}_1$ | $\mathbf{Q}_{\mathbf{2}}$ | $\mathbf{Q}_{\mathbf{3}}$ | $\mathbf{Q}_{\mathbf{4}}$ | | :—: | :—: | :—: | :—: | :—: | | $\mathbf{2 0 1 8}$ | 48 | 41 | 60 | 65 | | $\mathbf{2 0 1 9}$ | 58 | 52 | 68 | 74 | | $\mathbf{2 0 2 0}$ | 60 | 56 | 75 | 78 |
(i) Find the quarterly seasonal indexes for the mobile sold using the ratio to trend method.
(ii) Do seasonal forces significantly influence the sale of mobile? Comment.
(iii) Also find the deseasonalised values.
\(tan\:\theta =\frac{sin\:\theta }{cos\:\theta }\)

MST-014 Sample Solution 2023

untitled-document-16-9cbde385-ad0a-4c74-864f-362c1a2d74cc

Question:-01

  1. (a) State whether the following statements are True or False. Give reason in support of your answer:
(i) The R R R\mathrm{R}R – chart is suitable when subgroup size is greater than 10 .
Answer:
The statement “The R R RRR – chart is suitable when subgroup size is greater than 10″ is generally considered to be False.

Justification:

The R R RRR – chart, or range chart, is used in statistical process control to help evaluate the stability of a process in terms of the variation among the values within a sample (subgroup). However, there are some considerations regarding subgroup size:
  1. Small Subgroup Sizes: The R R RRR – chart is most effective and commonly used when the subgroup size ( n n nnn) is small, typically between 2 and 10. This is because the range is a simpler and more efficient calculation when dealing with smaller subgroup sizes.
  2. Large Subgroup Sizes: When subgroup sizes are larger than 10, the R R RRR – chart may not be the most appropriate choice for evaluating within-group variability due to the following reasons:
    • Sensitivity: The range is less sensitive to the spread of data as the subgroup size increases. It only considers the largest and smallest values and ignores the distribution of all the values in between.
    • Normality Assumption: The distribution of the range is highly dependent on the underlying distribution of the process data, and this dependency increases with subgroup size. For larger subgroups, if the data is not normally distributed, the control limits calculated for the R R RRR – chart may not be accurate or reliable.
    • Alternative Charts: The S S SSS – chart (standard deviation chart) is often recommended for larger subgroup sizes because it considers all data points in the subgroup, providing a more accurate and reliable measure of dispersion, especially when n > 10 n > 10 n > 10n > 10n>10.

Example:

Consider a subgroup of size 15 with the following values:
5 , 6 , 7 , 7 , 8 , 8 , 9 , 9 , 10 , 10 , 11 , 11 , 12 , 12 , 13 5 , 6 , 7 , 7 , 8 , 8 , 9 , 9 , 10 , 10 , 11 , 11 , 12 , 12 , 13 5,6,7,7,8,8,9,9,10,10,11,11,12,12,135, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 135,6,7,7,8,8,9,9,10,10,11,11,12,12,13
  • The range ( R R RRR) would be calculated as the difference between the largest and smallest values: R = 13 5 = 8 R = 13 5 = 8 R=13-5=8R = 13 – 5 = 8R=135=8.
  • However, this doesn’t give any insight into the variability of all the other values in the subgroup.
  • If there were outliers or shifts within the subgroup, the R R RRR – chart might not detect them effectively due to its insensitivity to the distribution of internal values.

Conclusion:

While the R R RRR – chart is a valuable tool in statistical process control, its suitability is generally constrained to scenarios with smaller subgroup sizes. For larger subgroup sizes, alternative charts, such as the S S SSS – chart, are typically recommended to provide a more accurate and reliable analysis of process variability.
\(\operatorname{cosec}^2 \theta=1+\cot ^2 \theta\)

Frequently Asked Questions (FAQs)

You can access the Complete Solution through our app, which can be downloaded using this link:

App Link 

Simply click “Install” to download and install the app, and then follow the instructions to purchase the required assignment solution. Currently, the app is only available for Android devices. We are working on making the app available for iOS in the future, but it is not currently available for iOS devices.

Yes, It is Complete Solution, a comprehensive solution to the assignments for IGNOU. 

Yes, the Complete Solution is aligned with the requirements and has been solved accordingly.

Yes, the Complete Solution is guaranteed to be error-free.The solutions are thoroughly researched and verified by subject matter experts to ensure their accuracy.

As of now, you have access to the Complete Solution for a period of 1 Year after the date of purchase, which is sufficient to complete the assignment. However, we can extend the access period upon request. You can access the solution anytime through our app.

The app provides complete solutions for all assignment questions. If you still need help, you can contact the support team for assistance at Whatsapp +91-9958288900

No, access to the educational materials is limited to one device only, where you have first logged in. Logging in on multiple devices is not allowed and may result in the revocation of access to the educational materials.

Payments can be made through various secure online payment methods available in the app.Your payment information is protected with industry-standard security measures to ensure its confidentiality and safety. You will receive a receipt for your payment through email or within the app, depending on your preference.

The instructions for formatting your assignments are detailed in the Assignment Booklet, which includes details on paper size, margins, precision, and submission requirements. It is important to strictly follow these instructions to facilitate evaluation and avoid delays.

\(cos\left(2\theta \right)=cos^2\theta -sin^2\theta \)

Terms and Conditions

  • The educational materials provided in the app are the sole property of the app owner and are protected by copyright laws.
  • Reproduction, distribution, or sale of the educational materials without prior written consent from the app owner is strictly prohibited and may result in legal consequences.
  • Any attempt to modify, alter, or use the educational materials for commercial purposes is strictly prohibited.
  • The app owner reserves the right to revoke access to the educational materials at any time without notice for any violation of these terms and conditions.
  • The app owner is not responsible for any damages or losses resulting from the use of the educational materials.
  • The app owner reserves the right to modify these terms and conditions at any time without notice.
  • By accessing and using the app, you agree to abide by these terms and conditions.
  • Access to the educational materials is limited to one device only. Logging in to the app on multiple devices is not allowed and may result in the revocation of access to the educational materials.

Our educational materials are solely available on our website and application only. Users and students can report the dealing or selling of the copied version of our educational materials by any third party at our email address (abstract4math@gmail.com) or mobile no. (+91-9958288900).

In return, such users/students can expect free our educational materials/assignments and other benefits as a bonafide gesture which will be completely dependent upon our discretion.

Scroll to Top
Scroll to Top