Question 1

State whether the following statements are True or False. Give reasons in support of your answers.

Accepted Answer

The following statements regarding Industrial Statistics concepts are evaluated for their truthfulness, supported by relevant definitions, formulas, and principles from the MSTE-002 course material. Each sub-question is addressed individually, providing specific reasons for the True/False determination.

Question 2

Use the penalty (Big M) method to solve the following LP problem: Minimise Z = 5x1+ 3x2 Subject to the constraints 2x1+ 4x2 ≤ 12 2x1+ 2x2 = 10 5x1+ 2x2 ≥ 10 X1, X2 ≥ 0.

Accepted Answer

The Big M method, also known as the penalty method, is a powerful technique used in linear programming to solve problems that involve "greater than or equal to" (≥) constraints or equality (=) constraints. These types of constraints do not naturally provide an initial basic feasible solution, unlike "less than or equal to" (≤) constraints. The method introduces artificial variables to generate an initial basic feasible solution, penalizing them in the objective function to ensure they are driven

Question 3

A company has three production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirement of 5, 6, 7 and 14 units (in 100s) per week, respectively. The trans

Accepted Answer

The problem presented is an unbalanced transportation problem, as the total production capacity (supply) of the facilities is 34 units (7 + 9 + 18) and the total requirement (demand) of the warehouses is 32 units (5 + 6 + 7 + 14). To balance the problem, a dummy destination, D5, is introduced with a demand of 2 units (34 - 32). The transportation cost to this dummy destination from all facilities is considered 0.

| From/To | D1 (5) | D2 (6) | D3 (7) | D4 (14) | D5 (2) | Supply |
|:--------|:---

Question 4

Four professors are capable of teaching any one of four different courses. Class preparation time in hours for different topics varies from professor to professor and is given in the table below: Professor A B C D Linear Programming 2 15 13 4 Queuing Theory 10 4 14 15 Transportation Problem 9 14 16

Accepted Answer

The problem presented is a classic assignment problem, aiming to assign each of four professors to one of four courses to minimize the total preparation time. This can be efficiently solved using the Hungarian method, which is a specialized algorithm for such problems. The method systematically transforms the cost matrix to identify the optimal assignment.

First, we establish the initial cost matrix, where entries represent the preparation time in hours for each professor-course combination.

*

Question 5

In a railway marshalling yard, goods trains arrive at a rate of 36 trains per day. Assuming that the inter-arrival and service time distributions both follow exponential distribution with an average of 30 minutes, calculate the following:

Accepted Answer

This problem involves an M/M/1 queuing model, a fundamental concept in industrial statistics for analyzing systems with random arrivals and services. In such a model, both inter-arrival times and service times follow an exponential distribution. We need to determine the arrival rate (λ) and service rate (μ) from the given information to calculate the required queuing characteristics. There's a slight ambiguity in the problem statement regarding the inter-arrival time; we'll assume the direct rat

Question 6

Using the graphical method to minimise the time required to process Job 1 and Job 2 on five machines A, B, C, D and E, find the minimum elapsed times an idle times to complete both jobs. Job 1 Sequence: A B C D E Time (in hours): 1 2 3 5 4 Job 2 Sequence: C A D E B Time (in hours): 3 4 2 1 5

Accepted Answer

The graphical method is used to determine the optimal sequence and minimum elapsed time for processing two jobs on multiple machines, ensuring no machine is used by both jobs simultaneously. This method is particularly suitable for two-job problems on 'm' machines, as described in MSTE-002 materials.

First, we list the processing times and sequences for Job 1 and Job 2:

Job 1 Sequence: A (1 hr), B (2 hr), C (3 hr), D (5 hr), E (4 hr)
Total Processing Time for Job 1 = 1 + 2 + 3 + 5 + 4 = 15 hou

Question 7

A firm wants to know whether there is any linear relationship between the sales (X) and its yearly revenue (Y). The records for 10 years were examined and the following results were obtained: ΣΧ = 265, ΣΥ = 27.73, SSx = 285.6, SSy = 6.978 and SSxy = 57.456.

Accepted Answer

This question assesses the understanding of simple linear regression analysis, a core concept in Industrial Statistics (MSTE-002). It involves fitting a regression line, performing a hypothesis test for the significance of the independent variable, and evaluating the goodness of fit of the model. However, the provided data exhibits statistical inconsistencies, which will be highlighted during the analysis.

Linear regression aims to model the relationship between a dependent variable (Y) and an

Question 8

A researcher is interested in developing a linear model for the electricity consumption of a household having an AC (1.5 ton) so that she can predict the electricity consumption. For this purpose, she selects 25 houses and records the electricity consumption (in kWh), size of house (in square feet)

Accepted Answer

The researcher aims to develop a linear model for electricity consumption using Stepwise Selection, a method that systematically adds or removes predictors from a regression model based on their statistical significance. This approach combines elements of forward selection and backward elimination to arrive at an optimal set of regressors.

The objective is to predict electricity consumption (dependent variable, Y) using the size of the house (X₁, in square feet) and AC hours (X₂, for one month)

MSTE-002 Solved Assignment — January 2026 / July 2026

Industrial Statistics-II | IGNOU Post Graduate Diploma in Applied Statistics (PGDAST)

MSTE-002—January 2026 / July 2026

Industrial Statistics-II

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MSTE-002 Assignment Questions — January 2026

Q1. State whether the following statements are True or False. Give reasons in support of your answers.

Q2. Use the penalty (Big M) method to solve the following LP problem: Minimise Z = 5x1+ 3x2 Subject to the constraints 2x1+ 4x2 ≤ 12 2x1+ 2x2 = 10 5x1+ 2x2 ≥ 10 X1, X2 ≥ 0.

Q5. In a railway marshalling yard, goods trains arrive at a rate of 36 trains per day. Assuming that the inter-arrival and service time distributions both follow exponential distribution with an average of 30 minutes, calculate the following:

Q6. Using the graphical method to minimise the time required to process Job 1 and Job 2 on five machines A, B, C, D and E, find the minimum elapsed times an idle times to complete both jobs. Job 1 Sequence: A B C D E Time (in hours): 1 2 3 5 4 Job 2 Sequence: C A D E B Time (in hours): 3 4 2 1 5

Q7. A firm wants to know whether there is any linear relationship between the sales (X) and its yearly revenue (Y). The records for 10 years were examined and the following results were obtained: ΣΧ = 265, ΣΥ = 27.73, SSx = 285.6, SSy = 6.978 and SSxy = 57.456.

Q9. The following table represents the sales (in thousands) of mobile sets of a shop for 16 quarters over four years: Year Q1 Q2 Q3 Q4 2011 554 590 616 653 2012 472 501 521 552 2013 501 531 553 595 2014 403 448 460 480

Q10. Seven successive observations on a stationary time-series are as follows: 12, 14, 13, 10, 15, 12, 15