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:

i) Use the data to construct control charts for mean and variability and comments about the process. If process is out of control, then calculate the revised control limits.
ii) If the specification limits as the 8±2, then find the process capability. Does it appear that the process is capable of meeting the specification requirements?

The failure data for 40 electronic components is shown below:

 Estimate the reliability, cumulative failure distribution, failure density and failure rate functions.

A system has seven independent components and reliability block diagram of it shown blow:

Find reliability of the system.

A two-person zero-sum game having the following payoff matrix for player A

 (i) Check whether saddle point exit or not.
(ii) If saddle point does not exit then determine optimal strategies for both the manufacturers and value of the game.

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 non-conforming, 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%.
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?
iii) Find AQL and ATI

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 as the acceptance number. Suppose 3% nonconforming zippers are acceptable to the manufacturer and 8% nonconforming zippers are not acceptable.
Let incoming quality be 4%.
i) Construct an OC curve.
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)

Twenty samples each of size 10 were inspected. The number of defectives detected in each of them is given below: 0, 1, 0, 3, 9, 2, 0, 7, 0, 1, 1, 0, 0, 3, 1, 0, 0, 2, 1, 0 Find the control limits for the number of defectives and establish quality standards for the future. Plot the graph and interpret.

State whether the following statements are True or False. Give reason in support of your answer:
(a) Statistical quality control (SQC) is a technique of process control only.
(b) Twenty pieces of different length of cloth contained 2, 4, 1, 3, 5, 4, 2, 7, 3, 5, 2, 2, 4, 5, 6, 4, 2, 1, 2, 4 defects respectively. To check the process is under control with respect to the number of defects, we should use np-chart.
(c) If the probabilities are not associated with the occurrence of different states of nature, then the situation is known as decision making under risk.
(d) In single sampling plan, if we increase acceptance number then the OC curve will be steeper.
(e) A system has four components connected in parallel configuration with reliability 0.2, 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.

Times between successive crashes of a computer system were generated for a 6-month period and are given in increasing order as follows (time in hours):

The parameter a = 0.00435, mean = 1/α = 230 hrs.
Use the Kolmogorov-Smirnov test to examine the goodness of fit of exponential distribution

Generate a complete cycle for the LCG given below: x_i = (5x_i-1 + 3 )mod16, with xo= 5. A man tosses an unbiased coin ten times. Using the first ten random numbers generated above, obtain a sequence of heads and tails by taking Head (H) as u ≥ 0-5.

The distribution function of Pareto distribution is given by f(x) = 1 - (k/x)^a   , a >0 , 0 < k ≤ x.
Given a U~ U(0, 1), generate a random number from the above distribution, when a = 2 and k = 1. Suppose U = 0.5, then find x

Identify the design given in the following table and then carry out the analysis:

In the following data, two values are missing. Estimate these values by Yates method and analyse the data by suitable technique.

A researcher wants to test four diets A, B, C, D on growth rate in mice. These animals are divided into 3 groups according to their weights. Heaviest 4, next 4 and lightest 4 are put in Block I, Block II, and Block III, respectively. Within each block, one of the diets is given at random to the animals. After 15 days, increase in weight is noted, which is given in the following table:

Perform a two-way ANOVA to test whether the data indicates any significant difference between' the four diets due to different blocks. 

The following data relate to production in kg of three varieties P, Q, R of wheat:

 Is there any significant difference among the three varieties at 5% level of significance?

To determine the yield rate of wheat in a district of Punjab, 6 groups of 6 plots each were constructed. The data are given in the following table:

Select a cluster sample of 3 clusters from the above data and find its sample mean. Further, explain the procedure of two-stage sampling if we want to draw a sample of 6 plots. Which are the 6 plots in your sample?

A sample of 60 students is to be drawn from a population consisting of 600 students belonging to two villages, A and B. The means and standard deviations of their marks are give below:

What are the sample sizes for the two villages using proportional allocation technique? 

Draw all possible samples of size 2 from the population [2, 3, 4] and verify that E ( x̄ ) = x̄  . find variance of x̄

State whether the following statements are true or false and also give the reason in support of your answer:
(a) The total number of all possible samples of size 2 without replacement from a population of size 7 is 21.
(b) Consecutive 3 random numbers starting from 8937 by 'middle square method' are 8937, 8699, 6726.
(c) RBD is suitable in situations where it is not possible to divide the experimental material into a number of homogeneous blocks.
(d) As we increase the sample size, representativeness of the population by the sample decreases.
(e) In a big hall, there are 50 rows and each row has 60 students. A research scholar selects 10 rows randomly and then randomly selects 15 students from each selected row. It is an example of cluster sampling procedure

Prepare an informative and colourful comic strip for children on balanced diet (2-3 pages only). Read the comic strip in separate sessions with five school going children staying in your locality and :
i) Record the reactions of each child (indicate each child’s name, age, sex, socio-economic background and any other factor of importance).
ii) Analyze whether the message of comic strip was understood by each child by asking 2-3 questions. List the specific questions you asked.