) The marketing manager of a company recorded the number of mobiles sold quarterly for which are given in the following table:

Year	Quarter
2018		48	41	60	65
2019		58	52	68	74
2020		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. 

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%.
(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? 

State whether the following statements are True or False. Give reason in support of your answer:

(i) The 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. To improve the reliability of the system most, we
have to replace the component which reliability is 0.2. 

Consider the time series model

Where 
(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. 

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 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, then calculate the process capability index
Cpk and impetrate the result.
(iv) Also find the percentage of calls lie outside the specification limits assuming
that calls follow the normal distribution. 

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.

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 as follows:

Find reliability of the system.