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

Find reliability of the system.

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. 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). 

Differentiate between the autoregressive and moving average models of time series.

The failure data for 40 electronic components is shown below:

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

In single sampling plan, if we increase acceptance number then the OC curve will be steeper.

) 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. 

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. 

The R- chart is suitable when subgroup size is greater than 10.