The failure data for 40 electronic components is shown below:

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

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

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.

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). 

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

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? 

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

) 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. 

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).