A system has seven independent components and reliability block diagram of it shown as follows:
Find reliability of the system.
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) 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 | |
A system has seven independent components and reliability block diagram of it shown as follows:
Find reliability of the system.
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.
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).
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?
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:
| Time | Sample Number | ||||
| 1 | 2 | 3 | 4 | 5 | |
| 9 a.m | 8 | 9 | 15 | 4 | 11 |
| 10 | 7 | 10 | 7 | 6 | 8 |
| 11 | 11 | 12 | 10 | 9 | 10 |
| 12 | 12 | 8 | 6 | 9 | 12 |
| 1 p.m. | 11 | 10 | 6 | 14 | 11 |
| 2 | 7 | 7 | 10 | 4 | 11 |
| 3 | 10 | 7 | 4 | 10 | 10 |
| 4 | 8 | 11 | 11 | 11 | 7 |
Differentiate between the autoregressive and moving average models of time series.