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.
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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?
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.
Differentiate between the autoregressive and moving average models of time series.
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).
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.
A system has seven independent components and reliability block diagram of it shown as follows:
Find reliability of the system.