A system has seven independent components and reliability block diagram of it shown as follows:
Find reliability of the system.
Let’s determine the **system reliability** from the given reliability block diagram with seven components: - $$R_1 = 0.9$$ - $$R_2 = 0.8$$ - $$R_3 = 0.8$$ - $$R_4 = 0.8$$ - $$R_5 = 0.9$$ - $$R_6 = 0.9$$ - $$R_7 = 0.9$$ *** ## Step 1: Analyze the Paths Identify all possible parallel and series combinations: ### Three main paths from A to B: - **Path 1:** $$A \to a \to d \to _________ ________ ______ ___ _______ ____ ___ __________ _______ _________ _____ _____.
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Differentiate between the autoregressive and moving average models of time series.
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 | 19 | 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 |
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
(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
(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).
A system has seven independent components and reliability block diagram of it shown as follows:
Find reliability of the system.