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.
To estimate the Reliability (R(t)), Cumulative Failure Distribution (F(t)), Failure Density (f(t)), and Failure Rate (h(t)) functions numerically, we follow these steps: --- ### Step 1: Compute the Cumulative Number of Failures The cumulative number of failures at each time interval is calculated by summing up the failures from the start. | Operating Time (hrs) | Failures in Interval | Cumulative Failures | |----------------------|---------------------|----------------------| | 0 - 5 | 5 | 5 | | 5 - 10 | 7 | 12 | | 10 - 15 | 6 | 18 | | 15 - 20 | 4 | 22 | | 20 - 25 | 5 | 27 | | 25 - 30 | 4 | 31 | | 30 - 35 | 4 | 35 | | 35 - 40 | 0 | 35 | | 40 - 45 | 2 | 37 | | 45 - 50 | 1 | 38 | | ≥50 | 2 | 40 | Total number of components = 40 (since all components fail eventually). --- ### Step 2: Compute Cumulative Failure Distribution ________ ______ _________ __________ _______ ______ __________.
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A two-person zero-sum game having the following payoff matrix for player A
(i) Check whether saddle point exit or not.
(ii) If saddle point does not exit then determine optimal strategies for both the manufacturers and value of the game.
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 |
State whether the following statements are True or False. Give reason in support of your
(a) Statistical quality control (SQC) is a technique of process control only.
(b) Twenty pieces of different length of cloth contained 2, 4, 1, 3, 5, 4, 2, 7, 3, 5, 2, 2, 4, 5,6, 4, 2, 1, 2, 4 defects respectively. To check the process is under control with respect to the number of defects, we should use np-chart.
(c) If the probabilities are not associated with the occurence of different states of nature, then the situation is known as decision making under risk.
(d) In single sampling plan, if we increase acceptance number then the OC curve will be steeper.
(e) A system has four components connected in parallel configuration with reliability 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 2 as the acceptance nuraber. Suppose 3% nonconforming zippers are acceptable to the manufacturer and 8% oncoming zippers are not acceptable. Let incoming quality be 4%
i) Construct an OC carve
ii) Average outing quality (AOQ), if the rejected lots are scromed and all defective zippers are replaced by non-defectives
i) Average total inspection (ATI).
At a call omtre, 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 S-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 |
A system has seven independent components and reliability block diagram of it shown blow:
Find reliability of the system.
Twenty saraples each of size 10 were inspected. The number of defectives detected in cach of them is given below: : 0, 1, 0, 3, 9, 2, 0, 7, 0, 1, 1, 0, 0, 3, 1, 0, 0, 2, 1, 0 Find the control limits for the number of defectives and establish quality standards for the future. Plot the graph and interpost.