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 non-conforming the lot will be accepted. Otherwise, a second sample of size 5 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second saraple. Also AQI. and LTPD at 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?
iii) Find AQL and ATI
We will solve this problem numerically step by step. ### Given Data: - Lot size: \(N = 400\) - Sample size (first sample): \(n_1 = 12\) - Sample size (second sample): \(n_2 = 5\) - Accept/reject rules: - Accept the lot if fewer than 2 non-conforming printers in the first sample. - Reject the lot if more than 3 non-conforming printers in the first sample. - If exactly 2 or 3 non-conforming printers are found in the first sample, take a second sample. - Second sample rule: - If the total number of non-conforming printers across both samples is 3 or fewer, accept the lot. - Otherwise, reject the lot. - Incoming quality (defect rate): \( p = 4\% = 0.04 \) ______ __________ _______ __________ ________ ____ __________ _________ ______.
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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.
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 non-conforming the lot will be accepted. Otherwise, a second sample of size 5 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second saraple. Also AQI. and LTPD at 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?
iii) Find AQL and 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 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).
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 |
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.
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.