A glass manufacturer produces hand mirrors. Each mirror is supposed to meet company standards for such things as glass, color of handle, and so on. To control for these features, the company quality people randomly sample 40 mirrors in every shift and determine how many of the mirrors are out of compliance on at least one feature. Shown here are the data for 15 such samples.

An office supply company ordered a lot of 4,000 pens. When the lot arrives the company inspector will randomly inspect 15 pens. If more than three pens in the sample are non- conforming, the lot will be rejected. If fewer than two pens are non-conforming, the lot will be accepted. If two, three pens are non-conforming, a second sample of size 10 will be taken. The value of c₂ is 3. Suppose the inspector finds two nonconforming items 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 type of acceptance plan is used here?

ii) What is the probability of accepting the lot at the first sample?

iii) What is the probability of accepting the lot at the second sample?

A system having Weibull failure distribution with pdf as

i) Compute the reliability function of the system,

ii) find the reliability for a 100 days mission for θ = 2,

iii) show that the hazard rate is constant,

iv) find the MTTF, and

v) what is the life of the system if reliability of 0.90 is desired.

The system shown below is made up of ten components. Components 2, 3 and 4 are not identical and at least two component of this group must be available for system success.

What is the system reliability if R₁ = R₅ = 0.85, R₆ = R₇ = R₈ = 0.80

, R₉ = R₁₀ = 0.70 R₂ = 0.40, R₃ = 0.50 and R₄ = 0.60.

State whether the following statements are True or False. Give reason in support of your answer:

(a) The process capability of a manufacturing process of a certain type of bolt, with mean diameter 2 inches and standard deviation 0.05 inches, will be 0.30

(b) If the probability of accepting a lot of satisfactory quality is 0.9401, then the producer’s risk will be 0.9401.

(c) Hurwicz criterion is a method to solve the problems that involve decision-making under certainty.

(d) Two independent components of a system are connected in series. If the reliability of these components are 0.8 and 0.6 respectively, then the reliability of the system will be 0.92.

(e) For a two person zero sum game, the payoff matrix is given below:

A leather bag manufacturing company supplies bags in lots of size 150 to a buyer. A single sampling plan with n = 10 and c = 1 is being used for the lot inspection. The company and the buyer decide that AQL = 0.08 and LTDD = 0.16. If there are 15 defective bags in each lit, compute the

i) Probability of accepting the lot,

ii) Producer’s risk and consumer’s risk,

iii) AOQ, if the rejected lots are screened and all defective bags are replaced by non- defectives, and

iv) Average total inspection

In a small town, there are only two stores, ABC and XYZ that handle sundry goods. The total number of customers is equally divided between the two, because price and quality of goods sold are equal. Both stores have good reputation in the community, and they render quality good customer run annual pre-New Year sales during the first week of January. Sales are advertised through a local newspaper, radio and television media. With the aid of an advertising firm store ABC constructed the game matrix given below.(Figures in the matrix represent a gain or loss of customers).