Q.1) The mean value of the modulus of rupture of a large number of test specimens of green Sitka spruce has been found to be 5,600 Ib/in2.
a) If the standard deviation is 840 Ib/in2 & the distribution is approximately normal, the modulus of rupture will fall between 5,000 & 6,200 for what percentage of the specimens?
b) For what percentage will it be above 4,000?
c) Below 3,500?
Q.2) a) How many different hands of a 13-card might you have out of standard deck of 52 playing cards?
b) What is the probability of a 13-card hand containing all four aces?
c) What is the probability of a 13-card hand without an ace, king, queen, or jack?
d) What is the probability of a 13-card hand containing one or more aces?
Q.3) An acceptance plan calls for the inspection of a sample of 75 articles out of a lot of 1,500. If there are no nonconforming articles in the sample, the lot is accepted; with 7 or more, it is rejected. If a lot 5% nonconforming is submitted, what is the probability that it will be rejected? Solve using the poisson distribution as an app.
Q.4) Random Samples of 100 items are drawn from a continuous process that is known to produce 20% nonconforming items. Determine the probability of finding exactly 15 nonconforming items in a sample:
a) Using the exact binomial distribution.
b) Using the normal approximation to the binomial.
c) Using the poisson approximation to the binomial.
d) Comment on the relative accuracy of the approximations.
Q.5) The standard deviation of the measured values of a quality characteristic if 40.0 units. However, the standard deviation of the error of measurement of this characteristic has been determined to be 12.0 units.
a) Estimate the value of the true ó of this quality characteristic.
b) How much improvement in the measuring technique would be required to reduce the overall standard deviation to within 2% of the true standard deviation?
Q.6) It has been suggested that, when extremely high performance of certain missile components is required, a boundary on the stress requirement be set at 6 standard deviations of the stress requirement above the average stress. The average strength required of the article would then be set at 5 standard deviations of the strength of the component above this boundary.
A Certain critical electronic component must operate in a salt air environment at an average temperature stress of 300C. The standard deviation of this operating temperature is believed to be 50C.
a) What must be the minimum acceptable average strength, in terms of average failing temperature, of this component? Assume that the standard deviation of strength in this case is 3oC.
b) How much of a safety margin does the requirement provide in multiples of the standard deviation of the combined strength-stress Characteristic?
Q.7) a) Determine the D-R Single sampling plan to be used for a lot size of 250 items and an LTPD of 5% with a consumer’s Risk of 10% if the Process average is estimated at 1.1%.
b) What percentage of the product will be subject to sampling inspection with this sampling plan?
c) What is the probability of acceptance of a lot 4.0% nonconforming under this plan?
d) Compute the average total inspection (ATI) at 4.0% and at 1.1% assuming that rejected lots are screened.
Q.8) A certain manufacturing group decides to use a Dodge-Torrey CSP-2sampling inspection plan on a line of small motors. It is decided to inspect 10% of the units when sampling and to maintain a desired AOQL of 1.0%
a) Prepare a flowchart of the detailed operation of this plan.
Q.9) A known-sigma variables acceptance plan for a one-sided specification uses n=25 and k’=1.97. Compute the probability of acceptance of a 3% nonconforming lot assuming that the frequency distribution in the lot is normal and ó is esteemed correctly.
Q.10) Assume normal inspection, MIL-STD-414, Variability known, code letter H, 2.50% AQL, Single specification limit. Compute the probability of acceptance of a normally distributed lot containing 5% of nonconforming product if the ó of the lot is estimated correctly.
Q.11) Write short notes:
a) Uses of control charts
b) Principles of Statistical
c) Quality improvement by rejection of entire lots
d) Quality & Standardization