4) A product developer is interested in reducing the drying time of a primer paint. Two formulations of the paint are tested; formulation 1 is the standard chemistry, and formulation 2 has a new drying ingredient that should reduce the drying time. From experience, it is known that the standard deviation of drying time is eight minutes,and this inherent variability should be unaffected by the addition of the new ingredient. Ten specimens are painted with formulation 1 and another ten specimens are painted with formulation 2; the 20 specimens are painted in random order. The two-sample average drying times are X1=121 min and x2=112 min, respectively.What conclusions can the product developer draw about the effectiveness of the new ingredient, using a=0.05? Use the analysis of variance to test the hypothesis that different concentrations do not affect the mean tensile strength of the paper.

1) A Manufacturing process produces thousands of semi-conductors chips per day. On the average, 1% of these chips do not conform to the specifications. Every hour, an inspector selects a random sample of 25 chips and classifies each chip in the sample as conforming or non – conforming. If we let x be the random variable representing the number of non-conforming chips in the sample, then what is the probability distribution of x?why?

2) The diameter of a metal shaft used in a disk-drive unit is normally distributed with mean 0.2508 in. and standard deviation 0.0005 in. the specifications on the shaft has been established as 0.2500±0.0015 in. what fraction of the shafts produced conform to specifications?

5) The data shown in Table 6E.3 a re the deviations from nominal diameter for holes drilled in a carbon-fiber composite material used in aerospace manufacturing. The values reported are deviations from nominal in ten-thousandths of an inch. (a) Set up x-bar and R charts on the process. Is the process in statistical control? (b) Estimate the process standard deviation using the range method. (c) If specifications are at nominal +-100, what can you say about the capability of this process? (d)Calculate the PCR Cp

6) The fill volume of soft-drink beverage bottles is an important quality characteristic. The volume is measured(approximately) by placing a gauge over the crown and comparing the height of the liquid in the neck of the bottle against a coded scale. On this scale, a reading of zero corresponds to the correct fill height. Fifteen samples of size n = 10 have been analyzed, and the fill heights are shown in Table 6E.5. a)What control charts are more suitable to monitor the mean and variability of the process? b) Construct the control charts and set the valid control limits c) Is the process in control?

3) The time to failure for an electronic component used in a flat panel display unit is satisfactorily modeled by a Weibull distribution with B=1/2 and 0 =5000.Find the mean time to failure and the fraction of components that are expected to survive beyond 20,000 hours.

A company intending to produce components for a fit with guaranteed clearance / interference as given in Table Q2 (Jmin, Jmax Or Smin, Smax respectively). It has been experiencing problems when machining both holes and shafts caused by lack of process capability, see Manufacturing Methods in Table Q2. Maintaining fit characteristics transform the tolerances to suit company's capability implementing selective assembly method. 1. Determine tolerances of the mating parts based on the manufacturing methods 5. Calculate maximum and minimum interference / clearance for each group 4. Draft the tolerances, indicating the groups 3. Calculate upper and lower limit deviations for the hole and the shaft 2. Calculate the number of groups

You are employed as a quality engineer and you have been asked to help in designing a limit gauge for quality control of machined shafts. Your company quality policy requires prevention of acceptance of any defective parts. a) Using the appropriate approach allocate the tolerances for 'GO' and ʼNOT-GO' ends of a snapgauge for controlling diameter of a shaft ØAB . Support your answer with all relevant tolerance diagrams.Table 02 b) Using the diagram from part (a) showing the allocation of Limit Gauge tolerances, give an example of a situation where a shaft with a particular actual dimension is made in the tolerance, but when inspected by this Limit Gauge (worn, but still within the gauge tolerance),might be misjudged as bad. Plot it on the tolerance diagram.