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?

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?

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

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

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.

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.

Problem 1. Draw a Context diagram and a Data Flow Diagram for a manufacturing company with a material handling and financial system that works as follows: Widget Corporation makes high-tech fly swatters. The units include a mm-Wave RADAR system that makes a final tweak in the arc of the swing to ensure a successful "end-game". The supply chain follows a classical SIPOC approach: Raw materials arrive from the vendor and are inspected. The materials enter production, products are fabricated, tested, moved to a short- term warehouse, then shipped to distributors. Vendors are paid after incoming inspection verifies the raw materials and Distributors are invoiced after finance is notified that the products are shipped. Distributors have 30-days to pay for their products after invoicing.

Problem 2. Construct an FMEA of a simple, theoretical process, or a process that you have worked with. Please describe the process and its shortcomings, then construct the FMEA model based on your description. Include at least 2 but no more than 5 Failure Modes. Please suggest the issues that need to be resolved first using RPN. Briefly discuss costs and impacts associated with remedying the issues. Don't bother filling out the Resulting Status Columns, unless you have an actual example...

Assignment 6, 100 pts: Due on 04/27/2021 1. (10 pts) Referring to risk adjusted control chart, in order to detect a change in the system, which variables should one monitor, x, y, or z, and why? 2. (25 pts) Consider the example used in the class for linear regression (weight of the card- board). Using only the first 5 data points, fit a linear regression between weight (y) and humidity (x) and determine the values of Bo, B₁. Also, write down the matrices Y and X (see slide #10). Also, determine the values of ŷ and comapre with the corresponding values of y. 3. (25 pts) Two observable quality characteristic x₁ and ₂ of a production process is recorded for m = 50 samples with a sample size of n = 25. Assume that mean values of the quality characteristics and the covariance matrix were determined as: x 55 30 1 2 3 4 5 6 7 8 and S (a) Determine the UCL for a Hotelling T2 control chart. Consider a = 0.001. (b) The first 15 samples of the data is shown in Table 1. The data are sample means of each quality characteristic. Determine the T² for these 15 samples. Based on the UCL from part (a), do you see any out of control samples? Sample Number X1 X2 58 32 60 33 50 27 54 31 63 38 53 30 42 20 55 31 200 130 Table 1: Data for Exercise 4(b) 1 Sample Number 9 10 130 120 11 12 13 14 15 | X1 X2 46 25 |5049575875 55 29 27 30 33 45 27 4. (15 pts) Consider a T² control chart for monitoring p = 6 quality characteristics. Suppose that the sample size is n = 3 and there are m = 30 preliminary samples available to estimate the sample covariance matrix. Find the control limits assuming that a = 0.005. 5. (25 pts) In a large study, 942 women were surveyed and their daily dietary intake of Calcium, Iron, Protein, Vitamin A, and Vitamin C were recorded. Since we have 5 quality charac- teristic, p = 5. The sample average and sample covariance matrix for the dietary intake are: X = 624.0 mg 11.1 mg 65.8 g 839.6 μg 78.9 mg and S = 157829.4 940.1 6075.8 102411.1 2383.2 6701.6 137.7 940. 5.8 114.1 6075.8 114.1 934.9 7330.1 477.2 102411.1 2383.2 7330.1 2668452.4 22063.3 6701.6 137.7 477.2 22063.3 5416.3 The recommended intake of these nutrients are: Ho = 1000 mg 15 mg 60 g 800 με 75 mg Conduct hypothesis test (with a = 0.01) to verify if the average dietary intake meets the recommendations. Although it is not needed, you may check the data related to this problem on canvas Assignment 6 folder (Women's survey data). 2