1IE 361 Exam 1October 9, 2002Prof. Vardeman1. The viscosity of paint is measured with a "viscometer" in units of "Krebs."First, a standard liquid of "known" viscosity Krebs is tested with a company viscometer (by a single employee).*#a) measured values have a mean of Krebs and standard deviation of Krebs. What do the % """!*$Þ'Þ&*&>confidence limits then estimate? (Use 10 words or less.)*$Þ'„#Þ#'#ÐÞ&Î"!ÑÈb) Give % confidence limits for the bias of this viscometer. (No need to simplify.)*&c) Give 95% confidence limits for the "repeatability" standard deviation of this viscometer. (No need to simplify.)d) Suppose that the "reproducibility" standard deviation for use of the viscometer by company employees is aboutÞ) Krebs. What would you expect for a standard deviation of measured viscosities if many different employeesmeasure the viscosity of the standard liquid once each?& samples of paint dipped from different locations in single vat have measured viscosities with mean 91.6 Krebsand standard deviation 1.1 Krebs. (A single employee does all measuring.)e) Using both sets of measurements, estimate a standard deviation of actual viscosities (not including measurementerror) of such samples dipped from this vat of paint.2f) A standard error for the estimate in e) is approximately Krebs. What does this figure indicate about theÞ%%reliability of your answer to e)? (Use 10 words or less.)2. Kumala, Nithang, Pramadi and Simpson worked with a company on improving a paperwork process. Theydeveloped a method of scoring the correctness of employee handling of a particular kind of transaction on a scalefrom to . A large number of transactions were scored by this method and initial standards of and!"!!œ(!.5 œ## described the strongly left-skewed distribution of scores at the beginning of their involvement.a) What probability fact from Stat 231 suggests that (if the sample size is not too small) despite the fact that thedistribution of scores was skewed, "usual" control limits may be used for ? (Use 10 words or less.)Bb) Suppose that each month, of these transactions will be sampled and scored. Find standards given8œ&!control limits for the sample mean score. __________ __________PGPœYGPœBBc) Management clearly wanted high scores, and in particular individual scores below were considered*!"blunders." Your lower control limit in b) should be below and you should have an upper control limit that is*!less than . BRIEFLY say why such limits are not incompatible with management's goals for transaction scores."!!33. Olberding, Paulsen, Schreiner and Williams worked with a company on the milling of a high precision metalpart. Below are means and ranges for a critical dimension of this part from periodic samples of size . The8œ%units are inchabove inch.Þ!!!"Þ*%*!sample7.2511.5013.756.509.507.259.5013.5011.257.25697159912161510"#$%&'()*"!BBœ*(Þ#&VVœ"!)!!a) Find retrospective control limits for both sample means and ranges. For : For BlVÀ l l l l l l l l l l |b) Is there any evidence of process instability in the values given in the table? Explain.c) Supposing the process to be stable over the period of study, give estimates of the process mean and standarddeviation.d) Engineering specifications on the dimension being monitored were to (in the units above). Use this•"!$!fact, the estimates from c) and a normal distribution assumption to approximate the fraction of parts meetingengineering specifications.4IE 361 Exam IINovember 13, 2002Prof. Vardeman1. Bar stock of height and depth is crosscut at an angle to the front face as pictured below.LH ) The area of the face produced by the cut isEœLHsin)Suppose that , and vary with means in, in and radians and standardLHœ"Þ!!œ"Þ!!œ)...LH#)1deviations in, in and .02 radians. Find an approximate mean and standard555LHœÞ!"œÞ!"œ)deviation for (assuming that , and are independent). (Plug in completely, but no need toELH )simplify.)2. In a real application of control charting with attributes data, a company monitored the number ofcustomer complaints received on their "customer complaint hotline" for each of its food products.a) The "standard" complaint rate for a particular product is per week. What then are sensible control$limits for the number of complaints on this product received in a week "quarter"?"$5b) A company executive argues that "the correct" way to monitor complaints is in terms of "complaintsper unit sold" rather than "complaints per unit time." Last year, roughly units of a product"ß!!!ß!!!were sold and complaints received. Using the executive's idea, what are sensible control limits for the&!!number of complaints in a month where units of this product are sold?"!!ß!!!3. IE 361 students Olberding, Paulsen, Schreiner and Williams studied the performance of a CNCmachining process. A sample of parts was produced and a particular critical dimension measured8œ%!on each. Summary statistics for these (in units of inches above inch) were andÞ!!!"Þ#!)!Bœ)!Þ!&=œ%Þ'&)!„#!. In these units, engineering specifications on this dimension were .a) Give limits that you are % sure contain % of such dimensions. (No need to simplify.)*&**b) Give a % lower confidence bound for a process capability index that measures current performance*&(not potential). (Plug in, but again you need not simplify.)c) Here is a normal plot of the students' data. Say what it indicates about the practical usefulness of theanswers to a) and b) above and use it to explain the "process capability" to a non-quantitative person.64. A (real) US government (FDA) draft guideline prescribing the monitoring of the concentration of whiteblood cells in certain filtered blood products calls for the weekly testing of units. "Lack of control"8œ&is to be declared if any of these units has more than a specified concentration of white cells. Supposedly,a company is in compliance with government guidelines if % or less of all units produced have more&than the specified concentration of white boold cells.A certain producer of these blood products is in fact consistently producing only % of units that are&unacceptable in terms of the white cell concentration (and is therefore actually "in compliance" with FDAguidelines). What is the mean number of weeks the supplier will test until first having an "out of control"result?5. Ideally, two varaibles and measured on