Concept explainers
a
Interpretation: Economic tradeoff attendant for choosing a very small value of
Concept Introduction: : Poisson distribution is the probability distribution of discrete random variable series in which frequency of outcomes is calculated in a given period of time.
b
Interpretation: Economic tradeoff attendant for choosing a very small value of
Concept Introduction: : Poisson distribution is the probability distribution of discrete random variable series in which frequency of outcomes is calculated in a given period of time.
c
Interpretation:Economic tradeoff attendant for choosing a large value of
Concept Introduction: : Poisson distribution is the probability distribution of discrete random variable series in which frequency of outcomes is calculated in a given period of time.
d
Interpretation:Economic tradeoff attendant for choosing a small value for sampling interval
Concept Introduction: : Poisson distribution is the probability distribution of discrete random variable series in which frequency of outcomes is calculated in a given period of time.
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Production and Operations Analysis, Seventh Edition
- At Webster Chemical Company, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Even when the process is in control, an average of four lumps per tube of caulk will remain. Testing for the presence of lumps destroys the product, so an analyst takes random samples. The following results are obtained: Tube No. Lumps Tube No. Lumps Tube No. Lumps 1 6 5 6 9 5 2 5 6 4 10 0 3 0 7 1 11 9 4 4 8 6 12 2 Determine the c-chart two-sigma upper and lower control limits for this process. Is the process in statistical control?arrow_forwardThe weights of boxes of Oat Flakes within a large production lot are sampled each hour. Managers want to set control limits that include 99.73% of the sample means, and given is the population (process) standard deviation, which is 1.13. You are in charge of randomly selecting four boxes each hour, for three hours. The data you collected is located in the table below:Using an Xbar Chart, what are the upper and lower control limits? Sample Avg. of 4 boxes 1 16.8 2 17.1 3 17.2arrow_forwardEach day 500 inventory control records are cycle-counted for errors. These counts have been made over a period of 20 days and have resulted in the following proportion of records found in erroreach day: .0025 .0075 .0050 .0150 .0125 .0100 .0050 .0025 .0175 .0200 .0150 .0050 .0150 .0125 .0075 .0150 .0250 .0125 .0075 .0100a. Calculate the center line, upper control limit, andlower control limit for a p control chart.b. Plot the 20 points on the chart and determine which ones are in control.c. Is the process stable enough to begin using these data for quality control purposes?arrow_forward
- A manufacturing facility analyzes a lot-sample of 100 units out of a shipment of 10,000. The demodulator frequency is supposed to be within 53.5 and 54.5 MHz. The mean is 54.25 MHz with a standard deviation of 0.04 MHz. What is the CPK?arrow_forwardState True or False for the below two statements. 1. The purpose of process control charts is to detect the presence of natural variations. 2. Unlike process capability ratio (Cp), process capability index (Cpk) can possibly be negative.arrow_forwardThe central limit theorem:a) is the theoretical foundation of the c -chart.b) states that the average of assignable variations is zero.c) allows managers to use the normal distribution as thebasis for building some control charts.d) states that the average range can be used as a proxy forthe standard deviation.e) controls the steepness of an operating characteristiccurve.arrow_forward
- A manufacturing process that is in control, reports Select one: a. Favorable variances offset by unfavorable variances. b. Mostly favorable variances c. All favorable variances. d. No variances.arrow_forwardAbout the OC curve for p chart, which statement is INCORRECT? Select one: a. None of those listed b. There is one particular point on the OC curve at which β=1-α c. The y-axis of the OC curve is β d. The maximum β exists when p is equal to the center line of the control chart e. β is computed based on binomial distributionarrow_forward50 motor generators are inspected per day from a stable process. The best estimate of the fraction of nonconforming is 0.076. Determine the centeral line and control limits. On a particular day, 5 nonconforming generators were discovered. Is this process in or out of control? For the information given in the problem, construct a np-chartarrow_forward
- A pharmaceutical company producing vitamin capsules desires a proportion of calcium content between 40 and 55 ppm. A random sample of 20 capsules chosen from the output yields a sample mean calcium content of 44 ppm with a standard deviation of 3 ppm. Find the natural tolerance limits of the process. If the process is in control at the present values of its parameters, what proportion of the output will be nonconforming, assuming a normal distribution of the characteristic? Answer letters a, b, and c. a. Find the Cp index. Comment on the ability of the process to meet specifications. b. What proportion of the specification range is used up by the process? c. If it is easier to change the process mean than to change its variability, to what value should the process mean be set to minimize the proportion of nonconforming product?arrow_forwardWhen plotting values on a control chart, the first point that falls outside of the lower control limit (LCL) means Part 2 A. the process owner should take samples more frequently. B. a run has been encountered. C. a type I error has occurred. D. the cause should be investigated.arrow_forwardWhich of the following statements about Pareto diagrams is correct?a. The Pareto diagram shows the possible root causes of a problem along with the numberof defect occurrences.b. The Pareto diagram shows the process capability index over time.c. The Pareto diagram shows the mean of a random sample at various points in time.d. The Pareto diagram shows a visual representation of binary outcome variables.arrow_forward
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