Exam 16: Quality Control and Spc

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Discuss the difference between a continuous metric and a discrete metric, give examples of each, and list the common control charts associated with each.

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A continuous metric is one that is calculated from data that are measured as the degree of conformance to a specification on some continuous scale of measurement. Examples are length, weight, and time. Customer waiting time and order lead time are other examples. Continuous data usually require x-bar and R charts.
A discrete metric is one that is calculated from data that are counted. A dimension on a machined part is either within tolerance or out of tolerance, an order is either complete or incomplete, or a customer made a complaint or not about a service experience. We can count the percentage or number of parts within tolerance, the percentage or number of complete orders, and the percentage or number of complaints. These examples usually require a p- or c-charts.

Historically, the average proportion of defective bars has been 0.015. Samples of 100 bars each are taken. Construct a p-chart using z = 3. Suppose a sample had 0.044 defectives. What would you do?

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Evaluating the trade-offs between the costs of detecting and replacing a defective part or allowing it to continue on through the production process is related to

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A c-chart is used to monitor the fraction nonconforming, whereas a p-chart monitors the number of nonconformances per unit.

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The time to check out guests at a hotel was measured over the course of several weeks. Management believes that the target time for checking out guests should be between 2 and 4 minutes with a target of 3 minutes. The data gathered had a mean time of 2.75 minutes with a standard deviation of 0.4 minutes. Find and interpret Cp, Cpl, Cpu, and Cpk in the context of this situation.

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Testing whether a computer boots up the first time is an example of

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Collecting continuous data is usually easier than collecting discrete data.

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Quality control of front-office operations in services can effectively use many of the same techniques that are applied in manufacturing.

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If one was monitoring the average time to load a web page, the chart to use would be the

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Define and give an example of the three components of any control system.

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Statistical calculations will show that if p = .01, then the sample size needed to have at least a 95% chance of finding at least one nonconformance is

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If process quality approaches six sigma levels, then standard types of control charts are not useful.

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A company is measuring the time it takes to complete an order. Twenty five samples of size 6 resulted in an average time of 80 minutes with an average range of 20 minutes. Find control limits for the appropriate control charts) that would be used to monitor this process.

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A company that manufactures arrows for sale in archery stores is developing a new arrow with enhanced flight characteristics. From customer surveys the company has determined that the diameter of the arrow should be between 10.0 and 10.6 mm. They want to ensure the process they develop to produce the arrows will meet customer expectations; that is, the process capability index (Cp) will be greater than or equal to 1.00. a. What value of the standard deviation of the process will yield a Cp equal to 1.00? b. If the standard deviation of the process is actually .05, what would the diameter variation (UTL- LTL) of the arrow have to be to get a Cp of 1.00?

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Process capability quantifies the variation that results from common causes.

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Over-adjusting a process that is in control will usually increase the variation in the output.

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Define Statistical Process Control (SPC) and differentiate between common cause and (special or assignable) cause variation.

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An operator has determined what her percent defectives is for the machine which she operates. Based on several samples of 75 observations, she found p-bar to be 10%. She wants to set up a control chart using 3 standard deviation control limits. a. What is the upper control limit for a p chart? b. What is the lower control limit for a p chart?

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Over several days, 25 samples of 100 items each were tested for electrical resistance. A total of 60 items failed. Determine pˉ\bar { p } and the control limits for a p chart.

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Five samples were taken, with five observations each. The sample findings are listed below. The sample values represent service times in minutes. \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad  Observation Number \text { Observation Number } Sample Number 1 2 3 4 5 1 10.1 10.6 9.8 9.9 10.5 2 9.7 9.5 10.3 9.9 10.5 3 10.1 10.7 9.2 10.0 10.1 4 9.9 9.8 10.5 10.4 10.1 5 10.4 10.1 10.9 9.9 10.1 a. Determine the control limits for the R-chart. b. Would you conclude the R-chart is in statistical control and proceed to develop the x-bar chart?

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