In a control system, an accelerometer consists of a 4.70-g object sliding on a calibrated horizontal rail. A low-mass spring attaches the object to a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of 0.800g, the object should be at a location 0.500 cm away from its equilibrium position. Find the force constant of the spring required for the calibration to be correct.

The researchers also performed control treatments. Suggest two controls they might have used, and explain how each would be helpful in interpreting the results described

In the following, name the term defined or answer the question.

A Six Sigma process that is running at the center of its control limits would expect this defect rate.

Use the sample size formula to decide on a sample size large enough to avoid constructing a p-chart with a negative lower control limit.

b. $p_0=0.05$

In a particular set of experimental trials, students examine a system described by the equation

$$\frac{Q}{\Delta t}=\frac{k \pi d^2\left(T_h-T_c\right)}{4 L}$$

We will see this equation and the various quantities in it in Chapter 20. For experimental control, in these vials all quantities except $d$ and $\Delta t$ are constant. (a) If $d$ is made three times larger, does the equation predict that $\Delta t$ will get larger or smaller? By what factor?

On each of the previous 25 days, 100 electronic devices of a certain type were randomly selected and subjected to a severe heat stress test. The total number of items that failed to pass the test was 578. a. Determine control limits for a 3-sigma p chart. b. The highest number of failed items on a given day was 39, and the lowest number was 13. Does either of these correspond to an out-of-control point? Explain.

Describe some optimal control problems in your major field or in another area of interest to you. How difficult would it be to find the optimal controls?

A branch manager of a brokerage company is concerned with the number of undesirable trades made by her sales staff. A trade is considered undesirable if there is an error on the trade ticket. Trades with errors are canceled and resubmitted. The cost of correcting errors is billed to the brokerage company. The branch manager wants to know whether the proportion of undesirable trades is in a state of statistical control so she can plan the next step in a quality improvement process. Data were collected for a 30 -day period and stored in Trade.

a. Construct a control chart for these data.

b. Is the process in control? Explain.

c. Based on the results of (a) and (b), what should the manager do next to improve the process?

A federal agency has put you in charge of responding to the zebra mussel invasion. How would you try to control the mussel's spread and impact?

What type of loop, such as counter-control or sentinel-control, will you use in each of the following situations? a. Sum the following series: 1 + (2 / 1) + (3 / 2) + (4 / 3) + (5 / 4)+ ... + (10 / 9) b. Sum the following numbers, except the last number: 17, 32, 62, 48, 58, -1 c. A file contains an employee’s salary. Update the employee’s salary.

Air flows through the tapered duct, and during this time heat is being added that changes the density of the air within the duct. The average velocities are indicated. Select a control volume that contains the air in the duct. Indicate the open control surfaces, and show the positive direction of their areas. Also, indicate the direction of the velocities through these surfaces. Identify the local and convective changes that occur. Assume the air is incompressible.

You observe that a particular gene is being transcribed during development. How can you tell whether the expression of this gene is under transcriptional or translational control?

$$\begin{array}{|c|c|c|c|c|c|c|c|} \hline \# 1 & \# 2 & \# 3 & \# 4 & \# 5 & \# 6 & \# 7 & \text { \#8 } \\ \hline 162.2 & 165.8 & 156.4 & 165.3 & 168.6 & 167.0 & 186.8 & 178.3 \\ \hline 159.8 & 166.2 & 156.4 & 173.3 & 175.8 & 171.4 & 160.4 & 163.0 \\ \hline \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \hline 160.3 & 160.6 & 152.2 & 166.4 & 168.2 & 168.4 & 176.8 & 171.3 \\ \hline \end{array}$$

Prepare a control chart that specifies a centerline as well as an upper control limit (UCL) and a lower control limit (LCL).

The birth control shot is one of the most effective methods of birth control available, and it works best when you get the shot regularly, every 12 weeks. Under ideal conditions, only 1 % of women taking the shot become pregnant within one year. In typical use, however, 3% become pregnant. 7 Choose at random 20 women using the shot as their method of birth control. We count the number who become pregnant in the next year.

(a) Explain why this is a binomial setting.

(b) What is the probability that at least one of the women becomes pregnant under ideal conditions? What is the probability in typical use?