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Chapter 16: Q8E (page 689)

The table below gives data on moisture content for specimens of a certain type of fabric. Determine control limits for a chart with center line at height\(13.00\)based on\(\sigma = .600\), construct the control chart, and comment on its appearance.

Short Answer

Expert verified

The process is in control.

Step by step solution

01

Lower and upper limit

From

\(\begin{aligned}{l}LCL = {\rm{ lower control limit }} = \mu - 3 \cdot \frac{\sigma }{{\sqrt n }};\\UCL = {\rm{ upper control limit }} = \mu + 3 \cdot \frac{\sigma }{{\sqrt n }}\end{aligned}\)

we have

\(\begin{aligned}{l}LCL = {\rm{ lower control limit }} = 13 - 3 \cdot \frac{{0.6}}{{\sqrt 5 }} = 12.2\\UCL = {\rm{ upper control limit }} = 13 + 3 \cdot \frac{{0.6}}{{\sqrt 5 }} = 13.8\end{aligned}\)

02

Plot the chart

From the control chart, we can notice that all \(22\) values \(\bar x\) are within the limits, so the process is in control with respect to location.

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Most popular questions from this chapter

Refer to Exercise\(11\). An assignable cause was found for the unusually high sample average refractive index on day\(22\). Recompute control limits after deleting the data from this day. What do you conclude?

Consider the control chart based on control limits\({\mu _0} \pm 2.81\sigma /\sqrt n \)

a. What is the ARL when the process is in control?

b. What is the ARL when\(n = 4\)and the process mean has shifted to\(\mu = {\mu _0} + \sigma \)?

c. How do the values of parts (a) and (b) compare to the corresponding values for a\(3 - \sigma \)chart?

The following numbers are observations on tensile strength of synthetic fabric specimens selected from a production process at equally spaced time intervals. Construct appropriate control charts, and comment (assume an assignable cause is identifiable for any out of-control observations).

\(\begin{array}{*{20}{r}}{ 1. }&{51.3}&{51.7}&{49.5}&{12.}&{49.6}&{48.4}&{50.0}\\{ 2. }&{51.0}&{50.0}&{49.3}&{13.}&{49.8}&{51.2}&{49.7}\\{ 3. }&{50.8}&{51.1}&{49.0}&{14.}&{50.4}&{49.9}&{50.7}\\{ 4. }&{50.6}&{51.1}&{49.0}&{15.}&{49.4}&{49.5}&{49.0}\\{ 5. }&{49.6}&{50.5}&{50.9}&{16.}&{50.7}&{49.0}&{50.0}\\{ 6. }&{51.3}&{52.0}&{50.3}&{17.}&{50.8}&{49.5}&{50.9}\\{ 7. }&{49.7}&{50.5}&{50.3}&{18.}&{48.5}&{50.3}&{49.3}\\{ 8. }&{51.8}&{50.3}&{50.0}&{19.}&{49.6}&{50.6}&{49.4}\\{9.}&{48.6}&{50.5}&{50.7}&{20.}&{50.9}&{49.4}&{49.7}\\{ 10. }&{49.6}&{49.8}&{50.5}&{21.}&{54.1}&{49.8}&{48.5}\\{ 11. }&{49.9}&{50.7}&{49.8}&{22.}&{50.2}&{49.6}&{51.5}\end{array}\)

Observations on shear strength for 26 subgroups of test spot welds, each consisting of six welds, yield \(\Sigma {\bar x_i} = 10,980,\Sigma {s_i} = 402\), and \(\Sigma {r_i} = 1074\). Calculate control limits for any relevant control charts.

Calculate control limits for an\(S\)chart from the refractive index data of Exercise 11 . Does the process appear to be in control with respect to variability? Why or why not?
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