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# Upper and Lower control limits

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1. Which of the following situations suggest a process that appears to be operating in a state of statistical control?

a. A control chart with a series of consecutive points that are above the center line and a series of consecutive points that are below the center line.

b. A control chart in which no points fall outside either the upper control limit or the lower control limit and no patterns are present.

c. A control chart in which several points fall outside the upper control limit.

d. All of the above.

2. A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.

Day X (in minutes) R
1 58.5 5.1
2 47.6 7.8
3 64.3 6.1
4 60.6 5.7
5 63.7 6.2
6 57.5 6.0
7 55.0 5.4
8 54.9 6.1
9 55.0 5.9
10 62.7 5.0
11 61.9 7.1
12 60.0 6.5
13 58.3 5.9
14 52.0 5.2

Referring to the table, suppose the analyst constructs an R chart to see if the variability in production times is a control. What is the lower control limit for this R chart?

a. 4.84
b. 3.37
c. 2.98
d. 1.34

3. A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic.

Sample (Day) Number Favoring Incumbent
1 57
2 57
3 53
4 51
5 55
6 60
7 56
8 59

Referring to the table, what is the numerical value of the upper control limit for the p chart?

https://brainmass.com/statistics/multivariate-time-series-and-survival-analysis/upper-lower-control-limits-215421

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## Control limits problem

(Problem attached in excel file)

Sampling four pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results:

Hour X in " R in "
1 3.25 0.71
2 3.1 1.18
3 3.22 1.43
4 3.39 1.26
5 3.07 1.17
6 2.86 0.32
7 3.05 0.53
8 2.65 1.13
9 3.02 0.71
10 2.85 1.33
11 2.83 1.17
12 2.97 0.4
13 3.11 0.85
14 2.83 1.31
15 3.12 1.06
16 2.84 0.5
17 2.86 1.43
18 2.74 1.29
19 3.41 1.61
20 2.89 1.09
21 2.65 1.08
22 3.28 0.46
23 2.94 1.58
24 2.64 0.97
Develop appropriate control limits and determine whether there is any cause for concern in the cutting process.

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