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# Statistics - Measuring Quality

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I am trying to determine what to use in measuring the quality characteristics of my PC and Laptop business and also how often I should conduct a statistical analysis.

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PC AND LAPTOP BUSINESS: STATISTICAL ANALYSIS OF PERFORMANCE
QUALITY

Business performance may be measured in several ways: a) target sales as against actual sales, b) target profit as against actual profit, c) average daily/weekly/monthly sales and corresponding comparative and trend analyses, d) company sales and as against average industry sales, e) market share, and f) relationships of marketing efforts (e.g. advertisement to sales). Various statistics may be used to describe and interpret the quality of business performance.

Percentage
Target sales are often determined based on the goals and objectives of the company as against the company's available resources and with due consideration of marketing efforts that may be applied by the business. To measure the extent of which the business was able to meet its target sales, a simple statistics to utilize would be percentage of actual to target sales. A 90% actual sales as against target sales would indicate that the business is short of the targeted sales by 10%. While this would indicate inability in meeting target sales, quality of sales performance may be further determined by comparing such percentage with performances in the past or by comparing such percentage with that of other players in the industry.
Percentage may also be used to determine the extent of which target profits have been met such that a very low percentage may indicate a very low level of performance. It may also manifest that the business has not been managing its expenditures well, resulting to low level of ...

#### Solution Summary

The expert examines measuring the quality characteristics of my PC and Laptop business. A statistical analysis is determined.

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## Quality Management

(See attached file for full problem description)

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1. A study determines that 60% of the voters in a town intend to vote for the incumbent mayor. If a sample of 8 people is selected, the approximate probability that 6 of the 8 people surveyed intend to vote for the incumbent is (using the binomial probability formula):
a. 0.21
b. 0.47
c. 1.28
d. 0.60

2. The probability that exactly 2 heads will be tossed in 5 consecutive coin tosses is:
a. 0
b. 0.03125
c. 0.3125
d. 0.15625

3. A large-sample test to determine the average life of a type of alkaline battery is most likely to use the:
a. Normal distribution
b. Poisson distribution
c. Hypergeometric distribution
d. Binomial distribution

4. If the average of 0.5 customers arrive per minute at a ticket counter, what is the probability that exactly 4 customers will arrive in a 5-minute span?
a. 0.0534
b. 0.50
c. 0.68
d. 0.134

5. A firm wants to monitor the number of missed stitches on a line of sweaters being produced. The researchers will construct and use a(n) ________ chart to aid data interpretation.
a. p chart
b. u chart
c. c chart
d. x-bar chart

6. A p chart with variable sample sizes yields the following statistics:
Process average = 0.50; UCL = 0.80; average sample size is 100
For an observation of value 0.78 drawn from a sample of 90:
a. the point is under control for the average limit, so it will definitely be under control for the individual limit
b. the individual control limit must be calculated to determine if the point exhibits a lack of control
c. we can determine that the point exhibits a lack of control without the need to calculate the individual control limits.

7. Data from 30 subgroups of 100 units each yields a total of 150 defective units. The upper control limit on the np chart is:
a. 0.70
b. 5.00
c. 5.65
d. 11.54

8. A sampling process destroys the unit sampled, and because the process is continuous it is possible only to collect one sample at a time. The most appropriate chart to use is a(n):
a. x-bar chart
b. np chart
c. chart of individuals
d. c chart
9.
Production Run Subgroup Size # of defective Units
1 150 6
2 150 3
3 150 2
4 150 0
5 150 3
6 150 3
7 150 1
8 150 3
9 150 8
10 150 1
11 150 5
12 150 4
13 150 0
14 150 2
15 150 6
16 150 4
17 150 9
18 150 1
19 150 2
20 150 0

The most appropriate chart to analyze this data is the:
a. c hart
b. variable control chart
c. x-bar chart
d. p chart

The proportion nonconforming for the 9th production run is:
a. 0.04
b. 0.053
c. 0.08
d. 0.123

The upper control limit for the data is:
a. 0.032
b. 0.036
c. 0.056
d. 0.32

Which of the following production runs exhibits a lack of control in the process?
a. 17
b. 9, 17
c. 4, 13, 20
d. 4, 13, 17, 20

10. A firm will use a _______ when measuring nonconformities per unit with variable sample sizes.
a. p chart
b. np chart
c. c chart
d. u chart

11. Overstressing a product is a common cause of:
a. early failure
b. random failure
c. wear-out

12. A key component of training and education of product users.
a. adequate training and education of product users
b. redundant components
c. fail-safe design
d. comprehensive product knowledge
e. both a and d
f. all of the above

13. A metal rod used in connecting two subassemblies for a machine part must measure 2.35 cm in length. Any deviation causes a change in torsion ratios that materially affects the performance of the part. It costs the manufacturer \$24 to adjust the rod (under warranty) when a complaint is received. Based on past experience, the average customer has returned the subassembly if the rod measurement is off by at least 0.12 cm. The firm can adjust the rod for only \$4.50 at the factory.

The Taguchi loss function for the rod is:
a. L(y) = 24(y-2.35)2
b. L(y) = 24(y-0.12)2
c. L(y) = 1,666.67(y-2.35)2
d. L(y) = 1,666.67(y-0.12)2

What should the tolerance specification be before a factory adjustment is made?
a. 2.35 +/- 0.12
b. 0.12 +/- 0.052
c. 2.35 +/- 0.052

14. If a company benchmarks outside its own industry, it may find new ideas and processes that allow it to match or even surpass current industry leaders.
a. True
b. False

15. QFD attempts to measure the correlation between customer requirements and technical requirements, and the products technical performance to that of competitors, but does not evaluate regulatory requirements that might affect the product.
a. True
b. False

16. A binomial probability distribution:
a. has a constant probability of success in each trial
b. determines the result of a trial based on the results of the previous trial
c. has mutually exclusive outcomes
d. is determined from an infinite number of trials
e. both a and c
f. all the above

17. A large-sample test to determine the average life of a type alkaline battery is most likely to use the:
a. normal distribution
b. poisson distribution
c. hypergeometeric distribution
d. binomial distribution

18. The ______________ is used to evaluate the number of nonconformities in a unit.
a. p chart
b. u chart
c. c chart
d. x-bar chart

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