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Chapter 8: Problem 2

For the following random variables, indicate whether you would expect each to be \(L V, M V,\) or HV. (a) Time to complete this set of study questions (b) Time for a mechanic to replace a muffler on an automobile (c) Number of rolls of a pair of dice between rolls of seven (d) Time until failure of a machine recently repaired by a good maintenance technician (e) Time until failure of a machine recently repaired by a not-so-good technician (f) Number of words between typographical errors in the book Factory Physics (g) Time between customer arrivals to an automatic teller machine

Short Answer

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Question: Categorize the following random variables into Low Variability (LV), Medium Variability (MV), or High Variability (HV): a. Time to complete this set of study questions b. Time for a mechanic to replace a muffler on an automobile c. Number of rolls of a pair of dice between rolls of seven d. Time until failure of a recently repaired machine by a good maintenance technician e. Time until failure of a recently repaired machine by a not-so-good technician f. Number of words between typographical errors in the book Factory Physics g. Time between customer arrivals to an automatic teller machine Answer: a. MV b. LV c. HV d. LV e. HV f. MV g. HV

Step by step solution

01

Determine variability of time to complete study questions

Different students might take varying amounts of time to complete the questions, depending on their level of understanding and focus. Thus, the variability should be classified as Medium Variability (MV). #b. Time for a mechanic to replace a muffler on an automobile#
02

Determine variability of time for mechanics to replace muffler

Trained mechanics will have a similar time range to replace a muffler. Although some differences might exist between mechanics, the overall variability should be relatively low. Thus, we'll classify it as Low Variability (LV). #c. Number of rolls of a pair of dice between rolls of seven#
03

Determine variability of number of rolls to get a seven

The number of rolls to get a seven can have a high variability as it depends on luck and is a random event. We can classify this as High Variability (HV). #d. Time until failure of a recently repaired machine by a good maintenance technician#
04

Determine variability of time until failure for well-repaired machines

A well-repaired machine by a good technician should have a stable and prolonged functioning time. Misfortunes can happen, but generally, the variability should be low. We can classify it as Low Variability (LV). #e. Time until failure of a recently repaired machine by a not-so-good technician#
05

Determine variability of time until failure for poorly-repaired machines

A not-so-good technician might result in different levels of quality in the repair, leading to a more unpredictable time until failure. We can classify this as High Variability (HV). #f. Number of words between typographical errors in the book Factory Physics#
06

Determine variability of words between typographical errors

The number of words between errors depends on how well the book is edited, but generally, it has some level of consistency. However, it can still vary across different sections of the book, so we will classify it as Medium Variability (MV). #g. Time between customer arrivals to an automatic teller machine#
07

Determine variability of time between ATM customer arrivals

The time between customer arrivals at an ATM depends on various factors like location, time of day, and other external events. This makes it a highly variable event. We can classify it as High Variability (HV).

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Most popular questions from this chapter

\text { What happens to CT, WIP, } C T_{q} \text { and } \mathrm{WIP}_{q} as the arrival rate \(r_{a}\) approaches the process rate \(r_{e} ?\)

Why is the number of customers at the station an adequate state for summarizing current status in the \(M / M / 1\) queue but not the \(G / G / 1\) queue?

What is meant by steady state? Why is this concept important in the analysis of queucing models?

What type of manufacturing workstation does the \(M / G / 2\) queue represent?

What is the rationale for using the coefficient of variation \(c\) instead of the standard deviation \(\sigma\) as a measure of variability?
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