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Method of Analysis for Business Operations

  1. ABC Manufacturing has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is described by the probability distribution seen below:

(a) What is the expected number of breakdowns in any given day?

 (b) What is the variance for this distribution?

 (c) What is the probability that there will be at least 2 breakdowns in a day?

Number of breakdowns Probability
0 0.4
1 0.3
2 0.2
3 0.1
More than 3 0.0

 

  1. Expected number of break downs E(X)

E(X)=S*P(x)

0.4*0+ 0.3*1+2*0.2+3*0.1+ 3*0 = 1

  1. b) Variance

Var(x)=E((x-m)2)

X (x-m)2
0 1
1 0
2 1
3 4
More than 3 4

 

  1. Probability

(Render, Stair & Hanna,2012; Siegel, 2011; Anderson, Sweeney & Williams, 2011; Black, 2011).

 

  1. 2. The decomposition approach to forecasting (using trend and seasonal components) may be helpful when attempting to forecast a time-series. Could an analogous approach be used in a multiple regression analysis? Explain briefly.

There are four components of a time series, and these are a trend, cycle, seasonal and random variation. Trend variation deals with the long-run trend of sales, jobs, prices of financial assets as well as the rest of business besides economic series. Cyclical variation is relevant in a general business cycle that composes of a time of prosperity seconded by the time of business cycle such as recession, depression as well as recovery. This cycle lacks a constant time. There are considerable changes manifested over at least one year difference with respect to trend variation. Another component is seasonal variation. In this component, nearly entire businesses exhibit recurring seasonal patterns. For instance…………………….

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