2.4 Case Study Evaluations
2.4.2 Presenting Results
This case is also about developing and presenting results quickly to avoid being overcome by events that would diminish the value of the work or make the decision for you. In such cases, having a few generic presentation tools readily available can improve the chances of getting the message across to the right people in the time available. For this case study, a “tornado”
diagram was chosen to capture the range of uncertainties with a simple presentation. This type of stacked bar chart gets its name from its shape. Items with the greatest uncertainty – the largest positive and negative variances from a base case – are shown at the top while those with the least impact on the decision are at the bottom. The resulting inverted triangle shape focuses attention on the items with the greatest importance for the results, and helps drive a decision based on the certainty of information that is available at the time.
To construct a tornado bar chart from sensitivity studies in Excel, use a “stacked bar chart”
with two series, lower and higher earnings or returns, for each sensitivity case. Sort the cases in order of increasing absolute value using either the lower or higher series, to provide clarity and understanding for the audience. Figure 2.10 is an example Tornado diagram using the data shown in Table 2.1. In this example, Uncertainty E would be the focus of any discussion, with a possible mention of Uncertainty D. Notice also that Uncertainty E has a greater positive impact than negative. A strategy to help a project or decision based on this type of result could focus on the methods to ensure a positive outcome from Uncertainty E rather than passively accepting its potential.
Table 2.1 Example data for tornado diagram.
Study case Lower earnings Higher earnings
Uncertainty A −5 6
Uncertainty B −12 4
Uncertainty C −12 15
Uncertainty D −20 15
Uncertainty E −40 60
–60 –40 –20 0 20 40 60 80
Uncertainty A Uncertainty B Uncertainty C Uncertainty D Uncertainty E
Figure 2.10 Example tornado diagram.
The critical time factor of this case study will govern how the results are presented. Developing a formal PowerPoint slide presentation is probably not the best use of time. Instead, a quick e‐mail with the conclusion and a tornado diagram would be more effective. A phone call can be suitable but should be followed with an e‐mail to document the conversation and any decision.
2.4.3 Judgment Calls
The following assumptions help begin the evaluations and will be tested to determine their significance on the decision outcome.
1. Let the standard deviation (σ) around the mean time between TBC failures (“MTBF”) be 5% of the recommended maintenance interval – 1200 hours.
2. Assume there are two methods of arriving at the maintenance interval (MI):
(a) For the base case, assume the manufacturer has a small margin (δ) subtracted from the actual mean time to failure less two times the standard deviation (σ). That is, for Method 1: MI1 MTBF– – * . Assume the margin (δ) yields a cumulative 2 probability of a TBC failure of 1% at the recommended maintenance interval.
(b) In the alternative case, the manufacturer sets the maintenance interval at the actual mean time to failure less three times the standard deviation. The maintenance interval for Method 2 is: MI MTBF – *3 .
3. A catastrophic event would cost the company $25 million in addition to the planned HGPI outage.
You also have the following information:
• A standard HGPI inspection nominally costs the company $5 million and takes 3 weeks to complete.
• Natural gas has been purchased on a set schedule for the current month at $4.50/MMBtu.
Prices are not expected to change appreciably over the next several months.
• The corporate tax rate is 28%.
• Accounting for cycling operation (turndown or removing from service on a nightly basis) the capacity factor (CF) of the facility is 65%.
From the data and base case assumptions, the actual mean time to failure is equal to the recom- mended maintenance interval plus two times σ, plus a small margin.
2.4.4 Exercise
1. Use the Excel NORMDIST function to determine the manufacturer’s margin such that the cumulative probability of failure at the recommended maintenance interval is ~1% from 2(a) above.
2. Calculate the probability of failure at the recommended interval plus 800 hours.
3. Find the probability of failure at the end of the proposed 3 week run‐time extension.
4. Calculate the normal marginal cost of production ($/MWh) neglecting nonfuel operating and maintenance costs.
5. Calculate the spark spread ($/MWh) at the normal and temporary market power price for the 16‐hour daily peak.
6. Determine the probable lost profit opportunity that would occur from a 3‐month outage extension. The loss would include gross margin plus the differential maintenance cost due to a catastrophic failure that could occur within the 21‐day operating extension.
7. Calculate the base case probable gain or loss for extending the run time 21 days for the base case assumptions.
2.4.5 Sensitivities
Once a value for the base case has been determined, testing of the assumptions helps provide credibility or provides guidance to change the basis and arrive at a new base case. For this case study, there are a number of assumptions that should be tested, including:
• Engineering assumptions:
∘ The value of σ for the two methods of determining the maintenance interval – MI.
∘ The manufacturer’s margin – δ.
∘ The assumed method of setting the recommended maintenance interval (2σ + margin
“Method 1” versus 3σ “Method 2”).
• Commercial assumptions:
∘ The duration that prices will remain at current levels – three times the normal rate.
∘ The actual price that will exist during the assumed period of three weeks.
2.4.6 Exercise – Sensitivities
Even though management requested an engineer’s opinion, the engineer should not forget the commercial side of the equation. Commercial assumptions on price and quantity are often much less certain than engineering assumptions and can carry substantial impact on a decision.
For the above parameters, check the net value of the extended run time for changes of 50%
(worse) and 20% (better). That is:
• Method 1 σ: −50%, +20%.
• Manufacturer’s margin: −50%, +20%.
• Power price: −50%, +20%.
• Temporary increase period: −50%, +20%.
• Method 2: 3σ with no margin.
• Method 2 σ: −50%, +20%.
2.4.7 Presentation of Results
Use a stacked bar chart in Excel to prepare a “tornado” diagram. To do so, there will be two data series: the results with a positive impact over the base case, and those with negative impact. The axis categories are:
• Manufacturer margin.
• Method 1 σ.
• Method 2 3σ no Margin.
• Method 2 σ.
• Duration of high prices.
• Price.
There are positive and negative impact values for each category listed, some may be zero.
Assign colors for the two series to help convey the monetary meaning of the results. Plot the variances from the base case and provide appropriate labels for understanding.
Prepare an e‐mail with your conclusion and recommendation whether to take the outage immediately or delay for a specific period.