Earned value analysis and earned schedule

Lesson 7 defined the earned value measures. This lesson is about using them: reading trends rather than single values, converting schedule variance from dollars into time with earned schedule, setting variance thresholds, writing variance analysis that leads to action, and knowing the limits of the method. The aim is to get from 'the SPI is 0.89' to 'the structure is about three weeks behind because slab forming on level 3 is running at 85 % of budget productivity, and here is what we are doing about it.'

Trends, not snapshots

A single month's CPI or SPI says little on its own. A CPI of 0.97 might be improving from 0.90 or deteriorating from 1.05; the response should be very different. Earned value reports should therefore show both cumulative and current-period indices over time. Cumulative indices are stable and show the overall position; period indices are noisy but show what is happening now. When the period index stays below the cumulative one for several months, the cumulative index will keep falling.

# Cumulative and monthly CPI for the Riverbend structure account (amounts $1000)
ev = [0, 180, 640, 1_210, 1_820, 2_330, 2_780]      # cumulative earned value, months 2-8
ac = [0, 176, 655, 1_265, 1_915, 2_480, 2_960]      # cumulative actual cost
for m in range(1, len(ev)):
    month_cpi = (ev[m] - ev[m - 1]) / (ac[m] - ac[m - 1])
    print(f"Month {m + 2}: monthly CPI {month_cpi:.2f}   cumulative CPI {ev[m] / ac[m]:.3f}")

Month 3: monthly CPI 1.02   cumulative CPI 1.023
Month 4: monthly CPI 0.96   cumulative CPI 0.977
Month 5: monthly CPI 0.93   cumulative CPI 0.957
Month 6: monthly CPI 0.94   cumulative CPI 0.950
Month 7: monthly CPI 0.90   cumulative CPI 0.940
Month 8: monthly CPI 0.94   cumulative CPI 0.939

The monthly CPI fell below 1.0 in month 4 and has stayed there, between about 0.90 and 0.96. The cumulative CPI therefore keeps drifting down. Nothing in the trend suggests a recovery without action.

How stable is the CPI?

Research on large defense contracts in the United States, notably by David Christensen and colleagues in the 1990s, found that once a contract was about 20 % complete, its cumulative CPI rarely changed by more than about 10 % for the rest of the contract, and when it did change it usually got worse. Construction projects are less studied and differ in many ways, so the finding should be treated as a caution rather than a law. But the practical message is consistent with experience on building projects: early cost performance is a strong predictor of the final result, and a project manager who expects a poor cumulative CPI to recover by itself is usually disappointed. Lesson 9 uses this when choosing forecasting formulas.

The problem with SV in dollars

Schedule variance in dollars has a well-known flaw. At the end of a project, all the work is done, so earned value equals planned value equals BAC, and SV returns to zero and SPI to 1.0, even if the project finished months late. In the last third of a late project, SV and SPI drift back toward 'on schedule' and become misleading. They also say nothing directly about time: being $953,000 of work behind does not tell anyone how many weeks late the project is.

Earned schedule

Earned schedule (ES), introduced by Walt Lipke in 2003, fixes the problem by measuring schedule performance in time. ES is the time at which the planned value curve reached the current earned value: in other words, how far along the baseline the project has actually got. It is found by locating the period in which PV passed EV and interpolating within it.

Here \(C\) is the number of whole periods for which cumulative PV is less than or equal to EV, \(PV_C\) is cumulative PV at the end of period \(C\), and \(PV_{C+1}\) at the end of the next period. With ES and the actual time elapsed (AT), schedule variance and performance can be expressed in time.

# Earned schedule for Riverbend Commons at month 8 (amounts $1000)
pv = [0, 592, 1_185, 2_409, 3_160, 4_242, 5_872, 7_502, 8_860, 10_218, 11_576]   # cumulative PV, months 0-10
EV, AT, PD = 7_907, 8, 16          # earned value, actual time (months), planned duration
C = max(m for m in range(len(pv)) if pv[m] <= EV)
ES = C + (EV - pv[C]) / (pv[C + 1] - pv[C])
sv_t, spi_t = ES - AT, ES / AT
print(f"C = {C}; ES = {ES:.2f} months")
print(f"SV(t) = {sv_t:.2f} months ({sv_t * 4.33:.1f} weeks); SPI(t) = {spi_t:.3f}")
print(f"Dollar SPI for comparison: {EV / pv[AT]:.3f}")
print(f"Forecast duration at SPI(t): {PD / spi_t:.1f} months")

C = 7; ES = 7.30 months
SV(t) = -0.70 months (-3.0 weeks); SPI(t) = 0.912
Dollar SPI for comparison: 0.892
Forecast duration at SPI(t): 17.5 months

Riverbend Commons has achieved the planned value of month 7.3 by month 8, so it is about 0.7 months, or roughly three weeks, behind. If performance continues at SPI(t) = 0.912, the 16-month job would take about 17.5 months. That is a little worse than the 17 months the project team used for its general conditions forecast in Lesson 6, which is exactly the kind of difference the monthly review should discuss.

Earned value and the critical path

Earned value, including earned schedule, measures progress across all work, weighted by budget. The project's completion date, however, depends on the critical path (CON-210 Lesson 5). A project can show SPI(t) close to 1.0 because non-critical work is ahead, while the critical path is slipping; or it can show a poor SPI because non-critical work is behind, with no effect on the end date. Earned schedule is therefore a useful independent check on the scheduler's forecast, not a replacement for it. When the two disagree, look at the critical and near-critical activities: if they are behind, believe the worse figure.

Variance thresholds

No team can investigate every variance every month. Thresholds focus attention on the ones that matter. A typical approach sets thresholds on both percentage and absolute value, so that small accounts are not flagged for trivial amounts and large accounts are not let off because the percentage is small.

# Flag control accounts that breach thresholds (amounts $1000)
accounts = {  # name: (PV, EV, AC)
    "Site and foundations": (1_420, 1_420, 1_455), "Structure": (3_160, 2_780, 2_960),
    "Envelope": (1_644, 1_370, 1_390), "Mechanical and electrical": (1_324, 1_210, 1_200),
    "Interiors": (360, 175, 180), "General conditions": (952, 952, 978),
}
for name, (pv, ev, ac) in accounts.items():
    cv, sv = ev - ac, ev - pv
    flags = []
    if abs(cv) > 25 and abs(cv) / ev > 0.05: flags.append(f"CV {cv:+}")
    if abs(sv) / pv > 0.10: flags.append(f"SV {sv:+}")
    print(f"{name:<27} {'; '.join(flags) if flags else 'within thresholds'}")

Site and foundations        within thresholds
Structure                   CV -180; SV -380
Envelope                    SV -274
Mechanical and electrical   within thresholds
Interiors                   SV -185
General conditions          within thresholds

Structure breaches both cost and schedule thresholds. Envelope and interiors breach the schedule threshold. General conditions' CV of minus $26,000 is above the absolute amount but under 5 % of EV, so it is not flagged; it will be caught by the forecast change threshold if the overrun grows. Site and foundations is slightly over on cost but within both limits.

Variance analysis that leads to action

For each breach, the control account manager writes a short variance analysis. A good one answers four questions in plain language: what is the variance; what caused it; what will its impact be on cost and schedule at completion; and what is being done about it, by whom and by when. A poor one restates the numbers ('CV is −$180,000 because actual cost exceeded earned value') or blames the weather without evidence.

Using earned value in the weekly meeting

On self-performed work, the most useful earned value conversation happens weekly at crew level, in hours. A one-page sheet for each foreman showing budget hours, earned hours, actual hours, weekly and cumulative productivity factor, and the hours remaining at the current rate makes the numbers concrete. Crews that see their own figures every week, and are asked what is getting in their way, often identify the problems faster than any analyst: late drawings, missing materials, crane conflicts, an inspection backlog. The cost engineer's job is to make the numbers accurate and simple enough for that conversation.

Limits of earned value

Earned value is a powerful summary but it has limits. It measures performance against the baseline, so a bad baseline gives bad answers. It weights work by budget, so a cheap but critical activity has little influence on SPI. It says nothing about quality: work that will need rework has still been 'earned' unless the rules of credit remove it. And it depends on honest progress measurement, the step most open to optimism. Used with these limits in mind, alongside the schedule and the line-by-line cost forecast, it is the best early warning system a project has.