ACPM User Guide

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USER GUIDE FOR THE AMSAA-CROW PROJECTION MODEL(ACPM)

November 2009

U.S. ARMY MATERIEL SYSTEMS ANALYSIS ACTIVITYABERDEEN PROVING GROUND, MARYLAND 21005-5071

DISTRIBUTION LIMITED TO U.S. GOVERNMENT AGENCIES AND THEIR CONTRACTORS; ADMINISTRATIVE

OR OPERATIONAL USE; DECEMBER 2009. OTHER REQUESTS FOR THIS DOCUMENT SHALL BE REFERRED

TO DIRECTOR, U.S. ARMY MATERIEL SYSTEMS ANALYSIS ACTIVITY, APG, MD 21005-5071.


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This Page Intentionally Left Blank


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Table of Contents1 PROJECTION MODELS ........................................................................................................ 5

2 AMSAA-Crow Projection Model. ........................................................................................... 6

2.1 Option for Individual B-mode 1st Occurrence Time Data. ............................................... 8

2.2 Model Results. .................................................................................................................. 9

2.3 Goodness-of-Fit. ............................................................................................................. 11

2.3.1 Cramr-von Mises. .................................................................................................. 11

2.3.2 Chi-Square. ............................................................................................................. 11

2.4 Reliability Plots. ............................................................................................................. 13

2.5 Option for Grouped Data................................................................................................ 18

3 REFERENCES: ..................................................................................................................... 274 POC: ...................................................................................................................................... 27

TABLE OF FIGURES

Figure 1. ACPM Introduction Window .......................................................................................................................... 5

Figure 2. Selection Button ............................................................................................................................................ 7

Figure 3. ACPM Options Selection Window (Partial Window)...................................................................................... 7

Figure 4. Input Window for ACPM Individual B-mode 1st

Occurrence Time Data ........................................................ 8

Figure 5. Model Results for ACPM Individual B-mode 1st

Occurrence Time Data ........................................................ 9

Figure 6. Explanation Regarding Growth Potential for ACPM .................................................................................... 10

Figure 7. Cramr-von Mises Goodness of Fit .............................................................................................................. 11

Figure 8. Entering the Number of Groups for Chi-square Test ................................................................................... 11

Figure 9. Goodness-of-Fit (Chi-square Test) for ACPM ............................................................................................... 12

Figure 10. Plot of Expected versus Observed Number of B-modes ............................................................................ 13

Figure 11. Preparing to Plot Rate of Occurrence of B-modes - Ending Value ............................................................. 14

Figure 12. Preparing to Plot Rate of Occurrence of B-modes Starting Value .......................................................... 14

Figure 13. Plot of Rate of Occurrence of B-modes for ACPM ..................................................................................... 14

Figure 14. Entering Group Size for Plot of Moving Average for ACPM ....................................................................... 15

Figure 15. Plot of Rate of Occurrence of B-modes Versus Moving Average at Intersection of Curve for ACPM ....... 15

Figure 16. Entering Group Size for Plot of Moving Average for ACPM ........................................................................ 16

Figure 17. Plot of Rate of Occurrence of B-modes Versus Moving Average at Midpoint of Curve for ACPM ............. 16

Figure 18. Preparing to Plot Projected Expected Number of B-modes for ACPM ...................................................... 16

Figure 19. Plot of the Projected Expected Number of B-modes ................................................................................. 17

Figure 20. Scattergram for ACPM ............................................................................................................................... 18

Figure 21. Input Window for ACPM Grouped Data with sample data. ....................................................................... 20

Figure 22. Sample Output for ACPM for Grouped Data ............................................................................................. 21

Figure 23. Model Results for ACPM Grouped Data Goodness-of-fit .......................................................................... 22


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Figure 24. Plot of Expected versus Observed Number of B-modes ............................................................................ 23

Figure 25. Preparing to Plot Rate of Occurrence of B-modes Ending Value ............................................................ 24

Figure 26. Preparing to Plot Rate of Occurrence of B-modes Starting Value .......................................................... 24

Figure 27. Plot of Rate of Occurrence of B-modes for ACPM Grouped Data ............................................................. 24

Figure 28. Plot of the Projected Expected Number of B-modes ................................................................................. 25


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1 PROJECTION MODELS

Figure 1. ACPM Introduction Window

The reliability growth process applied to a complex system in development involves surfacing

failure modes, analyzing the modes to determine their root causes, and implementing corrective

actions to those modes deemed correctable. In this way, the system is matured with respect toreliability. The rate at which the reliability of a system is improved is determined by

the set of failure modes that are addressed by corrective actions, the effectiveness and timeliness of the corrective actions, and the rate at which new (correctable) failure modes are being surfaced.

Before expanding upon these concepts, the following definition is set forth: A reliability growth

projection is an estimate of a systems reliability at a current or future milestone based onplanned and/or implemented fixes, assessed fix effectiveness, and the statistical estimate of the

rate of occurrence of correctable failure modes.

Failure modes are divided into essentially two camps: A-modes and B-modes. An A-mode is a

type of failure mode such that when it is surfaced, no corrective action (fix) will be taken. Thisdecision to classify a failure mode as an A-mode is typically made when the mode cannot be

replicated or understood. Its contribution to the system failure intensity is recognized andaccounted for, even though no action is taken to mitigate it. Thus, A-modes are also referred to

as non-correctable failure modes.

A B-mode is a type of failure mode such that when surfaced, a corrective action will be

attempted. Thus, B-modes are also termed correctable failure modes. Reliability growth occurs


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by the application of effective corrective actions to surfaced B-modes. With regard to failure

modes, the following assumptions are made.

A large, unknown number (K) of B-modes reside in the system from the start of test, no new failure modes (A or B) are induced by attempted fixes, failure modes (A and B) are independent and in series, each occurrence of a failure mode (A, B, first occurrence or repeat) results in a

system failure,

each A-mode has a constant rate of occurrence, and each B-mode has a constant rate of occurrence, both before and after fixes.

The effectiveness of a corrective action is embodied in a measure (or assessment) referred to as a

fix effectiveness factor, which is typically assessed for each surfaced B-mode. A fixeffectiveness factor is often defined as the percent (proportion or fraction) decrease in the rate of

occurrence of a B-mode after a corrective action has been implemented. Fix effectiveness

factors may be assessed in the range [0,1]; although a corrective action rarely eliminates all

future occurrences of a particular B-mode.

There are two projection models in the suite. The first projection model is referred to as the

AMSAA-Crow Projection Model. This model is used to estimate the system failure intensity atthe beginning of a follow-on test phase based on information from the previous test phase. This

information consists of B-mode first occurrence times, the number of failures associated with

each B-mode, and the total number of A-mode failures (which includes both first occurrencesand repeats). Additionally, the projection utilizes engineering assessments of the planned

corrective actions to each B-mode surfaced during the test. This model assumes that all

corrective actions are delayed until the end of the current test phase but implemented prior to thestart of the follow-on test phase.

The second projection model in the suite is referred to as the AMSAA Maturity Projection

Model. This model can be applied to situations where one wishes to utilize test data generatedover one or more test phases to make projections. This model does not require that all fixes be

delayed until the end of the current test phase. It only assumes that fixes are incorporated prior

to the time at which the projection is made. Also, this model allows for projections at futuremilestones beyond the start of the next test phase.

2 AMSAA-Crow Projection Model.The AMSAA-Crow Projection Model (ACPM) is used in the case where all fixes to surfaced B-modes are implemented at the end of the current test phase prior to the start of the follow-on test

phase. Thus, all fixes are delayed fixes.

ASSUMPTIONS:1. System is undergoing development testing2. Corrective actions are implemented as delayed fixes at the end of the test phase


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Given these assumptions, this program computes projections at the start of the next test phase for the:

1. System failure intensity2. System mean time between failure

For a complete discussion of the model, refer to AMSAA Technical Report Number 357, dated

June 1982 and entitled An Improved Methodology for Reliability Growth Projections. Theauthor is Larry H. Crow.

Figure 2. Selection Button

Figure 3. ACPM Options Selection Window (Partial Window)

There are two options for this model.1. If the B-mode occurrence times are known, then use the first option for Individual B-

mode 1st

Occurrence Time Data.

2. If the actual B-mode occurrence times are unknown but you are able to determine thetime intervals and the number of new B-modes in each time interval, then use the second

option for Grouped Data.


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2.1 Option for Individual B-mode 1st Occurrence Time Data.

Figure 4. Input Window for ACPM Individual B-mode 1st Occurrence Time Data

To see how times are entered into the sheet, click on Input Sample Data into Table button.

The Total Test time (T) is 400, the number of distinct, observed B-modes (m), (first occurrences

only) is 16, and there are 10 non-correctable failures ( ) (A-mode failures). Finally, there aretwo choices for calculating the average fix effectiveness factor (FEF), which will have an impact

on the growth potential estimates and the projections (failure intensity and MTBF). The failureintensity growth potential is an estimate (not a confidence bound estimate) of the lower bound on

the system failure rate and assumes that all the B-modes in the system have been surfaced. The

reciprocal of the failure intensity growth potential is the MTBF growth potential, which

represents an upper bound on the system MTBF under the assumption that all B-modes in thesystem have been surfaced. The arithmetic average FEF is a straight average of all the fix

effectiveness factors, giving equal weight to each FEF regardless of the number of occurrences

of each B-mode. The weighted average FEF is weighted by the number of occurrences of eachB-mode. For our purposes, select the option for the arithmetic average FEF. At this point, the

input window should appear as follows.

After entering your data or using sample data, click the Solve button to continue.

AN


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2.2 Model Results.

Figure 5. Model Results for ACPM Individual B-mode 1st Occurrence Time Data

The top four lines display the total amount of test time, the number of (distinct) observed B-

modes, the number of B-mode failures (which includes first occurrences and repeats), and thenumber of A-mode failures (which also includes first occurrences and repeats). The next line is

an estimate of the initial B-mode failure intensity, and since all fixes are delayed, this estimate is

simply the total number of B-mode failures divided by the total test time. The next line is anestimate of the A-mode failure intensity, and it is calculated as the ratio of the number of A-

mode failures to the total test time.

The next four lines are estimates for the two parameters of the model. The first in this group of

four is an estimate for beta, which in the context of reliability projection is referred to as the

shape parameter. The estimate for beta will be greater than zero and can take on values less thanone, equal to one, or greater than one. An estimate for beta that is less than one implies that the

rate of occurrence of new B-modes is decreasing with time, which is an indication that the

system is maturing. An estimate for beta that is equal to one (or nearly equal to one) implies a

constant rate of occurrence of new B-modes, which would indicate that the system reliability isnot maturing with respect to time. An estimate for beta that is greater than one is a redflag in

terms of the reliability for the system and implies that the rate of occurrence of new B-modes isincreasing with time. One would not want to make reliability projections with this model if theestimate for beta were greater than or equal to one. The next line is the unbiased estimate for

beta, which is used for model goodness-of-fit purposes. Finally, the last two estimates in the


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group are for the scale parameter lambda, which is used in the calculation of the B-mode rate of

occurrence function.

The last two entrieson this window display the arithmetic average fix effectiveness and theweighted average fix effectiveness, respectively. A discussion of these two averages was

presented earlier.

The next panedisplays estimates for the rate of occurrence of new B-modes at time T. InAMSAA Technical Report Number 357 the rate of occurrence of new B-modes at Tis referred to

as h(T). Note that there are now two ways of determining that the system reliability is maturing.The first indication was the estimate for beta, which was calculated to be approximately 0.8. The

second indication involves the decrease in the estimated B-mode failure intensity from an initial

value of 0.08 to a value at Tof approximately 0.03.

The next pane from the top displays the bias term which is the product ofh(T) and the average

fix effectiveness factor chosen earlier. The bias term represents the portion of the failure

intensity that accounts for the unseen B-modes.

The bias term plus the term for the adjustment procedure (see AMSAA TR-357) essentially

determines the projected failure intensity, which is displayed in the third pane from the top. Theadjustment procedure is essentially the failure intensity growth potential. Since the estimate for

the growth potential assumes that all the B-modes have been surfaced, the growth potential is

valid only if the estimate for beta is less than one. In other words, the rate of occurrence of newB-modes must be decreasing for growth potentials to be meaningful. Select the Growth

Potential Explanation button for further discussion on this matter.

Figure 6. Explanation Regarding Growth Potential for ACPM

The last pane displays estimates for the MTBF projection and the MTBF growth potential.

These estimates are essentially reciprocals of the values in the third pane from the top.


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Note that estimates for the (1) failure intensity growth potential, (2) MTBF growth potential, (3)

failure intensity projection and (4) MTBF projection take into account the impact of A-modefailures, B-mode failures and fix effectiveness.

2.3 Goodness-of-Fit.2.3.1 Cramr-von Mises.A Cramr-von Mises goodness-of-fit statistic is used to test the null hypothesis that the AMSAA-Crow projection model adequately represents a dataset consisting of B-mode first occurrence

times. The null hypothesis is rejected if the Cramr-von Mises statistic exceeds the critical value

for a chosen significance level. For our dataset, the model cannot be rejected, even for asignificance level equal to 0.20. Therefore, we have statistical justification for utilizing the

projections offered by the model. Note that if we were to reject the AMSAA-Crow projection

model based on the Cramr-von Mises goodness-of-fit results, the growth potential estimates

would still be valid since they are independent of the model.

Figure 7. Cramr-von Mises Goodness of Fit

2.3.2 Chi-Square. Now select the Chi-square goodness-of-fit test button. The followingwindow will appear. Enter the number of groups in which to divide the data, our example willrequire 5.

Figure 8. Entering the Number of Groups for Chi-square Test


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Figure 9. Goodness-of-Fit (Chi-square Test) for ACPM

For the chi-square goodness-of-fit test for this option of the model, the number of degrees of

freedom equals k-2, where krepresents the number of groups. As a minimum, three groups are

required in order for there to be at least one degree of freedom for the test. More than threegroups are possible, subject to the constraint that the frequency of failures per interval is at least

three. (The constraint requiring an expected frequency per interval of at least 5, which was used

for the continuous tracking model, has been relaxed for this model.) Since there are 16 B-modesin our dataset, this means that the test can conceivably be run with as many as 5 groups. It is

often informative to run the test over the range of possible numbers of groups.

Note that the model cannot be rejected at the 20 percent significance level for one degree of

freedom. Further, the model could not be rejected at the 20 percent significance level for two

and three degrees of freedom as the chi-square statistics were 1.50 and 3.38, respectively. Basedon these tests, the applicability of the model for this dataset is accepted. Again, if we were toreject the AMSAA-Crow projection model based on the Chi-square goodness-of-fit results, the

growth potential estimates would still be valid since they are independent of the model.

Now select back and then SeePlots button to view some reliability graphs.


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2.4 Reliability Plots.

Figure 10. Plot of Expected versus Observed Number of B-modes

This is essentially a visual plot of the goodness-of-fit of the model. It shows how closely the

model, as represented by the smooth curve, captures the overall trend of the observed data points.Note the concave shape of the curve. This is an indication that the rate of occurrence of new B-

modes is decreasing with time. The model would represent a constant or increasing rate of

occurrence of new B-modes as a straight line or convex curve, respectively, in which case themodel should not be used to make projections with such a dataset.

Now select the Plot B-mode Rate of Occurrencebutton. You will be prompted twice to enterinput for the curve. The first prompt will request an ending point for the curve, and the second

prompt will request a starting point for the curve. With regard to the ending point, the model can

be used to make projections beyond the data if you are willing to accept the assumption that the

rate of occurrence pattern that the model predicts will continue to hold. Even with that

assumption, projections should probably be made only slightly beyond the range of the data.With regard to the starting point for this model, the rate of occurrence of new B-modes at the

origin is infinite, so a starting point greater than zero must be entered. These two entries and therate of occurrence curve follow.


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Figure 11. Preparing to Plot Rate of Occurrence of B-modes - Ending Value

Figure 12. Preparing to Plot Rate of Occurrence of B-modes Starting Value

Figure 13. Plot of Rate of Occurrence of B-modes for ACPM

The model is clearly showing that the rate of occurrence of new B-modes is decreasing. Thenext two plots continue with this theme but they introduce the notion of a moving average with

respect to the observed data. Moving average in this context is a method for estimating the rate

of occurrence based on groups of observed B-modes. Select the Plot rate of occ VS moving avgat intersectionbutton. Plotting the moving average at the intersection means the moving

average is plotted where it intersects the model curve. Again, you will be prompted to enter a

group size,where the group size is the number of B-modes per group over which the movingaverage is calculated. A group size of five B-modes is a reasonable compromise in such an


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analysis,but the use of different group sizes may be investigated. An advantage of the moving

average approach is that we do not assume any specific model or distribution. It is useful for

portraying a general trend in the observed B-mode occurrence rate with respect to time. Themoving average curve (in red) is plotted with the model curve (in blue) for comparison purposes.

Figure 14. Entering Group Size for Plot of Moving Average for ACPM

Figure 15. Plot of Rate of Occurrence of B-modes Versus Moving Average at Intersection of Curve for ACPM

The Figure 17 is a plot of the moving average at the midpoint, which means the moving averageis plotted at the midpoint of the group interval.

Click on Plot rate of occ VS moving avg at midpoint and enterfive when prompted to enter a

group size.


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Figure 16. Entering Group Size for Plot of Moving Average for ACPM

Figure 17. Plot of Rate of Occurrence of B-modes Versus Moving Average at Midpoint of Curve for ACPM

Next select the Plot Projected Expected Num B-modesbutton. You will be prompted to enteran ending value for the curve. With regard to the ending point, even though the model can

project the expected number of B-modes beyond the total test time T, choose a value carefully as

any point beyond the range of the data assumes that the pattern will continue to hold. For our

example, enter 500.

Figure 18. Preparing to Plot Projected Expected Number of B-modes for ACPM


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Figure 19. Plot of the Projected Expected Number of B-modes

If we accept the assumption that the rate of occurrence of new B-modes pattern continues to hold

beyond the range of the actual data, then the model predicts that an additional three B-modes are

expected to be surfaced with an additional 100 hours of test time. This type of information can

be helpful to management for purposes of planning test resources.

Finally, select the Scattergrambutton, which will display another visual goodness-of-fitpicture.


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Figure 20. Scattergram for ACPM

This is a plot, for each distinct B-mode, of the observed versus the estimated expected time to

first occurrence. Each individual plotted point is an ordered pair of x-y coordinates for each B-

mode, where the x-coordinate is the observed time to first occurrence and the y-coordinate is an

estimate of the expected time to first occurrence. A solid, diagonal line is plotted from the origin

(0,0) to the endpoint (T,T), where Tis the total amount of test time. This diagonal line representsthe case where the observed time to first occurrence equals the expected time to first occurrence

for each B-mode.

Besides the Print Form and navigation buttons that appear on this window, the Help button is a

useful tool that explains the previous six plots that have been displayed.

2.5 Option for Grouped Data.Navigate to the ACPM options selection window by using back and main buttons, then

choose the Grouped Databutton.


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Figure 20. ACPM Options Selection Window

Figure 21. Blank Grouped Data Inputs Window


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Figure 21. Input Window for ACPM Grouped Data with sample data.

There must be at least three groups, as this minimum number is required forparameter estimation as well as goodness-of-fit purposes.

The first group must start at test time zero. The groups must be contiguous, that is, there should be no gaps in the data as this

model does not handle missing data.

The groups do not have to be of equal length. At least two of the groups must have B-modes, as this minimum number is required

for parameter estimation purposes.

The number of A-mode failures is the total over all groups and includes first occurrences and

repeats. For our example, assume there are no A-mode failures. The number of B-mode failuresis the total over all groups and it includesfirst occurrences and repeats.

Select Solve to go to the Grouped outputs.


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Figure 22. Sample Output for ACPM for Grouped Data

The first five lines of output essentially write back the five entries made on the input window:

the number of groups, the total amount of test time, the total number of observed B-modes, the

total number of B-mode failures and the total number of A-mode failures. Any corrections thatneed to be made to the input at this point can be accomplished by selecting the Back button,

which will return you to the Input Window. Assume that the inputs were as intended and note

the last two lines of output. The arithmetic average fix effectiveness factor (FEF) is a straightaverage of all the individual fix effectiveness factors, which gives equal weight to each FEF

regardless of the number of occurrences of each B-mode. The arithmetic average fixeffectiveness is applied toward the unseen B-modes. The weighted average FEF is weighted bythe number of occurrences of each B-mode and is applied toward the B-modes surfaced during

test. For our situation, since there were no B-mode repeats, the arithmetic average fix

effectiveness and the weighted average fix effectiveness are equal. This means that, forprojection purposes, fix effectiveness is treated equally among all the B-modes.

Now select the Go to Goodness-of-fit Results button to obtain further model results.


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Figure 23. Model Results for ACPM Grouped Data Goodness-of-fit

Goodness-of-fit is used to determine model applicability for each dataset. A chi-square

goodness-of-fit statistic is used to test the null hypothesis that the AMSAA-Crow projection

model adequately represents a dataset consisting of grouped data (B-mode first occurrencetimes). The null hypothesis is rejected if the chi-square statistic exceeds the critical value for achosen significance level. The method is based on obtaining an expected frequency of B-mode

first occurrences per group of at least five, subject to the requirement of having at least three

groups. Adjacent intervals are combined, if necessary, to meet this expectation (therecombination procedure is performed automatically without user intervention).

The dataset for our example originally consisted of nine groups. The goodness-of-fit resultsindicate that recombination of a few of the groups was required to meet the expected frequency

condition. The final number of intervals after recombination turned out to be five, and this gave

rise to k 2 = 3 degrees of freedom, where krepresents the final number of groups. Note that the

model could not be rejected, even for a significance level equal to .20. Therefore, theapplicability of the model for this dataset is accepted.

Incidentally, even if the AMSAA-Crow projection model does not fit the data, the growthpotential estimates are still valid, provided the estimate for beta is less than one.

Now select the See Plots button to view available reliability plots.


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Figure 24. Plot of Expected versus Observed Number of B-modes

This is essentially a visual plot of the goodness-of-fit of the model. It shows how closely the

model, as represented by the smooth curve, captures the overall trend of the observed data points.In addition, there is a slight concavity to the curve, which indicates that the rate of occurrence of

new B-modes is decreasing. The model would represent a constant or increasing rate of

occurrence of new B-modes as a straight line or convex curve, respectively, in which case the

model should not be used to make projections with such a dataset.

Now select the Plot B-mode Rate of Occurrencebutton. You will be prompted twice to enter

input for the curve. The first prompt will request an ending point for the curve, and the secondprompt will request a starting point for the curve. With regard to the ending point, the model can

be used to make projections beyond the data if one is willing to accept the assumption that the

rate of occurrence pattern that the model predicts will continue to hold beyond the range of theobserved data. Even with that assumption, projections should probably be made only slightly

beyond the range of the data, as any change in environment beyond the observed data would

most likely disturb the pattern. With regard to the starting point for the curve, the rate of

occurrence of new B-modes at the origin is infinite, so a starting point greater than zero must bechosen. This exception at the origin is not a serious problem since the estimated rate of

occurrence of new B-modes beyond the origin (typically at T) is of most concern for projection

purposes. Also, the estimated initial B-mode failure intensity is not gained from this curve but isestimated by calculating the ratio of the total number of B-mode failures to the total test time

(under the model assumption that all fixes are delayed until T). The two curve entries and the

rate of occurrence curve follow. For this example, enter 4500 and select OK, and then enter100 and select OK.


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Figure 25. Preparing to Plot Rate of Occurrence of B-modes Ending Value

Figure 26. Preparing to Plot Rate of Occurrence of B-modes Starting Value

Figure 27. Plot of Rate of Occurrence of B-modes for ACPM Grouped Data

The model is clearly showing that the rate of occurrence of new B-modes is decreasing. Next

select the Plot Projected Expected Num B-modesbutton. Enter a value for the curve similar tothe previous curve, namely 4500.


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Figure 28. Plot of the Projected Expected Number of B-modes

With regard to the ending point, even though the model can project the expected number of B-

modes beyond the total test time T, choose a value carefully as an ending value beyond the range

of the data assumes that the pattern established by Twill continue to hold beyondT. If we acceptthis assumption, then the model predicts that an additional seven B-modes are expected to be

surfaced by the end of the next 882 hours of test time. This type of information can be helpful to

management for purposes of planning test resources.

Finally, select the Scattergrambutton, which will display another visual goodness-of-fit

picture.


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Figure 30. Scattergram for ACPM Grouped Data

This is a plot of the observed versus the estimated expected time at the end of each group. Each

individual plotted point is an ordered pair of x-y coordinates for each group, where the x-coordinate is the observed time at the end of the group and the y-coordinate is an estimate of the

expected time at the end of the group. The solid, blue, diagonal line is plotted from the origin

(0,0) to the endpoint (T,T), where Tis the total amount of test time. The diagonal line represents

the case where the observed time at the end of the group equals the expected time at the end ofthe group.


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3 REFERENCES:1. MIL-HDBK-189, Reliability Growth Management, 13 February 1981.2. Broemm, W., Ellner, P., and Woodworth, J., AMSAA Reliability Growth Guide, TR-652,

September 2000.3. Broemm, W., User Guide for the Visual Growth Suite of Reliability Growth Models, TR-

764, January 2005.

4 POC:James Arters, AMSAA

Anthony Serafino, AMSAA

Rebecca Wentz, AMSAA

Help

[email protected]
mailto:[email protected]:[email protected]:[email protected]

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