Problem Of The Month
April 1998--Production Reliability Example With Nameplate Ratings

The following problem, and solution, will illustrate features of WinSMITH Weibull (WSW) probability software for quantifying production reliability issues and establishing nameplate capacities from actual production data and benchmark data. WSW, version 3.0T and above, make process reliability issues easy to solve. You can download files from this website to repeat this analysis on your computer.

The Problem
The May 1997 and March 98 problems of the month showed how daily production quantities can be used to analyze plant production problems. The example below puts all of these ideas from the earlier web pages together.

Table 1
Daily Production Output (
K-lbs)

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

1023
692
1026
748
1008
372
558
347
347
1009
379
704
473
351
368
551
338
1006
312
816
899
433
344
375
791
369
1010
628
593
1024
524
495
290
827
211
988
1017
633
222
992
1014
457
1012
378
328
1005
773
1006
1019
473
522
514
928
433
358
365
1017
306
868
1014
876
949
1011
843
1026
767
1017
680
653
725
1019
346
567
521
567
418
1010
1008
438
1008
1023
1023
257
878
573
356
326
894
629
260

678

340

658

328

301

1026

987

376

357

991

372

382

343

403

375

300

1036

321

504

436

1011

232

495

367

843

1010

1022

495

1017

593

384

374

2

308

685

1009

343

1012

1024

588

344

338

339

759

300

902

445

364

852

355

861

381

315

673

1026

664

1016

1015

677

1010

832

1014

872

1010

719

358

1012

351

464

384

358

709

364

971

491

325

481

1006

1018

357

574

594

365

762

383

902

472

358

356

1005

349

893

975

843

967

322

1048

248

1021

1036

648

365

2

769

1027

622

1011

344

383

608

370

1008

480

555

348

1012

656

1008

1040

567

373

1033

364

489

253

763

1015

1010

868

683

432

431

1020

1017

334

370

831

317

363

768

254

705

1023

381

374

785

215

961

441

269

339

352

1020

660

364

1026

811

755

357

371

239

300

401

1038

370

915

1019

657

1009

598

1017

377

376

982

451

343

1018

743

859

481

807

358

661

343

329

596

352

774

360

374

376

560

825

226

983

1012

438

1009

347

477

380

347

1022

356

1017

1014

1017

322

1036

364

2

913

383

477

836

1019

350

384

424

356

230

1034

1011

358

874

372

533

999

1010

362

599

370

668

491

320

323

408

336

363

1042

1012

328

779

319

695

447

369

540

575

1015

405

357

1017

303

1012

916

357

1028

219

879

442

845

445

1015

336

1036

696

1012

1031

335

1021

669

1014

582

346

Daily output from a production plant is shown in Table 1. In lieu of "zero" output (which will not plot on a log scale), the zero production days are reported as 2-logs smaller than the least production reported (look for the days with reported production as 2 K-Lbs). This approximation results in very small errors, and this scheme allows 365 data points to show on the probability plot with down days shown as small values.

You can copy the data in Table 1 from your browser, or download the WSW file by clicking here for file APR98WPR.W. This special WSW file size is 11.2 KB. You can also download the Excel file as APR98WPR.XLS by clicking here-the 40 KB Excel file data is in chronological order and saved as an Excel 5.0 file. The Excel file is intended to show you the raw data in chronological order, and it is the same as Table 1 but concatenated into a single column of data plus a second column showing the production date.

You can use the special APR98WPR.W file with the demonstration version of WSW available from the demo webpage by clicking here. The WSW demo file is 1.2 Meg.
Special Demo Note:
If you enter raw data into the demo version of WSW it will randomize your data (after all, it's simply a demo version-you've got to purchase the real version). However if you import the data from the special file APR98WPR.W it will function as if the software is full strength and WILL NOT randomize the data. These two WSW files will allow you to "test drive the software before you purchase".

Let's assume you have installed the WSW demo program so it resides in C:\SMITHW directory and you have a subdirectory for your data in C:\SMITH\SMITHDAT. Let's furthermore assume the files APR98WPR.W and APR98WPR.XLS have been copied to C:\SMITHW\SMITHDAT so you know where to search for retrieval.

Start WSW from START\PROGRAMS\SUPERSMITH\SUPERSMITH WEIBULL DEMO icon. Import the file APR98WPR.W and note that the probability plot contains five straight line segments rather than a simple straight line. The probability plot is shown in Figure 1 where the line segments are highlighted with the oval linesa cause and effect relationship exist for each cusp and line segment which must be found and corrected.

Figure 2 shows how WSW is used to fit the data points to the line segments using two methods: 1) Sketch the line by eye to fit the points, and 2) Use an automatic feature of WSW to fit the data to a line segment. The line fit will begin with line segment 1 and moving upward to line segment 5.

For fitting lines to the production data, click on the WSW mixture icon (bottom row, second from the right). Choose process reliability, and select option "E" to add a line to the plot--then choose option "G" to drag a line which will fit the data by eyeball-fit to a straight line of your choice for segment 1. Choose the data point at 99% and drag the line through an eye-ball fit of the three data points at 2 and the single data point at the cusp for 200. When you release the mouse button, you will see the equation for line segment #1 is: b = 0.1676 and h = 1.77822E+14 as valid from ~100% to 99%. You can use the predict feature of WSW to find the X-value = 214 K-Lbs at 1% CDF or 99% reliability. Save these details for later use. If you want to view this line, click on option "V"-if you need to see the data points with large symbols, then click on option "R" and choose "Automatic".

For line segment #2, repeat the selection of option "E" followed by option "G" and drag a line from the 95% value to through the datapoint at 99% for a simple approach to the model-even though the concave nature of this segment does not give a tight representation to the concave data. The equation for line segment #2 is: b = 4.9047 and h = 549.996 as valid from 99% to 95% where X-value = 300 K-Lbs at 95% reliability. Record this data for later use.

For line segment #3, select option "E" followed by option "H" which will give a plot point fit by drawing a box around the data between 95% and 65% as shown in Figure 3. The equation for line segment #3 is: b = 8.9347 and h = 419.688 as valid from 95% to 65% where X-value = 396 K-Lbs at 65% reliability. Record this data for later use.

Click on option "V" for a view of the three line segments. WSW will limit the number of lines on the plot to keep things from getting too messy. Now as we work upward for line segments #4 and #5, the program will drop trend lines as new ones are added. (That's the reason we started modeling from the bottom to the top.)

Since we're getting into the upper reaches of the log scale, it's time to zoom-in for higher resolution. On the main menu, click on the magnifier icon and choose option "F" to lock the ranges to an X-value between 200 and 1200 and a Y-value between 70% and 0.1%. Now return to the mixture icon and process reliability.

For line segment #4, select option "E" followed by option "H" which will give a point plot fit by drawing a box around the data between 65% and 24% and when the "Only Line" dialog box opens, select line "1" as the replacement. The equation for line segment #4 is: b = 1.2328 and h = 773.336 as valid from 65% to 25.5% with X-value = 996 K-Lbs at 25.5% reliability. Record this data for later use.

For line segment #5, select option "E" followed by option "H" which will give a point plot fit by drawing a box around the data between 24% and 0.1% and when the "Only Line" dialog box opens, select line "2" as the replacement. The equation for line segment #5 is: b = 37.1194 and h = 995.812 as valid from 25.5% to ~0%. Record this data for later use. This tells the demonstrated production output of this process and it's just under 1000 K-lbs/day of output and the value displayed in Option "E" will be used for the calculations

Now it's time to draw the nameplate line. The nameplate line will usually (but not always) pass through the largest production quantity. It will have a desired slope determined by the coefficient of variation or by "best of class" performance from benchmark efforts. For this process, the "best of class" line slope is b = 50 and the nameplate line will be drawn thru the largest data point.

For the nameplate line, select option "F" followed by option "H" which will give a point plot fit by drawing a box around the single data point. The program recognizes that if you only select one data point, then you must supply the line slope, b. Supply 50 to the dialog box and when it asks which line you should use for the display, select option "3". Then the nameplate line segment is: b = 50 and h = 1010.26. Record this data for later use.

Notice how close the demonstrated output is to the nameplate capacity. This process is achieving 995.812/1010.26 = 98.6% of rated value, which shows a very small loss of 1.4% at the point estimate for capacity.

The line segments shows four cusps at these reliability levels and production quantities: 25.5% reliability at 996 K-Lbs output, 65% at 396, 95% at 300, and 99% at 214 K-lbs . Click on option "G" of the process reliability menu and enter the data in the order shown by choosing option "F" because we have the values needed for the analysis. (You can also select these cusps from the graph by point and click and WSW will write the data into the dialog box for you.) This information will be used to calculate the reliability losses between the cusps.

Finally, click on the green check mark of the process reliability menu to get the WSW analysis. The results are:

Process Reliability-
Data Set = [#1] Actual Data
Production Line = Eta 995.8110, Beta 37.11943
Nameplate Line = Eta 1010.26, Beta 50

Total Reliability [25.5-100%] Loss = 126416.1 K-Lbs

Process Reliability = 25.5%
25.5 - 65% Difference = 47,643.28 K-Lbs
65% - 95% Difference = 66,275.34 K-Lbs
95% - 99% Difference =   9,927.81 K-lbs
99%-100% Difference =   2,569.65 K-Lbs

Efficiency + Utilization (Production - Nameplate)
Loss = 6551.942 K-lbs

On a Pareto distribution, the total losses are:
126,416.1 = Reliability or 95.1% of the total problem
    6,551.9 = Efficiency + Utilization or 4.9% of the total problem
132,968.0 K-Lbs total loss problem or 133 days of hidden losses at 995.8 K-Lbs/day

Cutting the Pareto distribution into components.
65% - 95% Difference = 66,275. K-Lbs/yr #1 problem or 52.4% of reliability problem
25.5 - 65% Difference = 47,643. K-Lbs/yr #2 problem or 37.7% of reliability problem
95% - 99% Difference =   9,928. K-lbs/yr
99%-100% Difference =   2,570. K-Lbs/yr

This plant has a major reliability problem. The reliability losses are equivalent to 126,483/995.8 = 127 days of lost production at the demonstrated output. The problems are shown in Figure 4.

The number 1 reliability loss occurs during periods of production between 300 and 396 K-Lbs/day and the cause and effect issues associated with these cutback periods must be investigated to find the root cause of the losses.

The number 2 reliability loss occurs during periods of production between 396 and 996 K-Lbs/day. This appears to be the "transition" zone between the "no problem" zone and the "cutback" zone associated with the number 1 reliability problem. However, other cause and effect problems may exist and warrant good root cause analysis investigations.

Assume the gross margin lost by these problems is $0.15/Lb. The cost Pareto problem list shows the money lost problem and the ranking for problem solution:
66,275. K-Lbs/yr = $9,941,250/yr #1 reliability problem
47,643. K-Lbs/yr = $7,146,450/yr #2 reliability problem
  9,928. K-Lbs/yr = $1,489,200/yr #3 reliability problem
  6,552. K-Lbs/yr = $   982,800/yr #4 efficiency and utilization problem
  2,570. K-Lbs/yr = $   385,500/yr #5 reliability problem
                              $19,945,200/yr

WinSMITH Weibull software easily analyzes losses between actual data and the demonstrated production line along with differences between the demonstrated production line and the nameplate line. Unless engineers and production people see graphical evidence of the losses, seldom are the roots of the problem permanently eliminated.

Uses of the line segments will be illustrated in the May '98 problem of the month. The patterns formed by looking at production data as information from a black box is helpful for identifying major problems. Also when major problems have been corrected, this method provides information to show the improvements and savings.

Other pages you may want to visit concerning similar issue are:

       Production Output/Problems

       Six Sigma

       Coefficient of Variation

       Production Reliability Example With Nameplate Ratings

       Key Performance Indicators From Weibull Production Plots

       Process Reliability Plots With Flat Line Slopes

       Process Reliability Line Segments

       Papers On Process Reliability As PDF Files For No-charge Downloads

Comments:

Every plant needs a Pareto distribution of problems measured in money. For this plant, the #1 problem is worth $10 million and the #2 problem is worth $7 million. Everyone needs to attack the hidden factory issues using a priority! Keep plants running to generate gross margins by solving the big problems first.

 Return to the list of problems by clicking here. Return to top of this problem statement clicking here.

Refer to the caveats on the Problem Of The Month Page about the limitations of the following solution. Maybe you have a better idea on how to solve the problem. Maybe you find where I've screwed-up the solution and you can point out my errors as you check my calculations. E-mail your comments, criticism, and corrections to: Paul Barringer by     clicking here.

 Technical tools are only interesting toys for engineers until results are converted into a business solution involving money and time. Complete your analysis with a bottom line which converts $'s and time so you have answers that will interest your management team!

Last revised 4/20/2004
(c) Barringer & Associates, Inc., 1999

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