Andrew Vázsonyi led an interesting life. He collaborated with mathematician Paul Erdös, he was co-founder of The Institute of Management Sciences, and he wrote “Which Door has the Cadillac: Adventures of a Real-Life Mathematician”. Around 1970, Andrew Vázsonyi interviewed for a teaching job in Sauder School of Business, University of British Columbia. During the job interview, he taught us Gozinto Theory.

“Gozinto Matrix (Cacography of ‘goes into’): Matrix with a row for each part and a column for each next assembly and final product. Used to determine which parts (purchased or produced) are most relevant for the production system. This was created by the mathematician Andrew Vazsonyi, who credited as the source a fictitious Italian mathematician Zepartzat Gozinto, which means nothing else than ‘The Part that Goes Into’.” [https://www.allaboutlean.com/lean-glossary/]

If you don’t track parts’ lives by name and serial number, you need parts’ installed base to estimate their field reliability. How many service parts go into your products’ installed base? How old are they?

Apple Computer required the returns of failed parts so that we could try to figure out why they failed. For reliability estimation, I needed to convert Apple’s products’ installed base by age (sales) into parts’ installed base: HDDs, floppy disk drives, power supply, mother board, and other bits. BoMs that told me how many of each part went into each computer sold. With products’ installed base and parts’ returns counts by month, I made nonparametric estimates of all service parts’ field reliability and failure rate functions. I admit that I had to get Apple products’ installed base from industry publications.

Triad Systems Corp. (now www.epicor.com) sold software and computers to aftermarket auto parts stores. Triad collected two years of monthly parts’ sales data by store and zip code using a modem (US patent #5765143!). Triad also sold “catalogs,” which listed which vehicles parts go into and how many by year, make, model, and engine. Triad bought vehicle installed base by zip code from R. L. Polk & Company. I made nonparametric age-specific reliability estimates of auto parts, forecast parts’ demands by store and month, and recommended stock levels for stores’ service levels. If your auto parts store didn’t have the part you needed, it could have been my fault.

Compute Parts’ Installed Base by age

Excel workbook Gozinto.xls contains the following example; get it from  https://sites.google.com/site/fieldreliability/home/files-workbooks-etc/.

Table 1. Next assembly matrix N: products in columns B and C, parts in rows 2-5

Table 2. Product installed base by month shipped (Rows 12-13 in Gozinto.xls) including estimates of their monthly averages, variances, and covariances.

Table 3. Product installed base. Rows contain parts’ installed base by month

For example, part C is used only in product 2, 3 times. Product 2 sold 13 in January, so table 3 shows part C sold 39 in January. For example, part A is required twice for product one and once for product 2. The January demands for product 1 and 2 are 11 and 13 , so the January installed base for part A is 11*2+13*1 = 22+13 = 35.

Table 4. Formulas for table 3 is same in all 8 cells: Excel parentheses {.} and control-shift-enter puts results in appropriate cells.

What is the Distribution of Parts’ installed base?

See the product ships average and variance-covariance matrix in table 2? Those parameter values could have been estimated from past demands, regression,  subjective estimates, or comparable parts. What for?

Would you like to forecast the demand for parts? Expected demand is estimated by the actuarial forecast, SUM[n(s)a(t-s), s=1,2,…,t], where n(s) is the installed base of age s, a(t-s) is the corresponding actuarial failure rate estimate, and t is the period of the forecast.

Would you like to estimate a part’s demand distribution P[SUM[n(s)D(t-s])<=n] for stock level recommendations, fill rates, and service levels? (D(t-s) is the random demand rate for part of age t-s.) A “prediction” or “tolerance limit” on demand is an upper confidence limit on future demand. Table 3 of spreadsheet Gozintos.xls computes the mean and covariance matrix of a part’s demands in table 2 above, so that you could approximate random part installed base distribution with a normal or lognormal distribution.

Would like to estimate a multivariate demand distribution for ordering stocks of related parts simultaneously, for optimal opportunistic maintenance, or for recommending customers who buy part X should also buy part Y? Table 4 of spreadsheet Gozintos.xls asks for proposed stock levels of parts A, B, C, and D to simulate the probability of any stockouts.

References

Andrew Vázsonyi – Wikipedia/

Paul Erdős – Wikipedia