I am please to share that my new 4-part series on semi-repetitive processes will be published by Wiley, expectedly mid-February, 2026.
Once the series is on line, links will be added to this post.
Below, please find abstracts for all four parts of the new series.
Part 1: Engineering Implications of Semi-Repetitive Processes
Abstract: Process predictability may be impaired in two ways — by lack of process information and by lack of process repetitiveness (process is partially repetitive (semi-repetitive) or not repetitive at all). In this four-part series, we address statistical engineering implications of the latter, namely, how lack of complete repetitiveness affects engineering and managerial decisions, required in the analysis and design of semi-repetitive processes and in their management. In this first part, we deliver an overview of the other three parts of the series, addressing statistical engineering questions and problems this series is intended to respond to, and the adaptations needed (relative to repetitive or non-repetitive processes). In particular, we address the dual-component variation of semi-repetitive processes (second part), measuring process repetitiveness (third part) and assessing reliability of process-time predictions, as we move from repetitive to semi-repetitive to non-repetitive processes (fourth part).
Part 2: The Dual-Component Variation of Semi-Repetitive Processes
Abstarct: This is the second of a four-part series on engineering implications of semi-repetitive (SR) processes. In this part, we briefly summarize the “Random Identity Paradigm”, and in compliance with this paradigm make a distinction between two sources of variation affecting SR processes, identity/work-content instability and error. This dual-component variation affects appreciably distributions associated with SR processes. We formulate requirements for models of the dual-component variation and review examples of published models that fulfill these requirements. Adding a new requirement relating to error variation, a new model is partially developed that fulfills this requirement. The link between process repetitiveness and process predictability is addressed as preparation for the third part of this series.
Part 3: Measuring Repetitiveness of Semi-Repetitive Processes
Abstract: This is the third of a four-part series on engineering implications of semi-repetitive processes. In the fourth part, we address how process degree of repetitiveness affects its predictability. Here we explore measuring of process repetitiveness. A measure of the latter had been published, denoted Process Repetitiveness Measure (PRM). It is based on the standardized departure of the mode from the mean and is expressed in terms of the first four moments of the process distribution. Any measure that can be shown to be linearly related to PRM may obviously also serve to measure process repetitiveness. In this article, we explore two additional measures – a probability measure and one based on the coefficient of variation (CV). We show that CV is qualified for this role, having the added benefit of sparing the need to estimate third and fourth moments (known for their large standard errors). CV is appreciated both theoretically, by examining a small sample of arbitrarily selected statistical distributions, and empirically, using a database of surgery durations.
Part 4: Reliability of Process-Time Prediction for Semi-Repetitive Processes
Abstract: This is the fourth of a four-part series on “Engineering Implications of Semi-repetitive Processes”. In Part 3, we have examined and compared several candidate measures to evaluate process repetitiveness, the basis for evaluating predictability of a semi-repetitive process. In particular, we have evaluated the coefficient of variation (CV) and found it to be statistically linearly related to process repetitiveness measure (PRM), which measures process repetitiveness based on the standardized distance of the mode from the mean. In this entry, we employ CV to address how process degree of repetitiveness affects its predictability. More specifically, we formulate for semi-repetitive processes a statistical criterion by which to determine when process-time predictions cease to be acceptable due to insufficient process repetitiveness.
These days we mark anniversary to the assassination of President Kennedy (Nov. 22, 1963).
I was 16 at the time. Half a year after the event, I published an article in an Israeli youth journal, Ma-ariv La-Noar (published June 09 1964). The subject was the significance of having a ruler of a country who is young vs. having an elderly one.
I can add today a third option, I did not conceive of when I composed this essay. Indeed, this is an option pursued by the elderly President Trump: Have an elderly “ruler of a country”; However, let this ruler be surrounded by mostly young talented people!
Indeed, an optimal solution!
I read the original article once again these days (60 years after it was published), and really liked it. So did my close friends whom I have shown this article from days-past.
The article is attached herewith as a PDF file (Hebrew). Feel free to increase fonts as necessary.
In this post/podcast, we read end-time scenarios, as prophesized by Ezekiel (Chapter 38, “Gog and Magog”). This podcast replaces an earlier one with an enhanced audio file.
Following the audio is a YouTube podcast and then the text (Hebrew/English), available for download as a PDF file:
In a previous post, I related to the hidden message of the first chapter of Genesis, namely, that Jehovah/Elohim is not only God of creation, but also ruler of that which has transpired since, namely, God of history (The Hidden Message of the First Chapter of the Bible (Podcast)
Same is also reflected in the first of the Ten Commandments, where Jehovah “introduces” Himself not as ruler of nature, but as ruler of history.
One of the most incredible manifestations of God as ruler of history is revealed in Passover. The beginning of this festivity starts with the Seder (“Order”, as in “orderly row”). But order of what?
As it turns out, seven of the annual Jewish festivities, either declared in Torah, like Kippur, or those added later throughout Jewish history, like Purim, are each linked to a single day of the seven days of Passover. More specifically, each of these Jewish festivities starts on the same day of the week as the corresponding Passover day, to which it is linked.
An intriguing outcome of this finding, regarding Jewish calendar, is that seven specified Jewish festivities will always appear on different (non-overlapping) days of the week. This is an event highly unlikely to occur by random.
The table below displays results for the year 2025, followed by an eye-opening talk, based on classical Jewish sources:
This post displays direct links to all Bible Reads(Audio; Hebrew; Hebrew/English PDF), produced and posted on this Blog and on my personal YouTube channel (Earlier on the list later posted; First Bible read produced November 2024):
In this somber day, when thousands of Israelis line-up the streets and highways of Israel, escorting in their last journey the Bibas family, mother and two toddlers brutally murdered by Hamas while in captivity, I choose to read in their honor Psalm 83. Below the audio is a PDF file with the text (Hebrew/English) and a YouTube link:
In this post/podcast, we read from Torah: The Ten Commandments (Exodus, verses from Chapter 20) and Kedoshim Portion (Leviticus, verses from Chapter 19).
Following the audio is a YouTube podcast, and then the text (Hebrew/English), available for download as a PDF file:
On 25th of January, 2025, Hamas released four Israeli hostages (female soldiers abducted from their beds in a base in southern Israel on October 7th, 2023). The four women were forced to parade in the Palestine-Square of Gaza, to the cheers of a mob of Gazan Arabs, most of them armed, and then led to a raised platform, all smiles, to wave cheerfully to the cheering mob, so that no one has any doubt how much they have enjoyed their 477 days in the captivity of Hamas. Representatives of the Red-Cross were present, witnessing the shameful parade in Gaza, as the hostages were soon to be delivered to these representatives to be re-delivered same day to Israeli IDF.
For me, son to parents whose both families were exterminated in the Holocaust, my first association, as I was witnessing this shameful scene, was the story of the visit of the Red-Cross to Nazi-occupied Jewish Theresienstadt Ghetto
Here is from Wikipedia on the Nazi-occupied Jewish Theresienstadt Ghetto and the Red-Cross visit, June 1944, to the ghetto (referrals to references omitted):
“In February 1944, the SS embarked on a “beautification” (German: Verschönerung) campaign to prepare the ghetto for the Red Cross visit. Many “prominent” prisoners and Danish Jews were re-housed in private, superior quarters. The streets were renamed and cleaned; sham shops and a school were set up; the SS encouraged the prisoners to perform an increasing number of cultural activities, which exceeded that of an ordinary town in peacetime. As part of the preparations, 7,503 people were sent to the family camp at Auschwitz in May; the transports targeted sick, elderly, and disabled people who had no place in the ideal Jewish settlement”.
“In 1944, the ghetto was “beautified” in preparation for a delegation from the International Committee of the Red Cross (ICRC) and the Danish government. The delegation visited on 23 June; ICRC delegate Maurice Rossel wrote a favorable report on the ghetto and claimed that no one was deported from Theresienstadt. In April 1945, another ICRC delegation was allowed to visit the ghetto; despite the contemporaneous liberation of other concentration camps, it continued to repeat Rossel’s erroneous findings.”
In this post/podcast, we read end-time vision similalrly envisaged by prophets Isaiah (Chapter 2, read in full) and Michah (Chapter 4, partially read, verses 1:7).
Following the audio is a YouTube podcast, and then the text (Hebrew/English), available for download as a PDF file:
America (USA) has not allowed Israel to defend itself properly against the vicious raids, launched against her in the south-west part of the county (the west part of the Negev, bordering Gaza). This cost many Israeli lives.
Regrettably, now, a few days before termination of the Biden Administration, America (USA) finds itself unable to defend itself properly against the vicious raids of wildfires, launched against her in the south-west part of the country (California south). Unfortunately, this cost many American lives.
In this post we read end-time scenarios, as prophesized by Malachi (Chapter 3). Enhanced audio is linked, as of March 2025.
Following the audio is two YouTube podcasts (first is a newer one, with enhanced audio), and then the text (Hebrew/English), available for download as a PDF file:
In these agonizing times for the Jewish people, in general, and for Israelis, in particular;
As we are witnessing the nearly-daily ultimate sacrifice of our best;
In these agonizing days, we may draw comfort from the words of the Bible prophets.
In this podcast, Professor Haim Shore reads, in the original Hebrew and in his own voice, words of comfort and visions of brighter future, as conceived and prophesized by the Bible prophets.
Each newly-added episode will appear, within this post, as a single new podcast.
In this first episode we read, in Hebrew, from Isaiah 40 and 41. The read verses appear in a PDF file below.
Episode 1:“Comfort, comfort my people” (Isaiah, 40:1)
Biblical Hebrew assigns names to objects that are meaningful, not merely with respect to their physical properties, but also with regard to their functionality, and ultimately their destination, physically and spiritually.
Comment: A podcast is below the post. See also links to YouTube below.
Biblical Hebrew assigns names to objects that are meaningful, not merely with respect to their physical properties (as my research testifies; Math Unveils the Truth. Evron’s Video), but also with regard to their functionality, and ultimately their destination, physically and spiritually.
In an earlier post (here), we related to the biblical (and modern Hebrew) Gag (גג), meaning roof (read Hebrew right to left). We have demonstrated the gigantic spiritual significance that the Jewish faith attach to Gag, as an epitome for the disconnect between the two worlds, created “in the beginning” (Genesis 1:1):
“In the beginning, God created the heaven and the earth.”
No wonder, therefore, that this combination of a single double letter, גג, comprising the second most rare letter in biblical Hebrew (the most rare is Tet, ט), appears repeatedly in such names as Hagag, Hamman the Agagite, Gog and Magog (find details therein).
In this post, we address another combination of a two-letter Hebrew word, Gal (גל), comprising the third letter in the Hebrew alphabet, Gimel, plus the twelfth letter, Lamed (למד). Probably not accidentally, the name of the latter comprises letters of the Hebrew root, L.M.D, source for various Hebrew words all related to… learning.
This two-letter combination, Gimel and Lamed, surprisingly appears repeatedly in numerous words that seem not to share anything in common. Examples:
The Sin of the Golden Calf (Egel, עגל), the Sin of the Spies (Meraglim,מרגלים ), Exile (Galut, גלות), Redemption (Geula, גאולה), Revelation (Gilui, גלוי), Rolling over (Glila, גלילה), Wave (Gal,גל).
This same combination of letters is also embedded in names of two regions of Eretz Israel — Galilee (Galil, גליל) and Golan (Golan,גולן), the only two regions addressed in an account of the signs of End-times by Raban Gamliel (of first century CE, quoted in Mishna, Masechet Sotta, Ch. 9).
In this post, we explore whether all these words indeed share same rare combination, Gimel+Lamed, by random, or, conversely, perhaps some deeper significance is lurking underneath these seemingly unrelated words. Furthermore, we explore why Gal stands in stark contrast, indeed as the opposite, of what Gag symbolizes, namely, an epitome for the process of revelation (of what?), and of the final establishment of linkage between “the heaven and the earth”.
We start with a basic tenet of the Jewish faith, embedded in biblical Hebrew (as we shall soon see) and in the Hebrew Bible — God exists; However, God is concealed; And it is the task of the Jewish people, throughout the unfolding of Jewish history, to reveal Jehovah to the nations of the world, from the time of receiving the Ten Commandments at Mount Sinai to End-times, with the final redemption, when “…Jehovah dwells in Zion” (Joel 4:21).
This tenet is pervasive throughout biblical Hebrew and the Hebrew Bible. Let us address some examples.
“World” in Hebrew is Olam(עולם), having same three-letter root, A.L.M, from which such words are derived as “unknown” (as in a mathematical equation, Ne-elam, נעלם), Mystery (Ta-aluma, תעלומה) and else.
Question: What does Olam hide?
Answer:Olam is testimony to the concealed existence of Jehovah. And in linking Earth with Heaven, via a historic process carried out in cycles, like waves (גל), the existence of God (currently concealed) is gradually revealed to humankind.
Another three-letter Hebrew root for the hiddenness of God (and also other uses) is S.T.R. From this root such Hebrew words are derived as to hide (Le-Histater), or a concealed spot (Seter, Mistor). In the Bible, prophet Isaiah (45:15) outcries:
“Indeed, you are a hiding God (El Mistater), God of Israel, savior”.
The book of Esther (אסתר), thence, becomes a historic testimony to the truth of the prophet’s outcry, and to its realization: Although Jehovah is not mentioned in Esther, not even once, it is amply clear that the “God of Israel” is “behind the scenes”, saving the Jews from the first ever attempt to inflict Holocaust on the Jewish people.
Similarly, we find in Psalms (89:47):
“Till when, Jehovah, will you hide thyself (Tistater), for ever?…”.
See also Psalms (90:1).
Interestingly, the English word, standing for the story of the unfolding of human affairs throughout the ages is…History (containing the Hebrew root for hiding, S.T.R). Obviously, “history” did not originate in biblical Hebrew.
The first appearance of Gal (גל) in the Bible may be regarded as epitome to the enduring role of the Jewish people throughout the ages.
Jacob, at the command of his father, Isaac, travels to Paddan-Aram to his family-relative, Laban, to look for a wife (Genesis 28:5). Approaching destination, Jacob encounters Rachel, Laban’s daughter who was a shepherdess, reaching the well to water Laban’s flock. Jacob hurriedly rolls over the stone that covered the well’s mouth (Genesis 29:10):
“…and Jacob went near, and rolled (ויגל) the stone from the well’s mouth, and watered the flock…”.
And the Jewish people are tasked, throughout ages of Jewish history, to repeat the same act of Jacob, allowing the nations of the world, over and over again, to “drink” fresh water while the well’s mouth is still covered. This task of the Jewish people started with receiving the Ten Commandments at Mount Sinai, and will end at End-times, when “Jehovah dwells in Zion” (Joel 4:21), hidden no more.
How is Gal connected to all these?
Gal, גל, which originally means wave, is a symbol for the historic development, carried out in cycles (like waves) of exile and redemption, Galut and Geula, first from Egypt, then with the destruction of the First Temple, then with the destruction of the Second Temple. With each wave, ignorance of God (“concealment of God”) is slowly dissolving, knowledge of Jehovah becomes more prevalent, and progress is achieved towards the ultimate outcome (Joel 4:21).
Each and every biblical Hebrew word relating to this historic process, which the Jewish people was tasked to fulfill via the Covenant, is affiliated with Gal (גל). From the exile in Egypt and away from the Promised Land (Galut), to the two sins of the Children of Israel on their way to the promised land (Sin of the Egel; Sin of the Meraglim, which caused a mini-exile of forty years in the Sinai desert), to exiles following the destruction of the two temples, to redemption (Geula, return from exile to Eretz Israel), to the War of Gog and Magog and ultimately to the final outcome, revelation (Hitgalut). Each of these descriptive words of historic processes has embedded within it the rare combination of Gal. And this historic progress is moving us towards the end of Jehovah concealment, the disconnect between heaven and earth, to be replaced by the ever-lasting time of Jehovah’s revelation (Hitgalut, Gilui; Malachi 3:1):
“Behold, I send my messenger, and he shall clear the way before me; and suddenly shall the Lord, whom you seek, come to his temple; and the messenger of the covenant, whom you desire, behold, he shall come, says the Lord of hosts”.
Finally, why Gag (גג) symbolizes disconnect between “Heaven and Earth”, while Gal (גל) represents the opposite?
Simply:
Gag (גג) comprises two identical letters. The physical world (Earth) is all there is. This implies stagnation, stalemate, standstill — no progress, no development, no learning. Transition from the first to second (identical) letter is immaterial. Nothing is changed. The physical world is all there is.
The first letter of Gal (גל) is the same as that of Gag, representing the physical world (Earth). However, the second letter, ל, is different. It is named Lamed (meaning learning), and perhaps expectedly its upper left part is pointing upward, towards Heaven. Gal implies a dynamic process, progressing in waves, connecting heaven and earth, learning of God requirements and moving forward towards the total and general knowledge of Jehovah so that the God of Israel is concealed no more (Isaiah 11:9):
“They shall do no harm nor destroy in all of my holy mountain; for the earth shall be filled with knowledge of Jehovah as the water covers the sea”.
To further learn how Galilee (Galil, גליל) and Golan (Golan,גולן) are part and parcel of End-time scenarios, and therefore part of the historic process leading to “Jehovah dwells in Zion”, view lecture by Rav Ynon Kalazan (Hebrew): Rav Ynon Kalazan on Signs of End-times and Current Events
Galileo Galilei (1564-1642) was an astronomer who, with his observations based on a new telescope that he had invented, helped spread the new Helio-centric world view initiated by Copernicus (to replace the Geo-centric world view that dominated world-view for 1500 years prior; see Wikipedia, Geocentric Model). Galileo was engaged most of his life in learning the cyclic motion of celestial objects, combining his observations with mathematics. It is indeed surprising that Galileo carried a name that implies, in Hebrew, cycles. Galgal in Hebrew is “wheel”, Maagal is “circle”, and Galil in biblical Hebrew means Galilee (a region in Eretz Israel), but also, in biblical Hebrew, something that turns around an axis, like door. In modern Hebrew Galil means “cylinder”. See: Galileo Galilei.
Interestingly, Small-Gematria of Gag and Gal are equal (6). The latter value represents, in Jewish tradition, the physical world (like the six sides of a cube).
My new paper (Why the Mode Departs from the Mean ) has been accepted for publication in Communications in Statistics – Theory and Methods. It is now published (Open Access; Online April, 14, 2024).
One reviewer, in particular, has captured well the significance of the new paper, and its ramifications for Statistics.
How humble Moses presents himself to God, receiving his life-mission which he feels unfit for, and his eventual two important legacies for human civilization:
For millennia, Jewish rabbis, and other scholars of monotheistic faith, have related to the Hebrew-Bible text as mathematical precise (even when this term was obviously not used).
The objective of this podcast is to demonstrate this precision with three examples (of many), where translation is causing the original Hebrew-text meaning to be lost:
Living in the period of the Geo-Centric worldview, a Jewish Rabbi wondered (claimed) that it is the sun that should be named Eretz (Hebrew for Earth). With the later science-based shift towards the Helio-Centric worldview (Sun is “still”, Earth is “running” around it), biblical Hebrew once again proved to describe accurately physical reality:
In this post, we address the relationship between Pi and the only two biblical Hebrew words of Genesis 1:1 relating to the physical world (marked in red), namely: “And the Earth”.
We have written several posts about the relationships between Pi and the first verse of the Bible, as revealed in Oren Evron research work (for example, here1, here2, here3). In this post we add another finding of our own, relating to Gematria values of the seven letters comprising the two words.
As explained and demonstrated elsewhere (here2), there are two types of Gematria values: regular Gematria and small Gematria. The latter is traditionally defined in Jewish scholarship as the sum total of the Gematria values of individual letters comprising the word, with the zeros deleted; for example, the letter Yod (10) is counted as 1, the letter Resh (200) as 2 and so on.
Let us examine small Gematria of the seven letters comprising the two marked words :
First letter: 6 (letter “ו”); Second letter: 1 (letter “א”); Third letter: 4 (letter “ת”, value of 400 in regular Gematria); Fourth letter: 5 (letter “ה”); Fifth letter:1 (letter “א”); Sixth letter: 2 (letter “ר”, value of 200 in regular Gematria); Seventh letter: 9 (letter “ץ”, value of 90 in regular Gematria).
Living in the period of the Geo-Centric worldview, a Jewish Rabbi wondered (claimed) that it is the sun that should be named Eretz (Hebrew for Earth). With the later science-based shift towards the Helio-Centric worldview (Sun is “still”, Earth is “running” around it), biblical Hebrew once again proved to describe accurately physical reality:
The Ten Commandments, in their original biblical Hebrew, are — The Ten Devarim, or Ten Dibrot (the singular of which is Diber); The Holy of Holies, where the tablets with the Ten Commandments were held in the Jewish temple, is — Dvir; A plague is — Dever.
All these share a common root in biblical Hebrew — D.B.R (ד.ב.ר).
Accurate prediction of surgery-duration is key to optimal utilization of operating theatres. Yet, current predictions, based on best available statistical and AI techniques, are highly inaccurate. This causes operating rooms worldwide to operate in a sub-optimal mode. Based on personal experience, supported by recently published three peer-reviewed articles, we believe that the poor state-of-the-art of current predictive methods for surgery-duration is traceable to a single cause. What is it? What is the remedy?
Literature
[1] Shore, H (1986). An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres. J. Statist. Com. Simul. 1986; 23:157-81. Available on Shore’s ResearchGate page.
[2] Shore, H (2020). An explanatory bi-variate model for surgery-duration and its empirical validation, Communications in Statistics: Case Studies, Data Analysis and Applications, 6:2, 142-166, DOI: 10.1080/23737484.2020.1740066 .
[3] Shore, H (2021a). SPC scheme to monitor surgery-duration. Qual Reliab Eng Int. 37: 1561– 1577. DOI: 10.1002/qre.2813 .
[4] Shore, H (2021b). Estimating operating room utilisation rate for differently distributed surgery times. International Journal of Production Research. DOI: 10.1080/00207543.2021.2009141
A magnifying glass directed at the fundamental transformation that the Israeli society is going through, shifting personal responsibility, mandated by free-will, to the responsibility of court of law:
Israelite prophets, whose prophecies are everywhere in the Jewish Bible, right left and center, explicitly stated that God, the creator of “The Heaven and The Earth”, had spoken to them.
One-way flow of Information is characteristic to black holes. However, it also forms the basic human condition, regarding communicating with “the other side”. Is this similarity coincidental?
Jewish Kosher laws, seemingly arbitrary and devoid of any possible rational justification, in fact are based on a very deep principle of how we should conduct our lives to maintain health, spiritually and physically.
The detailed answer, based on the Jewish Hebrew Bible (Torah, the prophets), on in-dept analysis of biblical Hebrew words and traditional Jewish interpreters — may surprise you:
The answer to this intriguing question may surprise you. The true meaning of the Eighth Commandment, according to traditional Jewish scholarship, is not what it appears to be.
So where prohibition on stealing, in the common sense of the word, does appear in the Ten Commandments?
Talk of Avinoam Ben-Mordechai with Haim Shore (originally published, August 6, 2020; Produced by Avinoam Ben-Mordechai; Episode 2 of 2; Published with permission):
Haim Shore Blog 