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enBenchmarking and the Absolute Benchmarking Process Efficiency Ratio
http://www.leanmath.com/blog-entry/benchmarking-and-absolute-benchmarking-process-efficiency-ratio
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Neil always used to confound and shock me. He was always pursuing perfection. And I would always retort something like, “But, the real world isn’t perfect.”</p>
<p>Over the years, I slowly realized the value and wisdom of Neil’s mindset. It is consistent with traditional lean thinking (as long as it does not paralyze the PDCA cycle), and it helps drive innovation and the right thought process. I have found that lean thinkers not only benchmark themselves against the competition, they also benchmark themselves against perfection. This is where math can help.</p>
<p>In order to truly benchmark ourselves against perfection, one can use the absolute benchmarking process efficiency (ABPE) ratio. Where:</p>
<p>ABPE = 100% * (Minimum effort required to complete task)/(Actual effort required to complete task)</p>
<p>Using the example of an insurance company executing a policy renewal, the minimum effort represents the effort required to change a few bits in computer memory that indicate the policy is renewed. The actual effort required is the time invested contacting the insurer, recording their information in a log, having the staff type the info into a risk analysis tool, reviewing the results, and mailing the customer their new policy.</p>
<p>In manufacturing, the minimum effort required to make a plastic bottle using injection molding is the effort required to inject plastic into a mold and to extract the bottle from the mold. The actual effort is the effort to inject plastic into a mold, plus all the effort required to eliminate voids, all the effort that goes into the defective bottles that were made when the machine started up, all the effort to recycle those defects, and all the effort that goes into normal yield loss.</p>
<p>In health care, the ABPE ratio can be used to look at activities like administering flu shots. Ultimately, the goal is to deliver a vaccine, so the minimum amount of effort is the effort required to deliver the vaccine. (Admittedly, there is some record keeping that needs to be done as well.) Whereas the actual effort includes the effort to produce the flu shot availability campaign, setup and reconfigure the space, deliver the flu shots, etc, etc, etc.</p>
<p>Example: Logging onto my computer</p>
<p>My login process is a follows:</p>
<ol><li>Open laptop.</li>
<li>Press the on button.</li>
<li>Wait for machine to boot up.</li>
<li>Type in password.</li>
<li>Wait for password to be verified.</li>
<li>Wait for laptop to load applications.</li>
</ol><p>The entire process takes about 150 seconds.</p>
<p>Estimating how long it should take ideally is where it gets interesting. One could easily imagine that the ideal situation is one in which I open my laptop, it uses facial recognition to authenticate who I am, and it is ready to use. Maybe it will take awhile to get there, so as a conservative estimate of the ideal state, let’s use my smartphone as a benchmark.</p>
<p>The smartphone login process is:</p>
<ol><li>Press the home button.</li>
<li>Swipe the home screen.</li>
<li>Enter password.</li>
</ol><p>The entire process takes approximately 7 seconds. In which case the ABPE ratio is:</p>
<p>ABPE = 100% * (7 s / 150 s) = 5%</p>
<p>Clearly, there is a huge efficiency opportunity! And now I understand why I get so frustrated every time that I log into my laptop.</p>
<p>Tips:</p>
<ol><li>Be certain to use the same units of measure in the numerator and the denominator. Often times dollars are a convenient choice. Simply convert lost time to dollars. Defects to dollars. And don’t forget that overhead costs will already be in dollars.</li>
<li>Use the broadest scope possible. In the insurance renewal example discussed above, if one limits their scope to typing the log info into a risk analysis tool, their calculation of the ABPE ratio would stipulate that the log file is the starting point. But, from an absolute efficiency standpoint, the log file doesn’t have to be created. The information could be directly entered into the risk tool, eliminating the need for the log file altogether. Limiting the scope can make the ABPE ratio artificially high.</li>
<li>Challenge the start and end states. For example, if you are a high-volume gear manufacturer and the machining process starts with a solid piece of metal, ask yourself: could you start with a block of metal that has a hole in it so you don’t have to drill a hole every time? Or could you change the end state, so the gear is put into reusable packaging instead of disposable packaging? Or could packaging be eliminated altogether?</li>
</ol><p>Notes:</p>
<p>The Absolute Benchmarking Process Efficiency (ABPE) ratio is similar to Process Cycle Efficiency which is the ratio of the processing times (on the critical path of a value stream) to the total lead time for the value stream. The difference is that Process Cycle Efficiency essentially looks at the time to produce something versus the lead time, whereas ABPE measures how efficient a value stream is in absolute terms, and by doing so deeply challenges the production process. Not only does it ask the question: Can we do the process quicker? But it also asks the question: Can we do the process using fewer resources? Using less energy? Using less space? Etc.</p>
<p> </p>
</div></div></div>Mon, 05 Jun 2017 22:56:42 +0000drmike166 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/benchmarking-and-absolute-benchmarking-process-efficiency-ratio#commentsNew Book, New Look, and New Content
http://www.leanmath.com/blog-entry/new-book-new-look-and-new-content
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p><img style="float: right; width: 137px; height: 183px;" class="media-element file-default" data-delta="1" alt="" title="" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/Lean%20Math%20Cover_0.gif" width="216" height="288" /><strong>New Book.</strong> A handful of weeks ago, SME published our new book, <a href="http://leanmath.com/product/lean-math"><em>Lean Math: Figuring to Improve</em></a>. It is, and was, undoubtedly a labor of love…or at least the 444-page labor of Dr. Mike (aka Michael O’Connor) and me. I invite you to download a free chapter (see the sidebar on the right), along with the accompanying cover, pre-pages and four example math entries to get insight into the book’s purpose, approach, and content and what other lean practitioners think about the work.</p>
<p>My original vision for the book was one of relatively low effort for me (I was worn out after writing the <a href="http://leanmath.com/product/kaizen-event-fieldbook"><em>Kaizen Event Fieldbook</em></a>) and one of high utility for all those lean practitioners who had something better to do than constantly re-invent or re-research the lean math wheel every time they had to size a kanban. It sounded like a perfect combination!</p>
<p>Of course, the low effort notion was TOTALLY misguided. Lean actually requires a ton of math. The more I dwelled on the lean mathematical landscape, the more it seemed to expand. Eventually, I decided I needed a co-author because, frankly, the scope was too darn big AND I needed someone a lot smarter than me to write all of that hard six sigma stuff. And then there’s the need for precision, imagine that(!) …and the use of realistic examples.</p>
<p>There were times that Dr. Mike and I were sure we knew how Napoleon felt during his disastrous invasion of Russia during 1812. As in, this is a really, really, bad idea and we’ll be lucky if some of us, any of us, ever get back home.</p>
<p>Anyway, eventually we, including our publisher, SME, thought it would be a good idea to stop writing (that’s why Lean Math is ONLY 444 pages) even though there are certainly other areas to explore. We sincerely think that this work will help you on your lean journey. Please, as previously mentioned, download the free chapter et al and decide for yourself.</p>
<p><strong>New Look.</strong> One thing that you may notice is that this website has a brand new look! We’ve revamped the menu, graphics, and offerings. We hope that you will agree that the changes are an improvement to the user experience. This leads us to the promise of…</p>
<p><strong>New Content.</strong> What good is a new look without new content? So, here’s a promise from us that we’ll be getting fresh content on this site with some regularity. This also includes expanding our inventory of <a href="http://leanmath.com/basic-page/lean-math-templates">free templates</a>.</p>
<p>We sincerely hope that we can continue to make Lean Math a useful destination for the lean practitioner.</p>
</div></div></div>Thu, 01 Jun 2017 12:31:22 +0000markrhamel165 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/new-book-new-look-and-new-content#commentsInventory Record Accuracy
http://www.leanmath.com/blog-entry/inventory-record-accuracy
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p>How you measure Inventory Accuracy depends on where you stand.</p>
<table><tbody><tr><td>SKU</td>
<td>Value</td>
<td>Book</td>
<td>Actual</td>
<td>Adjustment</td>
<td>$$$</td>
</tr><tr><td>29907</td>
<td>$1.00</td>
<td>100</td>
<td>95</td>
<td>-5 (5%)</td>
<td> -$5.00</td>
</tr><tr><td>15302</td>
<td>$2.50</td>
<td>170</td>
<td>175</td>
<td>+5 (2.94%</td>
<td>+$12.50</td>
</tr><tr><td>JSD35</td>
<td>$0.75</td>
<td>800</td>
<td>790</td>
<td>-10 (1.25%)</td>
<td> -$7.50</td>
</tr><tr><td>Total</td>
<td> </td>
<td>1070</td>
<td>1060</td>
<td>-10 (0.93%)</td>
<td> $0.00</td>
</tr></tbody></table><p>Financial Adjustment Accuracy... 100% accurate, no balance sheet write off. Planning Accuracy (with 3% tolerance) .... = 2/3 = 67% accurate. Inventory Record Accuracy... = 0% accurate, all inventory records were wrong. %IRA = (number of correct inventory records)/(total number of inventory records checked)*100</p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/tags/inventory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Inventory</a></div></div></div>Sat, 22 Aug 2015 00:09:10 +0000lloucka126 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/inventory-record-accuracy#commentsProduct Family Analysis
http://www.leanmath.com/blog-entry/product-family-analysis
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Value stream analysis is conducted typically for one specific product or service family at a time. In order to identify and distinguish families, lean practitioners use what is called a product family analysis matrix (a.k.a. product quantity process matrix (PQPr)). Many times the families can be easily discerned once the matrix is populated, other times, it is more difficult. The application of a dendogram or binary sort, can be helpful in these situations. Value stream analysis and, with it, flow kaizen, is central to any lean transformation and is specific to product or service families. This means typically one map set, both current and future state, per family. Clearly, it is important that the lean practitioner properly identify and discriminate between families before beginning any value stream mapping effort. Families are represented by products or services that share, more or less, the same common processing steps. The product family analysis matrix, also known as a product family matrix, process routing matrix or product-quantity-process (PQPr) matrix is a common tool for product family identification. At their most basic levels, the matrices reflect the product or process offerings on the y-axis and the process steps on the upper x-axis (<b>Figure 1</b>). The intersection between the x’s and y’s is indicated by an “x” or checkmark, a zero or one, or the frequency/quantity (i.e., the products annual volume through a given process). The intersections, or “clusters,” represent product family candidates. <a href="/sites/lean-math/files/blog/wp-content/uploads/2013/02/PQPr-Matrix.png"><img alt="PQPr Matrix" height="553" width="719" class="media-image alignnone size-full wp-image-380 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/blog/wp-content/uploads/2013/02/PQPr-Matrix.png" /></a> There are three methods of identifying product clusters – sorting by inspection; cluster identification using dendrograms; and binary sorting. We'll cover these topics in future postings. </p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/tags/systems" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Systems</a></div></div></div>Thu, 30 Apr 2015 22:54:50 +0000drmike112 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/product-family-analysis#commentsTaichii Ohno
http://www.leanmath.com/blog-entry/taichii-ohno
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p><a href="/sites/lean-math/files/blog/wp-content/uploads/2013/07/Taiichi-Ohno.jpg"><img alt="Taiichi-Ohno" style="width: 300px; height: 225px; float: left; margin-right: 1em;" class="media-image alignleft size-medium wp-image-734 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2013/07/Taiichi-Ohno-300x225.jpg" width="300" height="225" /></a>Born February 29, 1912, Taichii Ohno envisioned a way of working that would evolve into the Toyota Production System (TPS), now known widely as Lean. Several key elements of TPS include <em>takt</em> (interval or pace of customer demand), <em>muda</em> (the elimination of waste), <em>jidoka</em> (the injection of quality) and <em>kanban</em> (the cards used as part of a system of just-in-time stock control). Ohno was born in Dalian, in eastern China, he joined Toyota Automatic Loom Works in 1932. In 1943 Ohno switched to work as a production engineer for the Toyota car company, at a time when its productivity was far below that of America's mighty Detroit car industry. In 1956, Ohno visited US automobile plants, but his most important discovery was the supermarket, something unknown in Japan at the time. He marveled at the way customers chose exactly what they wanted and in the quantities that they wanted, and the way that supermarkets supplied merchandise in a simple, efficient, and timely manner. He took these observations back and incorporated then in further enhancements to the TPS kanban system. [<a href="http://www.toyotageorgetown.com/history.asp" target="_blank">1</a>] History of Toyota Motor Manufacturing Kentucky (TMMK) [<a href="http://www.economist.com/node/13941150" target="_blank">2</a>] Guru: Taiichi Ohno, in The Economist, July 3, 2009.</p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/tags/thoughts" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Thoughts</a></div></div></div>Mon, 02 Mar 2015 04:54:23 +0000lloucka113 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/taichii-ohno#commentsCombinations and Permutations. Count the Ways.
http://www.leanmath.com/blog-entry/combinations-and-permutations-count-ways
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p><strong>Combinations and Permutations</strong> How many different poker hands are there? How many different pizza orders can be made? How many different ways can this work schedule be filled out? How many different ways are there to arrange your books in a bookshelf? These are all examples of combinations and permutations. And knowing how to calculate them is a helpful tool for decision making. The basic equations are: . <a href="/sites/lean-math/files/blog/wp-content/uploads/2015/01/Combination1a.jpg"><img alt="Combination1a" height="224" width="472" class="media-image alignnone wp-image-1275 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2015/01/Combination1a-300x139.jpg" /></a> <strong>Permutations (with repetitions)</strong> <strong>Example:</strong> How many different ways can this work schedule be filled out? This is very straightforward. Suppose there are three operators (i.e. <em>n</em> equals 3) who have to cover of two shifts (i.e. <em>r</em> equals 2), then 9 possible work schedules that can be created. </p>
<table><tbody><tr><td width="25"> </td>
<td width="164"><strong>Shift 1</strong></td>
<td width="213"><strong>Shift 2</strong></td>
</tr><tr><td width="25">1</td>
<td width="164">A</td>
<td width="213">A</td>
</tr><tr><td width="25">2</td>
<td width="164">A</td>
<td width="213">B</td>
</tr><tr><td width="25">3</td>
<td width="164">A</td>
<td width="213">C</td>
</tr><tr><td width="25">4</td>
<td width="164">B</td>
<td width="213">A</td>
</tr><tr><td width="25">5</td>
<td width="164">B</td>
<td width="213">B</td>
</tr><tr><td width="25">6</td>
<td width="164">B</td>
<td width="213">C</td>
</tr><tr><td width="25">7</td>
<td width="164">C</td>
<td width="213">A</td>
</tr><tr><td width="25">8</td>
<td width="164">C</td>
<td width="213">B</td>
</tr><tr><td width="25">9</td>
<td width="164">C</td>
<td width="213">C</td>
</tr></tbody></table><p> The number of permutations is simply: <a href="/sites/lean-math/files/blog/wp-content/uploads/2015/01/Combination2.jpg"><img alt="Combination2" height="127" width="431" class="media-image alignnone wp-image-1276 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2015/01/Combination2-300x80.jpg" /></a> <strong>Permutations (without repetitions) </strong><strong> </strong> <strong>Example:</strong> How many different ways are there to arrange your books in a bookshelf, if you have 3 books (called A, B, and C)? Again this is a straightforward question. it is easy to quickly determine that the correct answer is 6. For the first book, there are three choices, for the second there are only two choices and only one choice for the last choice. So the total number of permutations in this case is This simple example gives insight into constructing the equation for the general case. For the first choice there are options, for the second choice there are options, and this process repeats times. This can be written as: <a href="/sites/lean-math/files/blog/wp-content/uploads/2015/01/Combination3.jpg"><img alt="Combination3" height="98" width="453" class="media-image alignnone wp-image-1274 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2015/01/Combination3-300x58.jpg" /></a> <a href="/sites/lean-math/files/blog/wp-content/uploads/2015/01/Combinations4.jpg"><img alt="Combinations4" height="302" width="447" class="media-image alignnone wp-image-1277 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2015/01/Combinations4-300x199.jpg" /></a> <strong>Combinations (with repetitions)</strong> <strong>Example:</strong> How many different pizzas can be made? Assuming that are n different kinds of pizza and you are ordering r pizzas. <a href="/sites/lean-math/files/blog/wp-content/uploads/2015/01/Combinations5.jpg"><img alt="Combinations5" height="199" width="485" class="media-image alignnone wp-image-1278 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2015/01/Combinations5-300x116.jpg" /></a> </p>
<table><tbody><tr><td colspan="2" width="253"><b>The six pizza orders (pizza pies come in flavors A, B, or C) that can be made with two pies are:</b></td>
</tr><tr><td width="128">A</td>
<td width="125">A</td>
</tr><tr><td width="128">A</td>
<td width="125">B</td>
</tr><tr><td width="128">A</td>
<td width="125">C</td>
</tr><tr><td width="128">B</td>
<td width="125">B</td>
</tr><tr><td width="128">B</td>
<td width="125">C</td>
</tr><tr><td width="128">C</td>
<td width="125">C</td>
</tr></tbody></table><p><strong>Combinations (without repetitions)</strong> <strong>Example:</strong> How many different poker hands are there? Here the relevant equation is: <a href="/sites/lean-math/files/blog/wp-content/uploads/2015/01/Combinations6.jpg"><img alt="Combinations6" height="238" width="485" class="media-image alignnone wp-image-1279 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2015/01/Combinations6-300x141.jpg" /></a> </p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/tags/basic-math" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Basic Math</a></div></div></div>Wed, 04 Feb 2015 20:42:47 +0000drmike125 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/combinations-and-permutations-count-ways#commentsPitch Interval for Same Pitch Products
http://www.leanmath.com/blog-entry/pitch-interval-same-pitch-products
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Pitch interval (<em>I<sub>p</sub></em>) can be thought of in two ways: 1) as a unit of time representing the (usually) smallest common pitch shared among a range of products, services, or transactions that are being produced, conveyed, performed, or executed by a given resource(s), and 2) as a count of the number of intervals of a common pitch over a period of time, typically a shift or day. <em>I<sub>p</sub></em> often serves as the time intervals reflected in the typical design of heijunka, leveling, or scheduling boxes or boards in which instruction or withdrawal kanban are loaded within the heijunka sequence (as accommodated by actual demand). Figure 1 captures the<em> I<sub>p</sub></em> math. This post is specific to products that share the same pitch. A future post will address <em>I<sub>p</sub></em> for products that have different pitches. Figure 2 provides some insight into heijunka box design and loading in the context of <em>I<sub>p</sub></em>.</p>
<div style="width: 1325px;display:block;margin:0 auto;"><a href="/sites/lean-math/files/blog/wp-content/uploads/2014/12/pitch-interval-fig-11.png"><img alt="Figure 1. Pitch interval formula tree" height="587" width="938" class="media-image size-full wp-image-1260 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/12/pitch-interval-fig-11.png" /></a> Figure 1. Pitch interval formula tree
<p> </p>
</div>
<p><strong>Where:</strong> <em>T<sub>a</sub></em> = available time for the period, typically a shift or day and expressed in seconds or minutes <em>P</em> = pitch for the resource(s) related to <em>T<sub>a</sub></em> and expressed in the same unit of time. GCD notation represents the greatest common divisor, also known as greatest common factor or highest common factor, for a given set (<em>a, b</em>…) <em>P<sub>n</sub></em> = each non-equal pitch amongst the various products for the resource(s) related to <em>T<sub>a</sub></em> and expressed in the same unit of time. <strong>Same Pitch Example:</strong> There are three products (A, B, and C), all of which share the same 20 minute pitch. See table below for the pitch calculation.</p>
<div style="width: 811px;display:block;margin:0 auto;"><a href="/sites/lean-math/files/blog/wp-content/uploads/2014/12/pitch-interval-table-1.png"><img alt="Table 1. Pitch calculation" height="596" width="801" class="media-image size-full wp-image-1259 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/12/pitch-interval-table-1.png" /></a> Table 1. Pitch calculation
<p> </p>
</div>
<p><a href="/sites/lean-math/files/blog/wp-content/uploads/2014/12/pitch-interval-3.png"><img alt="pitch interval 3" height="64" width="414" class="media-image aligncenter size-full wp-image-1261 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/12/pitch-interval-3.png" /></a>See Figure 2 for example heijunka box as loaded in an ABACABACAB sequence (a.k.a. heijunka cycle).</p>
<div style="width: 1370px;display:block;margin:0 auto;"><a href="/sites/lean-math/files/blog/wp-content/uploads/2014/12/pitch-interval-fig-2.png"><img alt="Figure 2. Heijunka box reflecting 20 minute intervals" height="536" width="1113" class="media-image wp-image-1262 size-full media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/12/pitch-interval-fig-2.png" /></a> Figure 2. Heijunka box reflecting 20 minute intervals.
<p> </p>
</div>
<p><strong>Remember, life is messy</strong>…and sometimes the math is too. The lean practitioner often needs to use his or her judgment when determining whether or not to round and how to round (up or down). Unfortunately, math rarely comes out perfect (as it magically does in most lean books). When addressing things like pitch intervals, know that rounding has practical implications. For example, rounding up the number of pitch intervals may require either the shortening of the pitch (remember <em>I<sub>p</sub></em> x <em>P</em> should closely approximate <em>T<sub>a</sub></em>) equally across all or some intervals. In the example above, by rounding up to 21 intervals, we are artificially speeding up takt time by two seconds per unit, and thus our pitch by 20 seconds. The cumulative effect is that the last pitch interval of the day actually finishes up 5 minutes early. The lean practitioner has some options here: 1) don’t sweat it and do nothing about the 5 minutes early thing, 2) use a 21 minute pitch after every third interval, or 3) tinker with something else. As you may discern from Figure 2, we think option one is fine. Know that the road to figuring out the best option often requires a good bit of PDCA. <strong>Related posts:</strong> <a href="http://leanmath.com/blog/2013/01/28/available-time-ta-andtar/">Available Time</a>, <a href="http://leanmath.com/blog/2013/12/11/heijunka-cycle/">Heijunka Cycle</a></p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/tags/time" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Time</a></div></div></div>Fri, 19 Dec 2014 20:51:03 +0000markrhamel124 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/pitch-interval-same-pitch-products#commentsHow bad could it be? - Risk Priority Numbers
http://www.leanmath.com/blog-entry/how-bad-could-it-be-risk-priority-numbers
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p style="text-align: left">Life happens. Sometimes it rains on wedding days. Sometimes a supplier misses a ship date, and sometimes there are glitches in our processes. The challenge for lean practitioners is what to do about this – especially since all of these things could happen.</p>
<p style="text-align: left"> One good answer is to constuct a Failure Modes and Effect Analysis (FMEA). This can be done for a process, or a new or existing product. The basic concept is to identify all of the potential failure modes and then rank them according to risk. Risk Priority Numbers (RPNs) are used to assess the risk of each failure mode.</p>
<p style="text-align: left"> A Risk Priority Number (RPN) is calculated as follows:</p>
<p style="text-align: left"> <a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/RPN-equation.jpg"><img alt="RPN equation" height="21" width="290" class="media-image alignnone size-full wp-image-1245 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/RPN-equation.jpg" /></a></p>
<p style="text-align: left"> That is, the risk associated with any failure mode is comprised of three parts:</p>
<ul style="text-align: left"><li>Severity – The more severe the failure mode, the higher the risk.</li>
<li>Likelihood – The more likely the failure mode, the higher the risk.</li>
<li>Detectability – The harder it is to detect and control the causes and conditions of a given failure mode, the higher the risk.</li>
</ul><p style="text-align: left"> Usually each of these factors is graded on a 0 to 10 scale. For Severity and Likelihood, the more severe the consequences or the more likely the failure mode is to occur, the higher the score. With Detectability, the harder the cause is to detect and control, the higher the score.</p>
<p style="text-align: left"> Once Risk Priority numbers have been established for all of the failure modes, the next step is to develop a risk mitigation strategy for the high risk items. That way these risks can be addressed proactively. The risk mitigation strategies are given a predictive Risk Priority Number (pRPN) which estimates what the risk priority number will be once the risk mitigation strategy has been put in place. These risk priority numbers can be helpful for identifying which risk mitigation strategies to implement first.</p>
<p style="text-align: left"> <a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/FMEA-pix.jpg"><img alt="FMEA pix" height="375" width="461" class="media-image alignnone wp-image-1244 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/FMEA-pix-300x243.jpg" /></a></p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/tags/thoughts" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Thoughts</a></div></div></div>Thu, 27 Nov 2014 19:52:07 +0000drmike123 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/how-bad-could-it-be-risk-priority-numbers#commentsCpk and the Mystery of Estimated Standard Deviation [guest post]
http://www.leanmath.com/blog-entry/cpk-and-mystery-estimated-standard-deviation-guest-post
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p>It all started when my colleague and I noted that we had used the same data to calculate <em>Cpk</em>, but ended up with different results. This led us down an Alice in Wonderland-like path of Google searching, Wikipedia reading, and blogosphere scanning. After several days of investigation, we determined that there was no consensus on how to properly calculate estimated standard deviation. Knowing that there must be a misunderstanding and that this should be purely an effort based on science, we decided to get to the bottom of this. My colleague and I decided that there was a need for a simple, accurate tool that anyone could use and afford. We wanted to break the economic and educational barriers that got in the way of conducting needed process capability studies. More on that in a bit. Our investigation revealed that the biggest confusion out there was with the following two symbols. <a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/levi1.png"><img alt="levi1" height="89" width="193" class="media-image aligncenter size-full wp-image-1222 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/levi1.png" /></a>Or, regular sample standard deviation vs. estimated standard deviation (sporting that little hat over the sigma). Regular sample standard deviation is used to calculate process performance, or<em> Pp/Ppk</em>. It is based on the actual data that your process has actually proven to perform in current reality (overall performance). Estimated standard deviation is used to calculate process capability, or <em>Cp/Cpk</em>. In other words, what is your process capable of when at its current “best” state (within subgroups)? This leads us to the simple tool that I referenced above.</p>
<h1>There’s an App for that</h1>
<p>The creation of “<em>Cpk</em> Calculator App” has been a long and winding road with a lot of research and validation (also known as PDCA). But, in the end we created a tool that automatically calculates standard deviation in 1 of 3 ways depending on data set characteristics (The biggest dilemma on the web):</p>
<p style="padding-left: 30px;">1. If data is in one large group, we use the regular sample standard deviation calculation:</p>
<p style="padding-left: 30px;"><a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/levi2.png"><img alt="levi2" height="118" width="227" class="media-image aligncenter wp-image-1223 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/levi2.png" /></a>Many people use the calculation above to calculate standard deviation and call it <em>Cpk</em>, when in reality what they are calculating is <em>Pp</em>, or <em>Ppk</em> as they are not using estimated standard deviation. <em>Ppk</em> is definitely the more conservative of the two as it’s based on the actual standard deviation, but for whatever reason <em>Cpk</em> has become the more famous of the two.</p>
<p style="padding-left: 30px;">And, they are often confused.</p>
<p style="padding-left: 30px;">2/3. If you collect your data in subgroups, there are two preferred methods of estimating standard deviation using unbiasing constants:</p>
<p style="padding-left: 30px;"><a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/levi3.png"><img alt="levi3" height="83" width="493" class="media-image aligncenter size-full wp-image-1224 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/levi3.png" /></a></p>
<p style="padding-left: 30px;"><em>R</em>bar / <em>d</em>2 is used to estimate standard deviation when subgroup size is at least two, but not more than four. The average of the subgroup ranges is divided by the <em>d</em>2 constant. This calculation is best when you tend to have many small sub groups of data.</p>
<p style="padding-left: 30px;"><a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/levi4.png"><img alt="levi4" height="239" width="241" class="media-image aligncenter size-full wp-image-1225 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/levi4.png" /></a>The calculations shown above reflect another way to estimate standard deviation that should be used when calculating estimated standard deviation of uneven sub groups, or sub groups larger than 4 data points.</p>
<p>
<video class="media-image media-element file-media-large" controls="controls" data-fid="182" data-media-element="1" height="360" width="480"><source src="http://www.youtube.com/watch?v=kpg_Havl8Qc" type="video/youtube"></source></video><br />
Please see these links for the <em>Cpk</em> Calculator App on <a href="https://play.google.com/store/apps/details?id=com.admapps.cpkcalculator">Google Play</a> (for Android) and the <a href="https://itunes.apple.com/us/app/cpkcalculator/id913749703?mt=8">Apple App Store</a>.</p>
<h1>More about <em>Cp</em>, <em>Cpk</em> vs.<em> Pp</em>,<em> Ppk</em></h1>
<p><em>Pp</em>, and <em>Ppk</em> are based on actual, “overall” performance regardless of how the data is subgrouped, and use the normal standard deviation calculation of all data (n-1). <em>Cp</em> and <em>Cpk</em> are based on variation within subgroups, and use estimated standard deviation. <em>Cp</em> and <em>Cpk</em> show statistical capability based on multiple subgroups. Without getting into too much detail on the difference in calculations, think of the estimated standard deviation as the average of all of the subgroup’s standard deviations, and ‘regular’ standard deviation as the standard deviation of all data collected. <strong><em>Cp</em> (process capability)</strong>. The amount of variation that you have versus how much variation you’re allowed based on statistical capability. It doesn’t tell you how close you are to the center, but it tells you the range of variation. Note that nowhere in this formula is the average of your actual data referenced. <a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/levi5.png"><img alt="levi5" height="91" width="241" class="media-image aligncenter size-full wp-image-1226 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/levi5.png" /></a><strong><em>Cpk</em> (process capability index).</strong> Tells you how centered your process capability range is in relation to your specification limits. This only accounts for variation within subgroups and does not account for differences between sub groups. <em>Cpk</em> is “potential” capability because it presumes that there is no variation between subgroups (how good you are when you’re at you best). When your <em>Cpk</em> and <em>Ppk</em> are the same, it shows that your process is in statistical control. <a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/levi6.png"><img alt="levi6" height="519" width="807" class="media-image aligncenter size-full wp-image-1227 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/levi6.png" /></a><strong><em>Pp</em> (process performance).</strong> The amount of variation that you have versus how much variation you’re allowed based on actual performance. It doesn’t tell you how close you are to the center, but it tells you the range of variation. <a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/levi7.png"><img alt="levi7" height="91" width="253" class="media-image aligncenter size-full wp-image-1228 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/levi7.png" /></a><strong><em>Ppk</em> (process performance index).</strong> <em>Ppk</em> indicates how centered your process performance range is in relation to your specification limits (how good are you performing currently). <a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/levi8.png"><img alt="levi8" height="135" width="372" class="media-image aligncenter size-full wp-image-1229 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/levi8.png" /></a></p>
<h1>What’s a "Good"<em> Cpk</em>?</h1>
<p>A <em>Cpk</em> of 1.00 will produce a 0.27% fail rate, or a theoretical 2,700 defects per million parts produced. A <em>Cpk</em> of 1.33 will produce a 0.01% fail rate, or a theoretical 100 defects per million parts produced. In reality, the <em>Cpk</em> that is acceptable depends on your particular industry standard. As a rule of thumb a <em>Cpk</em> of 1.33 is traditionally considered a minimum standard.</p>
<h1>Confidence Interval</h1>
<p>Confidence interval shows the statistical range of your capability (<em>Cpk</em>) based on sample size. Basically the larger the sample size, the tighter the range. The confidence interval shows that there is an x% confidence that your capability is within “a” and “b.” The higher the confidence interval, the wider the range. For example, if we report a <em>Cpk</em> of 1.26, what we are really saying is something like, “I don’t know the true <em>Cpk</em>, but based on a sample of n=145, I am 95% confident that it is between 1.10, and 1.41 <em>Cpk</em>.” This tells us that the larger your sample size, the tighter the range. Therefore, the more data you collect, the more accurate your measurement, and the more accurate your actual process capability, or performance. In most calculations 90 or 95% confidence is required, but confidence interval can be calculated at any %, just remember the fewer data points, the wider the confidence interval range. <a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/levi9.png"><img alt="levi9" height="86" width="564" class="media-image aligncenter size-full wp-image-1230 media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/levi9.png" /></a></p>
<h1>Real Life Application</h1>
<p>During the creation and testing of the <em>Cpk</em> Calculator App, we had the opportunity to test every scenario that we encountered in the real world. One of the real life scenarios that we ran into included a routine hourly check of a “widget’s” thickness that determined that the part was out of specification. After 15 minutes of data collection and testing on the floor using the app, we found that our process that normally had a <em>Cpk</em> of 1.3, now reflected a <em>Cpk</em> of 0.80. This led us to discover that the cutting machine cycle time had been reduced in an attempt to improve throughput and productivity by the machine operator. With that in mind, we reset the machine to original settings to confirm that we had found the root cause. Subsequently, we used the <em>Cpk</em> calculator as we gradually reduced cycle time as much as possible without negatively affecting process capability. In the end, we confirmed root cause, and implemented a new and improved cycle time for the piece of equipment. ________________________________________________________ <em><a href="/sites/lean-math/files/blog/wp-content/uploads/2014/11/Levi-Head-Shot-2.jpg"><img alt="Levi Head Shot 2" height="135" width="163" class="media-image alignleft wp-image-1213 size-full media-element file-media-large" typeof="foaf:Image" src="http://leanmath.com/sites/lean-math/files/wp-content/uploads/2014/11/Levi-Head-Shot-2.jpg" /></a>This post was authored by Levi McKenzie, a continuous improvement kind of guy who enjoys exploring new facets of lean methodology, facts, data, and making things faster and better. Levi Is a co-founder of Brown Belt Institute, a mobile app development company</em> <em>that focuses on providing useful lean six sigma tools that are inexpensive and easy to use for the "blue collar brown belt" sector.</em></p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/tags/measurement" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Measurement</a></div></div></div>Fri, 07 Nov 2014 01:16:01 +0000markrhamel122 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/cpk-and-mystery-estimated-standard-deviation-guest-post#commentsCargo Cult Statistics
http://www.leanmath.com/blog-entry/cargo-cult-statistics
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Did first-class passengers on the Titanic get preferential treatment during the evacuation? James Cameron’s movie certainly seems to suggest so, but let’s look at the data.</p>
<p> </p>
<table><tbody><tr><td width="111"></td>
<td width="152"><strong>Survived</strong></td>
<td width="134"><strong>Died</strong></td>
</tr><tr><td width="111"><strong>First class</strong></td>
<td width="152">203</td>
<td width="134">122</td>
</tr><tr><td width="111"><strong>Third class</strong></td>
<td width="152">178</td>
<td width="134">528</td>
</tr></tbody></table><p> </p>
<p>The data is compelling. 75% of the third-class passengers perished compared to only 38% for the first-class passengers. The statistically inclined among you might run a Chi-squared test to confirm these observations, and not surprisingly the results will be statistically significant. The difference in the proportion of first-class passengers that perished versus the proportion of third-class passengers that perished is unlikely to have occurred by chance. Well, that must be the end of the story. An analyst might create some pie charts or some stacked bar charts to illustrate the results, but that is the end of the story…right???...not quite.</p>
<p> </p>
<p>Consider a more detailed breakdown of the same data:</p>
<table><tbody><tr><td width="176"></td>
<td width="152"><strong>Survived</strong></td>
<td width="134"><strong>Died</strong></td>
</tr><tr><td width="176"><strong>First class</strong></td>
<td width="152"></td>
<td width="134"></td>
</tr><tr><td width="176">Men</td>
<td width="152">57</td>
<td width="134">118</td>
</tr><tr><td width="176">Women and children</td>
<td width="152">146</td>
<td width="134">4</td>
</tr><tr><td width="176"><strong>Third class</strong></td>
<td width="152"></td>
<td width="134"></td>
</tr><tr><td width="176">Men</td>
<td width="152">75</td>
<td width="134">387</td>
</tr><tr><td width="176">Women and children</td>
<td width="152">103</td>
<td width="134">141</td>
</tr></tbody></table><p>Now the data suggests a possible different story. With this data, it is now evident that 79% of the men died, compared to 37% of the women and children. So which was it? Was it class privilege or chivalry? Or was it something else?</p>
<p>These are questions of history, and there are many lessons to be learned from history. And there is much to be learned from the over simplistic analysis that suggested the cause was class privilege:</p>
<ul><li>Just because the numbers are overwhelming, it doesn’t mean your hypothesis is true.</li>
<li>When analyzing data, t is wise to remember the words of Sherlock Holmes; “when you have eliminated the impossible, whatever remains, however improbable, must be the truth”.</li>
</ul><p>The failure in the initial analysis was not a failure of mathematics or statistics, but a failure of the analyst. They failed to consider other alternatives. Richard Feynman described this error in his essay: Cargo Cult Science, in which he recommends, among other things, that we should not fool ourselves and we should not fool others. We accomplish these goals with a profound honesty, by challenging ourselves to look for other explanations, and by carefully performing and re-performing experiments. And while the systems that we study may be more complex and more dynamic than the systems that a physicist studies, there is no excuse for cargo cult statistics.</p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/tags/measurement" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Measurement</a></div><div class="field-item odd"><a href="/tags/thoughts" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Thoughts</a></div></div></div>Fri, 10 Oct 2014 03:18:07 +0000drmike121 at http://www.leanmath.comhttp://www.leanmath.com/blog-entry/cargo-cult-statistics#comments