Examples of Lean Six-Sigma Black Belt
course Material :
Hypothesis Testing, Type 1 and Type 2 errors, Alpha-risk, Beta-risk, Confidence Interval, Confidence Level, Power of Statistical Tests.
What are producer and consumer
Alpha risk is the risk of incorrectly deciding to reject the null hypothesis. If the confidence interval is 95%, then the alpha risk is 5% or 0.05.
Alpha error is also called False Positive, Producer Risk or Type 1 Error.
Confidence Level = 1 - Alpha
If not otherwise stated then an Alpha risk of 0.05 is assumed, making the confidence level = 95%.
Selecting an Alpha 5% signifies that there is a 5% chance that you were incorrect in rejecting the Null hypothesis.
It's the amount of risk you are willing to accept of making a Type I error.
Beta risk is the risk that you decide to accept the Null Hypothesis when in fact the reality is that the Alternative Hypothesis is true. In other words, when the decision is made that a difference does not exist when there actually is.
If the power desired is 90% that your testing will correctly identify the Alternative when the Alternative is correct, then the Beta risk is 10%.
The Beta risk being 10% means that there is a 10% chance that the decision will be made that there is no problem, and no action needs to be taken, when in reality there is a problem and some action does need to be taken. Or when the decision is made that a difference does not exist when there actually is a difference.
The Power of a test = 1 - Beta
Beta error is also called False Negative and Type II Error.
The Power is the probability of correctly rejecting the Null Hypothesis.
The Null Hypothesis is technically never proven true. It is "failed to reject" or "rejected".
"Failed to reject" does not mean accept the null hypothesis since it is established only to be proven false by testing the sample of data.
Consumer's risk = β = Beta Risk.
Type II error is known as the consumer's risk because the consumer has accepted a shipment that should be rejected. The shipment contains more than an acceptable number of defectives and will result in more waste or rework than anticipated.
Producer's risk, α = Alpha Risk
Type I error is referred to as the producer's risk because the producer made a good lot yet it was rejected.
An operating characteristic curve (OC curve) quantifies these risks on a graph that lets you choose the appropriate sampling plan for the risks you are willing to accept.
TAKT TIME VS CYCLE TIME
Thank you to Lean6Sigma4all and Daniele Giambra for sharing these excellent examples:
Method to calculate the Number of Resources / Workers needed
There could be 2 misunderstandings about how to calculate the Number of Resources that are needed to run a production line or manufacturing cell.
When you implement standard work you have to consider that a Takt Time (TT) is based on customer demand must first be established for the area in question, for example 30 seconds TT, this is equal to set a rate of 120 UPH (Units per Hour).
Therefore; the next question is how many workers are needed in the manufacturing area at this rate?
The answer depends on the total LABOR CONTENT in the area and its relation to demand (TT).
It’s also known as graph of “Takt Time vs Manual Cycle Time”, in many industries.
The more work content, the greater the number of workers that will be required; the less overall work content, the fewer workers that are needed.
I have found there is a misunderstanding of Overall Work Content, many people take the Cycle Time complete (Machine + Manual) wich is not right, they must use the “Manual” Overall Work Content (Total Manual Cycle Time)
Here is a PRACTICAL EXAMPLE
The calculation above shows that is possible to run this Manufacturing Cell with just 3 operators.
There is another misunderstanding about the representation of TT, many people don’t understand this concept how to interpret and calculate the Number of Resources when they have operators working in parallel.
For example; when there are operations that are not possible to be separated, the activity must be done from the beginning to the end by one operator at time; and if the cycle time is greater than Takt Time; then you need to use more than one operator to cover the rate needed, this means to have two or more operators working in parallel, for this case the Takt Time must be different.
You should never use the average of those operators as the Manual Work Content, you need represent as it is and make the calculations using other Takt Time equivalent.
Here is a PRACTICAL EXAMPLE:
The calculation shows that is possible to run this Manufacturing Cell with just 5 operators; please note that here there is two Takt Times, but do not get confuse at the end the Cell will run at 30 Seconds of Takt Time; equivalent to 120 UPH.
Mfano wa Lean Six Sigma Black Belt: Utafiti wa Nadharia, Aina ya 1 na Aina ya 2 makosa, Alpha-hatari, Beta-hatari, Confidence Interval, Confidence Level, Nguvu ya Majaribio ya Takwimu Hatari ya Alpha ni hatari ya uamuzi usio sahihi wa kukataa nadharia ya sifuri. Ikiwa kiwango cha uaminifu ni 95%, basi hatari ya alpha ni 0.05%. Alpha makosa pia huitwa makosa ya uongo chanya, hatari ya mtayarishaji au aina ya 1 makosa. Kiwango cha uaminifu: Alpha: Ikiwa haijulikani vinginevyo, hatari ya Alpha ni 0.05 na kiwango cha uaminifu ni 95%. "Alpha 5% inamaanisha kuna uwezekano wa 5% kwamba umekosea katika kukataa nadharia ya ""null.""" Ni kiasi cha hatari wewe ni tayari kukubali ya kufanya aina ya I kosa. Hatari ya beta ni hatari ya kukubali nadharia ya null wakati ukweli ni kwamba nadharia mbadala ni kweli. Kwa maneno mengine, wakati uamuzi unafanywa kwamba tofauti haipo wakati kwa kweli ipo. Kama nguvu inataka ni 90% kwamba majaribio yako itakuwa sahihi kutambua mbadala wakati mbadala ni sahihi, basi hatari ya Beta ni 10%. "Hii ina maana kwamba kuna uwezekano wa 10% kwamba uamuzi utafanywa kwamba hakuna tatizo, na hakuna hatua inayohitaji kuchukuliwa, wakati kwa kweli kuna tatizo na hatua fulani inahitaji kuchukuliwa.""" Au wakati uamuzi unafanywa kwamba tofauti haipo wakati kwa kweli kuna tofauti. "Kuna uwezekano wa kuwa na ""Beta-Beta"" makosa, ambayo pia huitwa ""Negative ya uongo"" na ""Kosa la Aina ya Pili.""" Nguvu ni uwezekano wa kwa usahihi kukataa Null Nadharia. Nadharia ya Null haijathibitishwa kamwe kuwa ya kweli. Ni "kushindwa kukataa" au "kukataa". "Kushindwa kukataa" haimaanishi kukubali nadharia ya null kwani imeanzishwa tu kuthibitishwa kuwa ni bandia kwa kupima sampuli ya data. Hatari ya watumiaji = Beta Aina ya pili ya makosa ni hatari ya watumiaji, kwa sababu watumiaji wamekubali usafirishaji ambao unapaswa kukataliwa. Usafirishaji una zaidi ya idadi inayokubalika ya kasoro na itasababisha taka zaidi au kazi mpya kuliko ilivyotarajiwa. Hatari ya Mtayarishaji: Alpha Hatari: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji: Hatari ya Mtayarishaji. Mzunguko wa tabia ya uendeshaji (OC) huonyesha hatari hizi kwenye grafu ambayo hukuruhusu kuchagua mpango sahihi wa sampuli kwa hatari unazokubali. "Kama ilivyoelezwa hapo juu, ""Mfano wa kutegemea"" ni mfano wa ""Mfano wa kutegemea"" na ""Mfano wa kutegemea"" ni mfano wa ""Mfano wa kutegemea"" na ""Mfano wa kutegemea"" ni mfano wa ""Mfano wa kutegemea"" na ""Mfano wa kutegemea"" ni mfano wa ""Mfano wa kutegemea"" na ""Mfano wa kutegemea"" ni mfano wa ""Mfano wa kutegemea"" na ""Mfano wa kutegemea.""" Wakati wa kutekeleza kazi ya kawaida, lazima uzingatie kwamba wakati wa Takt (TT) unategemea mahitaji ya wateja, lazima kwanza uanzishwa kwa eneo linalohusika, kwa mfano, sekunde 30 TT, hii ni sawa na kuweka kiwango cha 120 UPH (Vitu kwa Saa). Kwa hiyo; swali linalofuata ni ni wafanyakazi wangapi wanahitajika katika eneo la utengenezaji kwa kiwango hiki? Jibu inategemea jumla ya LABOR CONTENT katika eneo hilo na uhusiano wake na mahitaji (TT). Pia inajulikana kama grafu ya "Takt Time vs Manual Cycle Time", katika viwanda vingi. Kadiri kazi ilivyo kubwa, ndivyo idadi ya wafanyakazi itakavyohitajiwa; kadri kazi ilivyo ndogo, ndivyo idadi ya wafanyakazi itakavyohitajika. "Kama ilivyoelezwa hapo juu, ""Mashine ya jumla ya mzunguko"" ni sawa na ""Mashine ya jumla ya mzunguko"" na ""Mashine ya jumla ya mzunguko"" ni sawa na ""Mashine ya jumla ya mzunguko"" na ""Mashine ya jumla ya mzunguko"" na ""Mashine ya jumla ya mzunguko"" na ""Mashine ya jumla ya mzunguko"" ni sawa na ""Mashine ya jumla ya mzunguko"" na ""Mashine ya jumla ya mzunguko.""" Kuna kutokuelewana nyingine kuhusu uwakilishi wa TT, watu wengi hawaelewi dhana hii jinsi ya kutafsiri na kuhesabu Idadi ya Rasilimali wakati wana waendeshaji wanaofanya kazi sambamba. Kwa mfano, wakati kuna shughuli ambazo haziwezi kutenganishwa, shughuli lazima ifanywe kutoka mwanzo hadi mwisho na mwendeshaji mmoja kwa wakati; na ikiwa wakati wa mzunguko ni kubwa kuliko wakati wa Takt, basi unahitaji kutumia mwendeshaji zaidi ya mmoja ili kufunika kiwango kinachohitajika, hii inamaanisha kuwa na waendeshaji wawili au zaidi wanaofanya kazi sambamba. Kamwe kutumia wastani wa waendeshaji kama Manual Work Content, unahitaji kuwakilisha kama ni na kufanya mahesabu kwa kutumia nyingine Takt Time sawa. Kwa mfano, kwa mfano, unaweza kuendesha kiwanda cha Takt kwa dakika 30 na wakati wa Takt ni sekunde 30.