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運用實驗設計DOE Custom design,找出最佳奶茶配方

5歲活潑開朗的小男孩樂樂正為媽媽的生日禮物發愁,他和爸爸一起討論著該送媽媽什麼生日禮物。

爸爸提到了媽媽喜歡喝手搖飲料,於是樂樂想到可以自己親手做珍珠奶茶送給媽媽。然而,爸爸提醒他製作珍奶的關鍵組成並不容易找到。爸爸解釋試誤法需要耗費大量時間且結果不確定,爸爸進一步提議使用JMP來進行實驗設計,以更有效的方式找到媽媽喜歡的珍珠奶茶口味。

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樂樂:爸爸,媽媽的生日快到了,我想送媽媽一個禮物,但是我不知道要送什麼她才會喜歡。

爸爸:你應該送什麼媽媽都會很開心吧。

樂樂突然想到,並且說:媽媽喜歡喝手搖飲料,還是我來做一杯珍珠奶茶給她?

爸爸:可以啊,不過你知道怎麼做嗎? 例如泡紅茶的溫度跟珍珠怎麼煮?

樂樂:我不會,你幫我。

爸爸:網路上應該有這些製作的流程,不過什麼溫度跟煮多久這些關鍵的資訊網路上應該就比較少了,而且每個人的喜好不同,既然要送給媽媽一個特殊的生日禮物,我們就特別為她做一杯專屬於她的珍珠奶茶,做為生日禮物如何?

樂樂:好啊,可是我們要怎麼找到她喜歡的口味?世界上應該有無限多種口味吧,難道我們要做無限多杯嗎?

爸爸:沒錯,你說的把所有的可能都試過的方式就是所謂的窮舉法或是試誤法(Trial and error),但是這樣的方式會花很久的時間,也不一定可以得到比較好的配方組合。我們應該用JMP做實驗設計。

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什麼是JMP 實驗設計?

樂樂:JMP是什麼?實驗設計又是什麼?聽起來好像工程師做實驗,感覺好厲害喔!

爸爸:JMP是一個包含很多統計分析功能的軟體,而且你說的沒錯,它的其中一項強大的功能可以幫助我們設計出高效益的實驗。而且JMP的實驗設計還可以根據你的需求,設定因子的種類及範圍,加入你認為可能的效應模型以及你能夠執行的實驗次數等幫助我們建構在能力可及的情形下最優的實驗。

樂樂似乎聽不太懂,眼神又飄向還沒做完的樂高樹屋。

爸爸接著說:總而言之,我們只要跟他說我們紅茶茶包有哪些選擇,水溫可以控制在哪個範圍,泡茶希望的時間範圍,以及我們希望它做幾次實驗就好,它就會幫我們設計出實驗組合喔。

樂樂:喔,我懂了,就像我們出去玩,用行車導航幫我們設計導航路線一樣,跟他說去的地點跟我們現在的位置,就可以幫我們設計出最好的路徑

爸爸:沒錯,不過導航通常知道我們的目標,是花費最少的時間呢?或是走最短的路徑呢?在根據需求給我最建議的組合。而我們目前要做的,則是前期的資料蒐集,但是利用設定的實驗次數,盡可能廣泛的考慮所有可能,蒐集它的結果。之後再用這些數據,計算模型,得到最佳的預測

樂樂:所以我們現在就像是行車導航的工程師,運用JMP設計用來分析的實驗,然後再利用觀察的數據,找到怎麼走才會最快到達目的地嗎?

爸爸:沒錯,就是這樣,那我們現在利用JMP開始我們的實驗設計吧,珍珠奶茶工程師。

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樂樂跟爸爸決定先利用JMP的Design Of Experiment DOE(實驗設計)功能,找出如何泡出好喝的紅茶。

爸爸:我們先來找泡紅茶的配方吧,看看那些是重要的影響條件。

爸爸:我們來查網頁上面推薦的泡紅茶方法吧,先找到哪些是影響口味的關鍵條件,跟建議的條件設定,我們可以縮小我們的實驗範圍。

於是,爸爸跟樂樂根據網路上面的資訊,先找到適當的茶葉浸泡溫度及浸泡時間,以及推薦的水量/茶葉量的比例。另外,爸爸在附近的商點找到兩種品牌的茶葉,以及選擇自來水或是礦泉水作為泡茶的水,將所有關鍵參數整理如下(表一):

參數

資料類型

值(範圍/種類)

紅茶品牌

類別

A品牌

B品牌

泡茶水

類別

自來水

礦泉水

水量/茶葉量比例

連續

20~60

浸泡溫度(⁰C)

連續

70~100

浸泡時間(m)

連續

5~20

表一, 紅茶關鍵參數及範圍表

 

搜尋完需要的關鍵參數跟參數的範圍後,樂樂跟爸爸回到客廳坐下。

樂樂:那我們現在可以開始泡紅茶了嗎?

爸爸:還沒呢,因為我們目前還不知道各個實驗所需要設定的參數實際值,我們還需要一個小幫手幫我們設計出實驗。

爸爸:我們需要JMP幫我們設計出實驗的組合。

於是,爸爸在電腦上面打開了JMP統計軟體。

什麼是定製實驗Custom Design

爸爸:你看,如果我們需要JMP幫我們設計實驗,你可以點選菜單選項上的”DOE”欄位,這邊有很多可以使用各種DOE方法還有相關的DOE功能。如果你不是這麼了解各個DOE背後的原理跟適用的對象,我建議你可以先用custom design, 也就是定製實驗,作為一個起頭。

樂樂:為什麼用這個定製實驗?

爸爸:定製實驗的背後原理是最佳化實驗,他會根據我們給他的條件,包含我們覺得重要的關鍵條件、這些關鍵條件有沒有互相影響、我們想要得到什麼樣的結果,能夠做幾次的實驗次數等,去建議我們最好的實驗組合。

樂樂:就像導航一樣。

爸爸:這個好處就是很適合我們這些普通人,不是這麼了解DOE,但是又想做一個好的實驗設計的人使用。

樂樂:我以後會成為DOE的專家的,我只是現在還是小孩子,所以不會,等我長大我就會了。

爸爸:好好好,不過就算是DOE專家,對於目標是設計最有效益的實驗,他們也很常使用定製實驗作為實驗設計的切入點。所以我們現在就用定製實驗設計看看吧。

使用定製實驗設計,設定參數名稱、範圍與實驗次數

接著爸爸把參數跟範圍輸入custom design 平台(圖一)。

JMP Custom DesignJMP Custom Design

圖一,輸入響應結果及參數至custom design 平台

 

並將參數主效應及連續型參數的二次項跟連續型參數交叉項的效應項加入模型中(圖二)。

Michelle_Wu_7-1686549239255.png

圖二, 輸入相應效果項至模型中

 

樂樂:什麼是二次項跟交叉項,為什麼要加入他們?

爸爸:加入二次項效應是因為想要確認關鍵參數會不會有反曲現象,也就是在範圍中間有一個值讓結果產生極大或是極小值。交叉項的加入是想確認這些參數彼此之間會不會有加乘的效果影響,也就是除了本身主效應的影響外,某些條件配合起來會有額外的效應。

樂樂看到下面的畫面接著問,樂樂:這個就是設定我們要做幾次實驗嗎?

 

Michelle_Wu_8-1686549239256.png

圖三, 中心點&重複次數設置及實驗次數輸入

 

爸爸:對,這邊我們可以設定要不要加重複的實驗或是實驗要不要加中心點,下方的Number of Runs 可以選擇實驗次數,這邊有寫最少次數是12次(Minimum),JMP建議是16次(Default),你也可以自己設定一個能夠負擔的實驗次數(User Specified),我們還是用預設的16次(圖三)。

樂樂:為什麼是16次阿,越多次不是越好嗎?

爸爸:沒錯,不過通常因為時間或是錢不夠,我們會有一個預設可以執行的實驗次數。而這也是定製設計的優勢,定製設計可以根據這個需求設計實驗,而其他的實驗設計必須做到規定的實驗次數。另外一個重要的原因是,你不能喝茶,所以這16杯都是我要喝,爸爸喝16杯已經緊繃了,再多喝幾杯晚上可能睡不著覺了。

生成製作紅茶的參數組合,完成資料收集

樂樂跟爸爸接著完成custom design,產出製作紅茶的參數組合(圖四)。

JMP DOE參數組合JMP DOE參數組合

圖四, 實驗組合表格

 

接著爸爸跟樂樂按照這個參數組合表完成了實驗,爸爸依序評分並完成16次的評分結果(圖五)。

Michelle_Wu_10-1686549281867.png

圖五, 收集相應的實驗組合結果

 

喝了太多杯茶,爸爸邊打嗝邊說:我們終於完成實驗的資料收集。

使用JMP Fit Model 執行迴歸分析,進行模型預測

接著,我們可以按下左上方腳本儲存區內的”Model”去做後面的分析,JMP很貼心幫我們把後續的分析都打包在這個程式上,也就是我們可以直接JMP上的Fit model平台去執行迴歸分析,我們可以直接按下DOE表格上的”Model”來分析就好(圖六)。

 

Michelle_Wu_11-1686549325968.png

圖六, DOE實驗組合資料表上的Model 腳本

 

按下”Model” 後爸爸接著說:這邊可以讓我們選擇是否要在模型上增加效應項跟選擇做分析的方法,我們就”Stepwise”方法請JMP幫我們挑出適合的模型 (圖七)。

 

JMP Fit ModelJMP Fit Model

圖七, 迴歸模型起始平台

 

經過按壓幾次滑鼠的操作後,爸爸完成了報告(圖八),並用手指在電腦上面指出Effect summary 和summary of fit的結果。

爸爸:我把一些效應項p-value 超過0.05的項目依序排除模型,獲得一個更準確的模型,因為統計上來說P值如果超過0.05代表這個效應項對模型的影響不大,有沒有保留這個效應項沒有差別。另外,可以看到Summary of fit 這邊說模型的準度(R-square)達到0.997,代表這個模型對樣本點的解釋能力很強,也就是說這個對這些資料來說是一個好的預測模型

 

JMP Fit ModelJMP Fit Model

圖八, 迴歸模型分析報告

 

樂樂看了看說:為什麼浸泡時間的P值大於0.05可是沒有刪除阿?而且他旁邊有一個向上的指標。

爸爸:因為有其他的子項目必須被保留在模型中,你可以看到浸泡時間*浸泡時間這個項目小於0.05需要被保留,作為他的父項目,浸泡時間也需要被保留,而這個向上的指標就是在跟你說哪一些是有這樣問題的父項目,必須被保留下來。

爸爸繼續滾動滑鼠的滑輪,呈現報告的下半部。

察看Prediction Profiler 報告觀察每個參數對結果的變化

爸爸接著說:我們往下找到報告的Prediction Profiler(刻劃器) 的報告,這裡將模型用互動性圖片呈現,可以幫助我們更快了解每個參數的改變會對味道造成什麼樣的改變。你可以看到下方有參數的名稱,他的軸(X軸)就代表我們設定的參數值,然後左邊的軸(Y 軸),代表味道的得分預測值。如果你想要知道不同的條件的得分,你只需要把下方的參數值調整到你設定的值,就可以得到預測的味道結果喔,例如我選擇A茶葉,用自來水泡,水量/茶葉量的比例我選擇40, 浸泡溫度為80, 浸泡時間我選擇15,當我這樣更改…你看,預測結果就出來了,只有4.83分(圖九)。

 

JMP Prediction ProfilerJMP Prediction Profiler

圖九, Prediction Profiler(刻劃器)

 

爸爸邊說邊拖曳滑鼠改變參數的設置,樂樂瞪大眼睛,似乎感覺到不可思議。

樂樂:他會直接根據你的調整直接在圖片上改變預測的味道分數,好酷。

爸爸:對阿,這個互動的功能比較好操作也讓大家比較好懂模型。我們來仔細看看這個圖形,其實這個圖形也大致可以告訴你往哪個方向調整會得到比較高的味道分數,也就是比較好喝。例如,我們看第一個的茶葉圖,B茶葉就比A茶葉高,可以知道B茶葉有一個比A茶葉好喝的趨勢,同理,礦泉水泡的茶比自來水泡的好喝,以及浸泡時間大約在10~15分鐘會比較好喝,給你玩玩看。

 

JMP Prediction ProfilerJMP Prediction Profiler

圖九, Prediction Profiler(刻劃器)

 

樂樂迫不及待的開始拉動各個參數設定,玩了一下後他提出了一個疑問。

樂樂:爸爸你看,我改變水量/茶葉量的比例大小,其他的參數會跟著有點變化欸,有的會整個變高變低,有的會稍微改變形狀,好奇怪喔。

爸爸:欸,你很厲害喔,你有發現這個小小的變動。這些小小的變動是來自於調整參數帶來的效果,所以其他的參數會形狀不變的上升,如果你發現隨著原本參數值的改變,其他參數的形狀有明顯的變異,例如原本是左上右下的變成左下右上,那就代表這個其中的交叉項的影響很厲害。另外你看有一些參數的趨勢線不是直線,而是彎曲的線,有一個最大值或是最小值,就代表他的2次項的效果影響程度很高。

樂樂似懂非懂的點了一下頭,然後接著問:所以我這樣就可以預估所有可能的結果嗎?

爸爸回答說:這是一個好問題,我們剛剛做的事情是請JMP根據我們收集的這些資料提供我們一個預估的模型,但是這些資料是根據我們一開始界定的範圍內廣泛均勻的取點,盡可能的看所有範圍內的各點表現,但是對於範圍外的參數組合,這個模型的預測能力會比較不好,所以我們盡可能不做原本實驗設計範圍外的預測比較好,但是對於範圍內的大部分所有參數組合,我們可以用這個模型預測一個準確的結果。

 

接下來,我們要來做今天的重點步驟:找到最好喝的參數條件組合,你可以調整刻劃器上的參數設定,看看你找到最高分的組合是怎樣的組合。

樂樂點了點頭,又是一陣在Prediction Profiler上的參數設定調整。

Prediction Profiler中,找出最佳參數組合

樂樂:爸爸,我找到一個9.47分的,我選擇B茶葉,用礦泉水泡,水量/茶葉量的比例我選擇60, 浸泡溫度為89.5, 浸泡時間我選擇11.9,結果就是9.47的味道分數,很厲害吧。

爸爸:不錯喔,已經很高了,那你覺得還會有更高分嗎?

樂樂:可能會有吧,因為我沒全部都設定過看他的分數。

爸爸:這個時候就是要在展現JMP魔法的時候啦,你看我可以在JMP Prediction Profiler上開起set desirability,設定目標,例如這議題我們味道分數愈高愈好,我們就可以選擇Maximum 去設定結果為望大,也就是越大越好並利用Maximize Desirability 的功能,去求得完成的目標的最佳參數組合(圖十)。或是選擇Maximize and Remember 去尋求最佳參數組合並記錄在報告內。

 

螢幕擷取畫面 2023-06-12 135841.png

圖十, (左, 中)Set Desirability設置意願值函數, (右)最大化意願值Maximize Desirability

 

爸爸在Profiler 上按下Maximize and Remember快速找到最佳參數組合並將其記錄在報告上 (圖十一)。

Michelle_Wu_22-1686549468115.png

圖十一, Maximize and Remember結果

 

樂樂:這也太快太方便了吧!

爸爸:對阿,通常資料分析花最多時間的就是收集資料,JMP可以節省更多分析的時間,所以很多需要運用資料做統計分析的公司都會使用這個軟體加快分析的時間。其實比較你手動得到的參數組合跟最佳的組合只差了一點點,你也很厲害了。另外,連續型的參數,例如浸泡溫度,91.02894,實際上並不好管控,也許我們可以用91或是90去替代設定。

樂樂跟爸爸接著討論了一下各參數條件的設定,最後用B茶葉,礦泉水,水量/茶葉量的比例55, 浸泡溫度為90, 浸泡時間我選擇12.5,最為最後的關鍵參數條件設定(圖十二)。

 

Michelle_Wu_23-1686549468117.png

圖十二, 根據實驗設計得出的最佳預測結果

 

樂樂:耶!那我們接下來要做奶茶跟珍珠嗎?

爸爸看了一下時間,接著說:媽媽快要回來了,如果要當成媽媽生日的驚喜,我們先趕快把實驗的器具收一收不然會被發現。奶茶跟珍珠我們下次再來做實驗,找好的配方組合,這會運用到其他DOE的技巧喔。

樂樂開心的說:好,那我們趕快收一收,我好期待喔。

爸爸跟樂樂趕在媽媽回家前把實驗收拾乾淨,一顆小小的DOE種子卻在樂樂心中慢慢發芽。

 

>>下集將分享如何透過JMP DOE實驗設計平台,製做出好吃的珍珠。<<

 

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Last Modified: Jun 12, 2023 11:14 PM