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DOE粘度：混合因子か連続因子か？制約条件とカテゴリカル添加剤の管理

カスタム設計で DOE 問題を提起する方法が適切であるかどうか疑問に思います。

私たちの目的は、3 種類の増粘剤の粘度への影響とそれらの相互作用を研究することです。

添加剤は、単独で使用した場合に報告されている効果に基づき、低せん断勾配、中せん断勾配、高せん断勾配に分類されています。一度に1つの添加剤のみを使用するため、同じせん断勾配で作用する添加剤間の相互作用は、本分析には関係ありません。

比率に関しては、当初は混合設計として扱うことを検討しましたが、最終的には連続因子を選択しました。これは、式の残りの部分も粘度に影響を与えるため、切片値がゼロにならないと判断したためです。

当初のバージョンでは、以下の要素を考慮し、90回の実験計画を作成しました。しかし、複数の添加剤を最大濃度（0.4）で組み合わせると、配合が濃すぎて測定できないことが判明しました。そのため、3つの水準すべてが0.4となる点が少なくとも11点あり、測定不能となります。さらに、異なるカテゴリーに対応するものの濃度が0となる点が11点存在し、これは添加剤を一切加えない製品の11回の繰り返しに相当します。

したがって、制約を追加することを検討しました。

実現可能性の面では、各ポイントの測定が可能であるという確信が高まりました。無添加製品の表現も向上しました。

しかし、いくつか疑問があります。

• 最低 0.1 のレートを課すのは正しかったのでしょうか?
• もしそうなら、現在の計画に加えて、添加物なしの製品の追加測定を 11 回実行し、レート 0 の 11 ポイントを手動で追加することには、何か利点がありますか?
• この問題全体を表現するためのより良い方法はあるでしょうか?
• カテゴリーの1つに新しい増粘剤を導入したい場合、どうすればよいでしょうか？3段階のカテゴリ因子を4段階の因子に変換する方法がまだ見つかっていません。

関連する場合、私は JMP 19.0.0 を使用しており、これが最終表のスクリプトです:

もっと見る...

New Table( "Custom Design",
	Add Rows( 90 ),
	New Table Variable( "Design", "Custom Design" ),
	New Table Variable( "Criterion", "D Optimal" ),
	New Script(
		"Model",
		Fit Model(
			Effects(
				:low sheer additive, :mid sheer additive, :high sheer additive,
				:low sheer amount, :mid sheer amount, :high sheer amount,
				:low sheer additive * :mid sheer additive,
				:low sheer additive * :high sheer additive,
				:low sheer additive * :low sheer amount,
				:low sheer additive * :mid sheer amount,
				:low sheer additive * :high sheer amount,
				:mid sheer additive * :high sheer additive,
				:mid sheer additive * :low sheer amount,
				:mid sheer additive * :mid sheer amount,
				:mid sheer additive * :high sheer amount,
				:high sheer additive * :low sheer amount,
				:high sheer additive * :mid sheer amount,
				:high sheer additive * :high sheer amount,
				:low sheer amount * :mid sheer amount,
				:low sheer amount * :high sheer amount,
				:mid sheer amount * :high sheer amount,
				:low sheer additive * :mid sheer additive * :high sheer additive,
				:low sheer additive * :mid sheer additive * :low sheer amount,
				:low sheer additive * :mid sheer additive * :mid sheer amount,
				:low sheer additive * :mid sheer additive * :high sheer amount,
				:low sheer additive * :high sheer additive * :low sheer amount,
				:low sheer additive * :high sheer additive * :mid sheer amount,
				:low sheer additive * :high sheer additive * :high sheer amount,
				:low sheer additive * :low sheer amount * :mid sheer amount,
				:low sheer additive * :low sheer amount * :high sheer amount,
				:low sheer additive * :mid sheer amount * :high sheer amount,
				:mid sheer additive * :high sheer additive * :low sheer amount,
				:mid sheer additive * :high sheer additive * :mid sheer amount,
				:mid sheer additive * :high sheer additive * :high sheer amount,
				:mid sheer additive * :low sheer amount * :mid sheer amount,
				:mid sheer additive * :low sheer amount * :high sheer amount,
				:mid sheer additive * :mid sheer amount * :high sheer amount,
				:high sheer additive * :low sheer amount * :mid sheer amount,
				:high sheer additive * :low sheer amount * :high sheer amount,
				:high sheer additive * :mid sheer amount * :high sheer amount,
				:low sheer amount * :mid sheer amount * :high sheer amount
			),
			Y( :Y )
		)
	),
	New Script(
		"Evaluate Design",
		DOE(
			Evaluate Design,
			X(
				:low sheer additive, :mid sheer additive, :high sheer additive,
				:low sheer amount, :mid sheer amount, :high sheer amount
			)
		)
	),
	New Script(
		"Constraint",
		{1 * :low sheer amount + 1 * :mid sheer amount + 1 * :high sheer amount <=
		0.40000000000000002, 1 * :low sheer amount + 1 * :mid sheer amount + 1 *
		:high sheer amount >= 0.10000000000000001}
	),
	New Script(
		"DOE Dialog",
		DOE(
			Custom Design,
			{Add Response( Maximize, "Y", ., ., . ),
			Add Factor( Categorical, {"L1", "L2", "L3"}, "low sheer additive", 0 ),
			Add Factor( Categorical, {"L1", "L2", "L3"}, "mid sheer additive", 0 ),
			Add Factor( Categorical, {"L1", "L2"}, "high sheer additive", 0 ),
			Add Factor( Continuous, 0, 0.40000000000000002, "low sheer amount", 0 ),
			Add Factor( Continuous, 0, 0.40000000000000002, "mid sheer amount", 0 ),
			Add Factor( Continuous, 0, 0.40000000000000002, "high sheer amount", 0 ),
			Set Random Seed( 538775543 ), Number of Starts( 195 ),
			Add Constraint(
				[1 1 1 0.40000000000000002, -1 -1 -1 -0.10000000000000001]
			), Add Term( {1, 0} ), Add Term( {1, 1} ), Add Term( {2, 1} ),
			Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {5, 1} ),
			Add Term( {6, 1} ), Add Term( {1, 1}, {2, 1} ),
			Add Term( {1, 1}, {3, 1} ), Add Term( {1, 1}, {4, 1} ),
			Add Term( {1, 1}, {5, 1} ), Add Term( {1, 1}, {6, 1} ),
			Add Term( {2, 1}, {3, 1} ), Add Term( {2, 1}, {4, 1} ),
			Add Term( {2, 1}, {5, 1} ), Add Term( {2, 1}, {6, 1} ),
			Add Term( {3, 1}, {4, 1} ), Add Term( {3, 1}, {5, 1} ),
			Add Term( {3, 1}, {6, 1} ), Add Term( {4, 1}, {5, 1} ),
			Add Term( {4, 1}, {6, 1} ), Add Term( {5, 1}, {6, 1} ),
			Add Term( {1, 1}, {2, 1}, {3, 1} ), Add Term( {1, 1}, {2, 1}, {4, 1} ),
			Add Term( {1, 1}, {2, 1}, {5, 1} ), Add Term( {1, 1}, {2, 1}, {6, 1} ),
			Add Term( {1, 1}, {3, 1}, {4, 1} ), Add Term( {1, 1}, {3, 1}, {5, 1} ),
			Add Term( {1, 1}, {3, 1}, {6, 1} ), Add Term( {1, 1}, {4, 1}, {5, 1} ),
			Add Term( {1, 1}, {4, 1}, {6, 1} ), Add Term( {1, 1}, {5, 1}, {6, 1} ),
			Add Term( {2, 1}, {3, 1}, {4, 1} ), Add Term( {2, 1}, {3, 1}, {5, 1} ),
			Add Term( {2, 1}, {3, 1}, {6, 1} ), Add Term( {2, 1}, {4, 1}, {5, 1} ),
			Add Term( {2, 1}, {4, 1}, {6, 1} ), Add Term( {2, 1}, {5, 1}, {6, 1} ),
			Add Term( {3, 1}, {4, 1}, {5, 1} ), Add Term( {3, 1}, {4, 1}, {6, 1} ),
			Add Term( {3, 1}, {5, 1}, {6, 1} ), Add Term( {4, 1}, {5, 1}, {6, 1} ),
			Set Sample Size( 90 ), Simulate Responses( 0 ), Save X Matrix( 0 ),
			Make Design}
		)
	),
	New Column( "low sheer additive",
		Character,
		"Nominal",
		Set Property( "Value Order", {Custom Order( {"L1", "L2", "L3"} )} ),
		Set Property( "Design Role", DesignRole( Categorical ) ),
		Set Property( "Factor Changes", Easy ),
		Set Values(
			{"L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1",
			"L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1",
			"L1", "L1", "L1", "L1", "L1", "L2", "L2", "L2", "L2", "L2", "L2", "L2",
			"L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2",
			"L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2",
			"L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3",
			"L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3",
			"L3", "L3", "L3", "L3", "L3", "L3"}
		)
	),
	New Column( "mid sheer additive",
		Character,
		"Nominal",
		Set Property( "Value Order", {Custom Order( {"L1", "L2", "L3"} )} ),
		Set Property( "Design Role", DesignRole( Categorical ) ),
		Set Property( "Factor Changes", Easy ),
		Set Values(
			{"L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L2", "L2",
			"L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L3", "L3", "L3", "L3",
			"L3", "L3", "L3", "L3", "L3", "L1", "L1", "L1", "L1", "L1", "L1", "L1",
			"L1", "L1", "L1", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2",
			"L2", "L2", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3", "L3",
			"L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L1", "L2",
			"L2", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L3", "L3", "L3", "L3",
			"L3", "L3", "L3", "L3", "L3", "L3"}
		)
	),
	New Column( "high sheer additive",
		Character,
		"Nominal",
		Set Property( "Value Order", {Custom Order( {"L1", "L2"} )} ),
		Set Property( "Design Role", DesignRole( Categorical ) ),
		Set Property( "Factor Changes", Easy ),
		Set Values(
			{"L1", "L1", "L1", "L1", "L1", "L2", "L2", "L2", "L2", "L2", "L1", "L1",
			"L1", "L1", "L1", "L2", "L2", "L2", "L2", "L2", "L1", "L1", "L1", "L1",
			"L1", "L2", "L2", "L2", "L2", "L1", "L1", "L1", "L1", "L1", "L1", "L2",
			"L2", "L2", "L2", "L1", "L1", "L1", "L1", "L1", "L2", "L2", "L2", "L2",
			"L2", "L2", "L1", "L1", "L1", "L1", "L2", "L2", "L2", "L2", "L2", "L2",
			"L1", "L1", "L1", "L1", "L2", "L2", "L2", "L2", "L2", "L2", "L2", "L1",
			"L1", "L1", "L1", "L1", "L2", "L2", "L2", "L2", "L1", "L1", "L1", "L1",
			"L1", "L2", "L2", "L2", "L2", "L2"}
		)
	),
	New Column( "low sheer amount",
		Numeric,
		"Continuous",
		Format( "Best", 12 ),
		Set Property( "Coding", {0, 0.40000000000000002} ),
		Set Property( "Design Role", DesignRole( Continuous ) ),
		Set Property( "Factor Changes", Easy ),
		Set Values(
			[0, 0, 0.10000000000000005, 0.1501747410225249, 0.40000000000000002, 0,
			0, 0, 0.20000000000000001, 0.40000000000000002, 0, 0, 0,
			0.19999999999999998, 0.40000000000000002, 0, 0, 0.079999999999999988,
			0.20000000000000001, 0.40000000000000002, 0, 0, 0, 0.20000000000000001,
			0.40000000000000002, 0, 0, 0.06802583802886511, 0.40000000000000002, 0,
			0, 0, 0.15999999999999998, 0.20000000000000001, 0.39999999999999997, 0,
			0, 0.080000000000000029, 0.40000000000000002, 0, 0, 0.10000000000000003,
			0.13883780667167989, 0.40000000000000002, 0, 0, 0, 0.10000000000000001,
			0.20000000000000001, 0.39999999999999997, 0, 0, 0.070000000000000034,
			0.40000000000000002, 0, 0, 0, 0.19999999999999998, 0.20000000000000001,
			0.40000000000000002, 0, 0, 0.063073352199479821, 0.40000000000000002, 0,
			0, 0, 0.10000000000000001, 0.19999999999999996, 0.19999999999999998,
			0.40000000000000002, 0, 0, 0, 0.20000000000000004, 0.40000000000000002,
			0, 0, 0.050000000000000017, 0.40000000000000002, 0, 0, 0,
			0.19999999999999998, 0.40000000000000002, 0, 0, 0.090000000000000024,
			0.13715600638057818, 0.40000000000000002]
		)
	),
	New Column( "mid sheer amount",
		Numeric,
		"Continuous",
		Format( "Best", 12 ),
		Set Property( "Coding", {0, 0.40000000000000002} ),
		Set Property( "Design Role", DesignRole( Continuous ) ),
		Set Property( "Factor Changes", Easy ),
		Set Values(
			[0, 0.40000000000000002, 0, 0.10495025895846891, 0, 0,
			0.10000000000000003, 0.23999999999999996, 0.20000000000000001, 0, 0,
			0.10000000000000003, 0.23999999999999999, 0.19999999999999998, 0, 0,
			0.40000000000000002, 0.019999999999999962, 0, 0, 0, 0.16000000000000003,
			0.40000000000000002, 0, 0, 0, 0.39999999999999997, 0.015747420986803484,
			0, 0, 0.20000000000000004, 0.40000000000000002, 0, 0.20000000000000007,
			0, 0, 0.40000000000000002, 0, 0, 0, 0.40000000000000002, 0,
			0.11324531058065736, 0, 0, 0.19999999999999996, 0.39999999999999997, 0,
			0.20000000000000001, 0, 0, 0.40000000000000002, 0.029999999999999999, 0,
			0, 0.15999999999999998, 0.39999999999999997, 0, 0.19999999999999998, 0,
			0, 0.40000000000000002, 0.029216023765151894, 0, 0, 0.19999999999999998,
			0.40000000000000002, 0, 0.20000000000000004, 0, 0, 0,
			0.15999999999999998, 0.40000000000000002, 0, 0, 0, 0.40000000000000002,
			0.049999999999999989, 0, 0, 0.10000000000000001, 0.23999999999999999,
			0.19999999999999998, 0, 0, 0.40000000000000002, 0.0099999999999999811,
			0.10660542813245405, 0]
		)
	),
	New Column( "high sheer amount",
		Numeric,
		"Continuous",
		Format( "Best", 12 ),
		Set Property( "Coding", {0, 0.40000000000000002} ),
		Set Property( "Design Role", DesignRole( Continuous ) ),
		Set Property( "Factor Changes", Easy ),
		Set Values(
			[0.39999999999999997, 0, 0, 0.14487500001900624, 0, 0.40000000000000002,
			0, 0.16, 0, 0, 0.40000000000000002, 0, 0.16, 0, 0, 0.40000000000000002,
			0, 0, 0.20000000000000004, 0, 0.10000000000000005, 0.23999999999999999,
			0, 0.19999999999999998, 0, 0.39999999999999991, 0, 0.016226740984330218,
			0, 0.10000000000000003, 0.20000000000000004, 0, 0.24000000000000005, 0,
			0, 0.39999999999999997, 0, 0.020000000000000018, 0, 0.40000000000000002,
			0, 0, 0.14791688274766282, 0, 0.39999999999999991, 0.20000000000000001,
			0, 0, 0, 0, 0.40000000000000002, 0, 0, 0, 0.10000000000000003,
			0.24000000000000005, 0, 0.19999999999999996, 0, 0, 0.40000000000000002,
			0, 0.0077106240353676525, 0, 0.40000000000000002, 0.20000000000000004, 0,
			0, 0, 0.20000000000000004, 0, 0.10000000000000002, 0.24000000000000002,
			0, 0.20000000000000001, 0, 0.40000000000000002, 0, 0, 0,
			0.40000000000000002, 0, 0.16, 0, 0, 0.39999999999999997, 0, 0,
			0.15623856548696785, 0]
		)
	),
	New Column( "Y",
		Numeric,
		"Continuous",
		Format( "Best", 12 ),
		Set Property(
			"Response Limits",
			{Goal( Maximize ), Lower( . ), Upper( . ), Importance( . )}
		),
		Set Values(
			[., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., .,
			., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., .,
			., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., .,
			., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., ., .]
		)
	),
	New Column( "Run Order",
		Numeric,
		"Continuous",
		Format( "Best", 12 ),
		Set Values(
			[50, 66, 33, 43, 45, 62, 73, 76, 5, 20, 79, 17, 18, 60, 84, 23, 72, 13,
			38, 82, 4, 27, 6, 55, 58, 24, 3, 2, 80, 16, 32, 64, 28, 26, 53, 11, 47,
			29, 59, 7, 83, 37, 49, 21, 68, 25, 57, 40, 63, 89, 54, 10, 81, 67, 1, 48,
			77, 39, 44, 42, 22, 9, 36, 8, 52, 51, 87, 19, 30, 74, 86, 65, 46, 78, 31,
			75, 70, 71, 34, 61, 85, 69, 15, 88, 14, 90, 56, 12, 41, 35]
		)
	)
)

実験計画法DOE粘度：混合因子か連続因子か？制約条件とカテゴリカル添加剤の管理

こんにちは@ピエリック 、

コミュニティへようこそ！

混合設計を使用しない理由がよくわかりません。混合設計は、因子が混合物の成分であり、合計量が特定の値になる場合に使用されます。混合設計は、成分の異なる比率の影響を示します。混合設計や要因設計では、処方の残りの部分が影響を与えるかどうかは想定されていません。処方の残りの部分が応答に影響を及ぼす可能性がある場合、なぜこれらの成分も含めないのですか？処方の残りの部分が何らかの溶媒である場合を除き、濃度/希釈度に基づいて粘度が増加または減少するのは正常であり、成分の比率よりも量に関心があるのではないでしょうか。

混合計画では、線形制約（すべての因子の合計が特定の値になる）により切片は主効果の一部となるため、切片は存在しません。これは、切片がゼロとなる場合とは異なるモデリングシナリオです。

情報が少なすぎるため、設計の制約、範囲、設定の根拠について議論することはできません。また、私はあなたのトピックのドメイン専門家ではないため、妥当かどうか議論することはできません。スクリーンショットの2番目の制約については、下限値（または因数記号の反対）の不等号を逆にする必要があるため、間違いがある可能性がありますが、JSLでは問題ないように見えます。

なぜ最小率を0.1としたのですか？ 0にすることで、全ての状況（成分の有無）を同じ設計で扱うことができ、手動で追加の実験を行う必要がなくなります（また、実験がランダム化され、分析が容易になります）。因子の非線形効果が予想される場合は、連続量因子のモデル項に二次効果を追加すれば、因子のレベルが3つになり、単純な欠落/存在の設計レベル設定を回避できます。

カテゴリ因子にレベルを追加する（または拡張計画に因子を追加する）には、簡単な手順が必要です。表に新しい行を追加し、拡張したいカテゴリ因子以外のすべての値を欠損値に設定します。この因子の新しいレベルを記述すると、計画を拡張する際に考慮されるようになります。 「計画への新しいレベルの追加」をご覧ください。

この回答がお役に立てれば幸いです。