1. the quality of being extremely thorough, careful, or strict
Usage: British spelling; American spelling is ‘rigor’
2. harsh or severe conditions; hardship
Usage: often plural: ‘rigours’

Examples

• The scientific study was conducted with great rigour.
• Academic rigour is essential for maintaining educational standards.
• The rigours of military training prepared them for combat.
• She applied intellectual rigour to her research methodology.
• The harsh rigours of winter made survival difficult.
• The professor demanded rigour in all student assignments.